metre.info - Dictionary of all derived metric measures

Encyclopaedia of the derived Units of the SI

Information about all derived metric units.

Derived units are measurement units that are defined in terms of the base units. Each of these units is obtained by multiplying or dividing base units. Conversion factors are never involved or needed; the derived units can be translated into base units without converting the measurement at all. In fact, the derived units are not even necessary for measuring since everything could be expressed in base units. However, derived units with their special names are much simpler to use and to remember than several powers of the base units (one newton is simpler than one kg × m/s²). This practice of using derived units also makes mistakes and confusion less likely.

Go to: becquerel, coulomb, degree Celsius, farad, gray, henry, hertz, joule, katal, lumen, lux, newton, ohm, pascal, radian, siemens, sievert, steradian, tesla, volt, watt, weber.

becquerel [Bq] The becquerel is the unit of activity, for example of a radioactive source.

One becquerel indicates one disintegration every second. It is dimensionally equivalent to hertz (one cycle per second) but used in different contexts. The becquerel is used to measure the rates of events that happen sporadically and unpredictably, not in a definite cycle.

The disintegration of radioactive atoms is such a sporadic event. Radioactive atoms are not stable; they fall apart after a certain period of time. This time is not a fixed period. Only the statistical likelihood of whether an atom might fall apart in a given time is known, not the exact point in time. Radioactivity is therefore sporadic and random. However, the behaviour of a large number of radioactive atoms can be exactly forecast, since a relatively large number of atoms will level out any unlikely statistical fluctuations.

Radioactive radiation exists in three different forms: Radioactive atoms can emit alpha-rays, beta-rays or gamma-rays. An alpha particle is a complete helium nucleus, which is the core of a helium atom. Beta particles are electrons. Gamma radiation is electromagnetic radiation. Each type of radiation has a different level of energy and interacts with matter in a different way. Becquerels measure all radioactive disintegrations the same way, regardless of the type.

A measure of 500 Bq could mean 500 gamma rays, 500 beta rays, 500 alpha rays per second or any combination of two or of the three different types of radiation.

Becquerel measures how radioactive something is. Usually it is used to quantify the amount of radioactivity in a given amount of matter. The radioactivity of different substances is usually compared in becquerel per kilogram.

It is named after the French physicist Antoine Henri Becquerel (1852–1908).

The name and the unit have been in use since 1975. Adopted by the 15th CGPM in 1975.

Reference points for becquerel (most commonly used as becquerel, kilobecquerel)

Limit value up to which food is considered safe 600 Bq per kilogram or per liter

Natural radioactivity of the human body 8 000 Bq

One gram of radium-226 37 GBq

Radiation released by a 20 kilotonne nuclear bomb 22 ZBq

coulomb [C] The coulomb is the unit of the quantity of electricity or electric charge.

Electric charge is carried by the elementary particle electron (or other electric charge carriers, such as electron-deficient atoms). Electricity is the flow of electrons. The electric charge of one coulomb is approximately equivalent to the electric charge of 6.241 506 × 10¹⁸ electrons (6.2 quintillion or 6 241 506 000 000 000 000).

Like all metric units for measuring electricity, the coulomb is defined in terms of the ampere. One coulomb is the quantity of electricity transported in one second by a current of one ampere (1 C = 1 A × s).

If a potential difference of one volt carries a charge of one coulomb, the field forces carry out one joule of work (1 C = J / V).

Two bodies with similar electric charges (both positive or both negative) repel each other; bodies with opposite electric charges (one positive, one negative) attract each other. The force acting between these bodies is called coulomb force. Its strength depends on the electric charge (measured in coulomb) and the distance between the bodies.

It is named after the French physicist Charles-Augustin de Coulomb (1736–1806).

The name and the unit have been in use since 1881. Adopted by the 9th CGPM in 1948.

Reference points for coloumb:

Elementary charge “e” (electric charge of a single electron): 160.217 6 zC (= 1.602 176 × 10^-19 C)

degree Celsius [°C] The degree Celsius is the most commonly used unit for measuring temperature.

In the 18th century, the need for an absolute temperature scale became more apparent. Without such a scale, temperatures in different locations could not be easily compared. The Swedish Astronomer Anders Celsius was one of the first scientists to attempt to develop such a scale. Using the boiling and the freezing points of water, the most important substance for life on earth, he defined the Celsius scale. The boiling and freezing temperature of water allow for easy reproduction and uncomplicated calibration of thermometers.

Required by this definition is the standard atmospheric pressure at sea level (101.325 kPa), since the boiling and freezing points of water change with the air pressure.

Celsius initially set the freezing point to 100 °C and the boiling point to 0 °C. After publishing his work, other scientists suggested that a reversal of the scale might be more useful. Anders Celsius accepted this proposal and changed his scale to today’s familiar 0 °C for the freezing point and 100 °C for the boiling point of water. Logically, temperature measurements should increase as it gets hotter.

Long after his death, it was suggested to name this temperature scale after its inventor. In 1948, it was officially decided to call the scale degree Celsius rather than degree centigrade or centesimal degrees. This decision was taken to honour Anders Celsius and to avoid confusion between centigrade and other measurements like centidegrees (of arc).

Scientists discovered later that another reference point is more useful for defining a temperature scale. There is a lowest temperature, at which all molecule movements come to a halt. This temperature, called absolute zero, is the coldest possible temperature. Nothing can be colder than absolute zero. Clearly, if absolute zero was the starting point of a temperature scale, negative temperatures could be avoided altogether (negative temperatures cause difficulties in certain calculations and comparisons).

This newer temperature scale, starting at absolute zero, was called kelvin. To make conversions between degrees Celsius and kelvin as easy as possible and to keep the convenient increments of the degree Celsius scale, the division of the degree Celsius scale were kept.

Degree Celsius is now defined as the kelvin temperature minus 273.15 (for example: 0 K = -273.15 °C; 100 K = -173.15 °C; 273.15 K = 0 °C). The numbers on the kelvin scale are simply shifted against the degree Celsius scale -- the magnitude of a temperature difference of 1 K is identical to a temperature difference of 1 °C. This new definition of the degrees Celsius scale leaves the actual scale unchanged; water still freezes at 0 °C and boils at 100 °C.

Kelvin tends to be used mainly by scientists working with temperatures below 0 °C, for most other purposes degree Celsius is used.

The correct symbol for degree Celsius is the degree sign (not a superscript zero or letter o), followed by the capital letter C. In the Unicode character encoding table, the degree sign is number U+00B0. For more information about special characters, please see the page of rules.

It is named after the Swedish astronomer Anders Celsius (1701–1744).

The unit has been in use since 1742, the name degree Celsius has been used since about 1850. Adopted by the 1st CGPM in 1889.

Reference points for degrees Celsius (most commonly used as degree Celsius):

Absolute zero (0 kelvin) -273.15 °C

Lowest temperature ever measured on earth (Antarctica) -89.2 °C

Temperature at which water freezes/thaws 0 °C

Room temperature 21 °C

Human body temperature 37 °C

Limit value up to which skin contact is not painful 45 °C

Highest temperature ever measured on earth (Libya) 58 °C

Temperature at which water boils 100 °C

farad [F] The farad is the unit of the capacitance of an electrical system (the capacity to store electricity).

When researching electricity, it was found that two conductors separated by an isolator could store much more electricity than just one conductor. Such a unit of two conductors separated by an isolator is called capacitor and is used in electrical circuits. The better the isolator, the larger is the amount of electricity that can be stored. This property of an electrical circuit is called capacitance – and is measured in farad.

The amount of electricity that can be stored in a capacitor varies with the voltage difference between the two conductors. That is why the storage capacity of conductors is not simply rated in coulomb (measure for quantity of electricity), but in farad, which relates the electrical charge, measured in coulomb, to the voltage, measured in volt.

One farad is the ability to store one coulomb of electrical charge per one volt of electric potential difference between two conductors. A capacitor has the capacitance of one farad if charging it with one coulomb produces one volt of potential difference (1 F = 1 C / V). The higher the voltage, the more electricity (coulombs) can be stored in a capacitor. The farad rating of the capacitor does not change.

When the voltage across a one farad capacitor changes at a rate of one volt per second (1 V / s), a current flow of one ampere results (1 A = 1 F × V / s).

It is named after the English chemist and physicist Michael Faraday (1791–1867).

The name and the unit have been in use since 1873. Adopted by the 9th CGPM in 1948.

Reference points for farad (most commonly used as microfarad, nanofarad and picofarad):

Capacitors used for radio frequencies, tuned circuits: 1 pF to 1 000 pF

Capacitors used for radio frequencies, blocking and bypassing: 1 nF to 100 nF

Capacitors used for audio frequencies: 0.1 μF to 100 μF

Capacitors used for power supply filters: up to 10 mF

gray [Gy] The gray is the unit for absorbed dose of energy or heat.

It refers to the energy deposited by any type of radiation in any type of material. Radiation carries energy; the absorbed dose is the amount of energy received per unit of mass.

One gray equals one joule of energy deposited per kilogram of absorber. The gray is mainly used for the effects of radioactivity. Its use as a measure for absorbing heat is rare.

Different types of radiation have different effects on living tissue. The gray does not take this into account; it simply measures the absorbed energy, regardless of radiation type. For measuring radiation effects on humans, see sievert. The gray describes a measurable property. The actual effects on living tissue are more difficult to measure; the sievert describes in effect an estimated property.

It is named after the English physician and radiologist Louis Harold Gray (1905–1965).

The name and the unit have been in use since 1975. Adopted by the 15th CGPM in 1975.

Reference points for gray (most commonly used as milligray and gray)

Average dose of cosmic radiation per year 450 µGy

Dose affecting fertility temporarily 0.15 Gy

Dose causing skin burns 3 Gy

Dose causing permanent sterility 3.5 Gy

Dose causing visual impairment 5 Gy

Dose causing skin scaling and blistering 10 Gy

henry [H] The henry is the unit of inductance of an electrical system (the capacity to store energy in the form of a magnetic field).

An inductor in its simplest form is just a wire loop or coil. Electric current flowing through the wire generates a magnetic field in the coil. This magnetic field induces a potential difference within the coil which is called self-induction voltage.

If the electric current is changed, the voltage also changes.

One henry is defined as the inductance of an electric circuit that produces one volt when the electric current changes by one ampere per second (1 H = 1 V × s / A). If the current changes faster (several ampere per second), the voltage also increases.

The electric current of one ampere passing through an inductor of one henry produces a magnetic flux of one weber (1 Wb = 1 H × A).

Above it is explained that an electric current in a coil induces a magnetic field. However, the reverse is also true:

If the source of the magnetic field is external (not created by the flow of electric current through the coil), a current will be induced in the wire. The induced voltage depends only on the speed at which the magnetic flux changes (measured in weber per second: 1 V = 1 Wb / s). However, the induced current, measured in ampere, depends on the inductance of the coil, measured in henry. A coil with an inductance of one henry induces a current of one ampere with a magnetic flux of one weber (1 H = 1 Wb / A).

The inductance of an inductor depends on its physical properties, such as the number of coils, the radius of the coils and the material around which the coil is wound. The larger the number of coils, the higher is the inductance. Inductors are used in generators to produce electric power (generators simply move an inductor relative to a magnetic field to produce electricity) and in transformers to change the voltage of electricity.

It is named after the US physicist Joseph Henry (1797–1878).

The name and the unit have been in use since 1890. Adopted by the 9th CGPM in 1948.

Reference points for henry (most commonly used as millihenry and microhenry)

hertz [Hz] The hertz is the unit of the frequency of a periodic phenomenon.

One hertz indicates that one cycle of the phenomenon occurs every second. It is dimensionally equivalent to becquerel but used in a different context, i.e. hertz is used to measure regular, periodic cycles, not random events. For most work much higher frequencies than one cycle per second are needed, such as the kilohertz [kHz] and megahertz [MHz].

Most often, hertz is used to measure frequencies of the electromagnetic spectrum (radio waves, etc.) and the frequencies of sounds (pressure waves transmitted through the air). When measuring such waves, hertz describes how many peaks (or troughs) of a wave can be observed in one second.

Hertz is named after the German physicist Heinrich Rudolf Hertz (1857–1894).

The name and the unit have been in use since 1928. Adopted by the 9th CGPM in 1948.

Reference points for hertz (most commonly used as hertz, kilohertz and megahertz)

In most countries, the standard for the frequency of AC (alternating current) electricity is 50 Hz. The most sensitive human ears can hear sound waves with frequencies between 20 Hz and 20 000 Hz.

Frequencies of the electromagnetic spectrum
Radio frequencies	10 kilohertz to 300 megahertz
AM radio	535 kilohertz to 1700 kilohertz
FM radio	88 megahertz to 108 megahertz
Microwaves	300 megahertz to 300 gigahertz
Radar	300 megahertz to 30 gigahertz
Infrared light	300 gigahertz to 400 terahertz
Visible light	400 terahertz to 750 terahertz
Ultraviolet light	750 terahertz to 30 petahertz
X-rays	30 petahertz to 100 exahertz
Gamma rays	more than 100 exahertz

joule [J] The joule is the unit of work, energy and quantity of heat.

The unit is pronounced as “jewl”.

Work is a force acting upon an object, causing it to move (work = force × displacement). One joule is the amount of work done when a force of one newton moves through a distance of one meter in the direction of the force (1 J = N × m). Time is not a consideration in this equation. It does not matter how long the force takes to move the object.

Work is also a power applied over a period of time (work = power × time). One joule therefore equals one watt of power radiated or dissipated over one second (1 J = 1 W × s).

All different types of energy (mechanical, chemical, thermal, radiation, nuclear and electric) are also expressed in joule.

Kinetic energy is the energy of motion (kinetic energy = 0.5 × mass × speed × speed). One joule is equivalent to the kinetic energy of two kilograms of mass moving at one meter per second (1 J = 0.5 × 2 kg × (1 m / s)² = 1 kg × m² / s²).

As explained above, mechanical energy, measured in newton meters [N∙m], and electrical energy, measured in watt seconds [W∙s], can both be converted to joules without a conversion factor. One joule equals one newton meter and also equals one watt second (1 J = 1 N∙m = 1W∙s). For electrical energy, watt hours [W∙h] or kilowatt hours [kW∙h] are most commonly used. To convert joule in watt hours or kilowatt hours, the following exact conversions are used (because 1 h = 3 600 s):

1 kJ ≈ 0.278 Wh

1 Wh = 3.6 kJ

1 MJ ≈ 0.278 kWh

1 kWh = 3.6 MJ

Joule is most commonly used to express the heating energy (or thermal value) of different types of fuel, to measure the heat created by chemical reactions and for nutritional purposes.

Joule is named after the English physicist James Prescott Joule (1818–1889).

The name and the unit have been in use since 1882. Adopted by the 9th CGPM in 1948.

Reference points for joule (most commonly used as joule, kilojoule and megajoule)

Adult humans need to eat food containing about 10 000 kilojoule every day; this varies from about 7 000 kilojoule for inactive females over 56 years of age to 14 700 kilojoules for very active 18 to 35 year old males.

The human body consumes about 250 kJ/h hour when lying down, 500 kJ/h when standing, 750 to 1 250 kJ/h for walking and 2 650 kJ/h for jogging.

Thermal value of common fuels (the quantity of heat or energy contained in these substances)
Natural gas	35.9 MJ/m³	47.2 MJ/kg
Liquid gas	113.5 MJ/m³	48.1 MJ/kg
Brown coal	17.4 GJ/m³	20.5 MJ/kg
Hard coal	24.2 GJ/m³	31.9 MJ/kg
Firewood	6.8 GJ/m³	13.9 MJ/kg
Heating oil	37.9 GJ/m³	44.1 MJ/kg
Petrol	32.4 GJ/m³	46.3 MJ/kg

Specific heat capacity of some materials (energy needed to heat up 1 kg of the substance by 1 °C)
Water at 20 °C	4 186 J∙kg∙°C
Aluminium at 27 °C	963 J∙kg∙°C
Carbon at 27 °C	709 J∙kg∙°C
Iron at 27 °C	449 J∙kg∙°C
Copper at 27 °C	385 J∙kg∙°C

katal [kat] The katal is the unit of catalytic activity.

It is a special name for mole per second (1 kat = 1 mol / s). The unit is pronounced “cattle”. Katal is used especially in the fields of medicine and biochemistry.

A catalyst has an activity of one katal if it enables a reaction to proceed at the rate of one mole per second (a catalyst is a substance, which initiates or facilitates a chemical reaction). The higher the katal measure, the better the catalyst.

When the katal is used, the substance being measured should be specified by reference to the measurement procedure, which must identify the indicator reaction.

The CGPM has introduced this unit to stop the usage of other, non-coherent units for mole per second. While the CGPM usually does not aim to increase the number of derived units, exceptions are being made for the areas of human health and safety, where standardized and consistent measures are especially important.

The name “katal” is derived from the Greek word “katalysis”, meaning dissolution.

The name and the unit have been in use since about 1960. Adopted by the 21st CGPM in 1999.

lumen [lm] The lumen is the unit of luminous flux.

Lumens measure luminous flux, which is the light flowing out of a light source or the light flow received by a surface.

The lumen is defined in terms of the base unit candela. Candelas take the sensitivity of the human eye into account; both candelas and lumens are therefore true measures of how much light a human sees.

One lumen is equal to the amount of light given off by a light source of one candela intensity radiating equally in all directions. The light source is taken to be a uniform point, which shines in all directions.

The candela itself is defined as light given off in a certain direction through a certain angle only. The definition for candela uses the unit steradian to define this angle. Steradian is the unit of solid angle (an angle covering three dimensions). One steradian refers to an angle that covers about 8 % of a sphere or ball. An angle of about 12.6 (the exact number is 4 × π) steradians covers a whole ball, just like an angle of 360° covers a whole circle.

Candela is a measurement of the light given out through a small angle only. Only this beam of light is measured; whether the light source emits only this beam of light or radiates light in all directions, is not taken into account.

In contrast, lumen measures the total light emitted or received. If the light source was a small point, radiating evenly in all directions, a light source of 1 candela would produce about 12.6 lumens (candela times the number of steradians in a full globe). The exact number is 1 candela = 4 × π lumen. In this ideal case, candela measures only 1/12.6 of the light emitted.

This formula is correct for light sources like the sun, but artificial light sources do not give off light evenly in all directions. For such light sources the output in lumens has to be measured. A standard light bulb emits light fairly evenly in all directions, but a fluorescent tube emits much more light vertically to the tube than parallel to the tube. Additionally, a fluorescent tube is a long object and its geometry must be taken into account. Therefore, the formula 1 candela ≈ 12.6 lumen holds true only for ideal light sources.

As a result, a light bulb with 110 candelas can have a luminous flux of 1 000 lumen, whereas a fluorescent tube of 250 candela can have a light output of 3 500 lumen.

Lumens are more common in everyday life than candelas. The output of light sources, for example light bulbs, is measured in lumen. The higher the rating in lumen, the brighter is the light bulb.

When the lumen was first added to the metric system in 1948, it was called “new lumen” to avoid confusion with earlier definitions of the lumen. Later, the qualifier “new” was dropped.

Lumens are also used to measure energy efficiency of light sources

Energy efficiency of light bulbs can be calculated in luminous flux per power used (lumen / watt). The more lumens per watt a light bulb produces, the more energy efficient is it.

The name and the unit have been in use since about 1925.

Adopted by the 9th CGPM in 1948.

Reference points for lumen (most commonly used as lumen)

Energy saving light bulb, 16 W 900 lm

Soft white standard light bulb, 60 W 490 lm

Linear halogen light bulb, 300 W 4 800 lm

lux [lx] The lux is used to measure the illuminance.

The lux is used to measure how brightly lit an area is, that is how much light it receives. One lux means that the area of one square meter receives the luminous flux of one lumen. One lux is therefore defined as one lumen per square meter (1 lx = 1 lm / m²).

The lumen takes the sensitivity of the human eye into account, lux and lumen are therefore a true measure of how much light a human sees.

Lux does not measure how bright a surface or an object appears – it just measures how much light is received by the surface or the object. If a white sheet of paper and a black sheet of paper receive the same amount of light, the white sheet will appear brighter, because it reflects more light. The measure for brightness, which takes this property of objects to reflect or to absorb light into account, is candela per square meter (cd / m²).

Lux is frequently used in laws and standards that define the minimum brightness for certain places like offices, schools, etc. Factors like the ability to see (naturally, humans cannot see in the dark), the ability to see colours, and even concentration depends on the illuminance or brightness of a room or workspace.

Studies have shown that by increasing the illuminance from 90 to 500 lux, the memory of humans improves by 16 %, logical thinking by 9 % and the speed and accuracy of manual calculations by 5 %.

The name and the unit have been in use since 1889.

Adopted by the 9th CGPM in 1948.

Reference points for lux (most commonly used as lux)

Moon light on a clear night outside 0.1 lx

Dimly lit hallway 20 lx

Room, no reading required 300 lx

Illuminance required in an office 500 lx

Well lit workspace 1 000 lx

Illuminance required in a clockmaker’s workshop 1 500 lx

Cloudy day outside 10 000 lx

Sunny day outside 100 000 lx

newton [N] The newton is the unit of force.

One newton is the force required to give a mass of one kilogram an acceleration of one meter per second per second (acceleration is measured in meters per second per second, meaning that every second an object gains a speed increase of one meter per second – this is equal to gaining 3.6 km/h every second). 1 N = 1 kg × m / s².

A force is commonly a push or pull – physics defines it as a quantity that changes the motion, size or shape of a body.

A very common force, important for all life on earth, is gravitation. On our planet, the earth’s mass exerts a gravitational force on all things, which we experience as weight. This gravitational force varies, depending on many factors, for example the distance to the earth’s centre and even the density of the geologic formations in the earth’s crust.

Consequently, the weight of all things varies, depending on their location. On the surface of the moon, where the gravitational force is exerted by the mass of the moon, not the earth, things have only 1/6 of the weight they have on earth. This is because the surface gravity of the moon is only 1/6 of the gravity of the earth.

On earth, the standard acceleration of gravity (the average at sea level) is 9.806 65 m/s². If this factor is multiplied with the mass of an object (in kilograms), the result is the force or the weight that this object creates. One kilogram creates a force of 9.806 65 newton. One newton corresponds to the gravitational force exerted on an object with the mass of about 102 g.

It is named after the English mathematician and physicist Isaac Newton (1642–1727).

The name and the unit have been in use since 1904. Adopted by the 9th CGPM in 1948.

ohm [W] The ohm is the unit of resistance of an electrical conductor.

Ohms measure resistance, usually of an electric circuit. Electrical resistance is the property of a substance which makes it resist the flow of electric current. If two locations with a different electric potential (different voltage) are connected, an electric current will flow from one location to the other. The amount of the current (amperage) depends on the electric potential difference (voltage difference) and on how much the connection (conductor) between the two locations resists the flow of electricity. The higher the resistance, the more difficult is it to make electricity flow through.

One volt is required to make a current of one ampere flow through a resistance of one ohm. If the resistance is 10 ohms, 10 volts are required to achieve the flow of one ampere. One ohm is therefore defined as being equal to the resistance of a circuit in which a potential difference of one volt produces a current of one ampere (1 Ω = 1 V / A).

Good electrical conductors, like copper, have a low resistance (small number of ohms); good insulators, like porcelain or glass, have a very high resistance (high number of ohms). The lower the resistance in ohms, the better suited is a substance to conduct electricity. The higher the resistance in ohms, the better suited is a substance to insulate from electricity.

Resistance of different materials is often compared in “Ohm-metres”, meaning the resistance of a piece of material which has an area of one square meter and is one meter long.

If electric current flows through a resistor, the voltage drops. By measuring this drop in voltage and the current, the resistance can be calculated. Resistors also consume power; the power, in watts, consumed by a resistor is the drop in voltage multiplied by the amperage (1 W = 1 V × 1 A). A resistor of one ohm therefore consumes one watt of power. That is why the resistance in electric cables and networks has to be kept as low as possible.

The ohm is the only unit whose symbol is a Greek letter instead of a standard Latin letter. The symbol “Ω” is the last letter of the Greek alphabet, known as “omega”. In the Unicode character encoding table, the Greek capital letter omega is number U+03A9. For more information about special characters, please see the page of rules.

It is named after the German physicist Georg Simon Ohm (1789–1854).

The name and the unit have been in use since 1867. Adopted by the 9th CGPM in 1948.

Reference points for ohm (most commonly used as ohm, kiloohm, megaohm)

Resistance of 1 m² of silver per meter 15.9 nΩ

Resistance of 1 m² copper per meter 16.5 nΩ

Resistance of 1 m² iron per meter 100 nΩ

Resistance of 1 m² carbon per meter 35 μΩ

Resistance of 1 m² glass per meter 10 GΩ to 100 TΩ

Resistance of 1 m² hard rubber per meter 10 TΩ

Internal resistance of the human body 100 to 500 Ω

Resistance of wet skin 1 000 Ω

Resistance of dry skin 500 kΩ

pascal [Pa] The pascal is the unit of pressure or stress.

Pressure is the amount of force per area. If a force is applied to a surface, that surface is under pressure. There are several types of forces; a force can for example be a traditional mechanical force, like pulling or pushing, or gravitational, electromagnetic, etc.

One pascal is the pressure generated by the force of one newton acting on an area of one square meter (1 Pa = 1 N / m²).

All fluids and gases exert pressure on objects immersed in them. An example of this is air pressure or water pressure.

Pressure also results from the gravitational force of the earth on a body. Every object on earth is pulled by the gravitational force of the earth and exerts a pressure on the surface underneath the object. This is why historically pressure was expressed in weight per area. For example, a pressure could have been given as the force exerted by ten kilograms on an area of one square meter. Measuring pressure in such units should be avoided to eliminate confusion and to establish better comparability of measures. In order to convert such a measurement into pascals, the mass (in kilograms) must be multiplied with the standard acceleration of gravity (9.806 65 m/s²). This calculation converts the mass into a force (using the average gravitational force on earth at sea level) and force per area equals pressure.

If the pressure created by the mass of an object and the gravitational force has to be calculated, the mass in kilograms must be multiplied with the above mentioned standard acceleration of gravity (9.806 65 m/s²) and divided by the affected surface area in square meters. This will give the result in pascals.

For example, a car weighing 1 000 kg and standing on its four wheels, (each having a contact area of 0.005 m²), creates a pressure of 490 kPa (1 000 kg × 9.806 65 m/s² / 0.02 m² = 490 332.5 Pa).

It is named after the French mathematician, physicist and philosopher Blaise Pascal (1623–1662).

The name and the unit have been in use since 1956. Adopted by the 14th CGPM in 1971.

Reference points for pascal (most commonly used as pascal, kilopascal)

Normal blood pressure 16 kPa

Average atmospheric pressure at 5 500 m above sea level 50.7 kPa

Normal fluctuations of atmospheric pressure at sea level 98.5 kPa to104 kPa

Standard atmospheric pressure at sea level 101.325 kPa

Minimum water pressure for household water pipes: 200 kPa

Normal air pressure for many car tyres 220 kPa

Under the stiletto heels of an average-sized woman 7.6 MPa

For each meter of depth under water, a swimmer will be subjected to an additional 9.81 kPa pressure.

radian [rad] The radian is the unit of plane angular measure.

Radian is the metric base unit for measuring an angle.

A much more familiar measure for angles is the degree of arc (symbol °). The degree of arc is also part of the metric system as an alternative measure for angles, but it is defined in terms of the base unit radian.

The radian is not based on degrees, but on the circular number π (pi).

π is the ratio of the circumference of a circle to its diameter. This constant of nature is about 3.141 593 and is used in most calculations relating to circles.

One radian is about 16 % of a circle and about 6.3 radians cover a complete circle, just as 360° also cover a full circle. The exact figures are: One radian is 1 / (2 × p) of a circle (» 0.159 of a circle). 0.5 × p radian (» 1.571 radian) is a quarter of a circle, 1 × p radian (» 3.141 radian) is half a circle and 2 × p radian (» 6.283 radian) is a full circle.

This number of 2 × π radians (about 6.283) in a circle was chosen because of the formula for calculating the surface area of a circle: area = 2 × π • radius².

Therefore, the surface area of a circle with a radius of 1 meter is 2 × π square meters (about 6.283 m²). The surface area of a circle with a radius of one centimeter is 2 × π square centimeters (about 6.283 cm²).

Using the radian as measure for angles thus eliminates the number π from many calculations.

An angle of 2 radians in a circle of one meter radius covers a surface area of 2 square meters. Radians seem complicated at first, but they greatly simplify such calculations.

However, much more common in everyday use is the unit degree of arc [°] for measuring angles. The degree of arc subdivides a full circle into 360 parts.

The official definition of the radian is: One radian is equal to the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

The name and the unit have been in use since 1873.

Adopted by the 11th CGPM in 1960.

Reference points for steradian (most commonly used as steradian)

Circle		Radian		Degrees of arc	Compass
0 of a circle	0 of a circle	0 rad	0 rad	0°	North
1/8 of a circle	0.125 of a circle	0.25∙π rad	≈ 0.785 398 rad	45°	Northeast
¼ of a circle	0.25 of a circle	0.5∙π rad	≈ 1.570 796 rad	90°	East
3/8 of a circle	0.375 of a circle	0.75∙π rad	≈ 2.356 194 rad	135°	Southeast
½ of a circle	0.5 of a circle	1∙π rad	≈ 3.141 593 rad	180°	South
5/8 of a circle	0.625 of a circle	1.25∙π rad	≈ 3.926 991 rad	225°	Southwest
¾ of a circle	0.75 of a circle	1.5∙π rad	≈ 4.712 389 rad	270°	West
7/8 of a circle	0.875 of a circle	1.75∙π rad	≈ 5.497 787 rad	315°	Northwest
1/1 of a circle	1 of a circle	2∙π rad	≈ 6.283 185 rad	360°	North
1/10 of a circle	0.1 of a circle	π/5 rad	≈ 0.628 319 rad	36°
1/100 of a circle	0.01 of a circle	π/50 rad	≈ 0.062 832 rad	3.6° = 3° 36′
1/(2∙π) of a circle	≈ 0.159 155 of a circle	1 rad	1 rad	180/π° ≈ 57.296° ≈ 57° 17′ 44.81″
1/360 of a circle	≈ 0.002 778 of a circle	π/180 rad	≈ 0.017 453 rad	1°

siemens [S] The siemens is the unit of electric conductance.

Conductance is the ability of an electric conductor to conduct electricity. The higher the conductance, the easier is it for electricity to flow through a conductor. Conductance is the inverse of resistance; a conductor is the opposite of a resistor. The unit siemens is the reciprocal of the unit for electric resistance, the ohm (1 S = 1 / Ω). The lower the resistance in an electric circuit (in ohm), the higher is the conductance (in siemens).

One siemens is one ampere per volt (S = A / V), meaning a conductor with one siemens conductance carries one ampere of current for every one volt of electric potential difference.

Good electrical conductors, like copper, have a high conductance (high number of siemens); good insulators, like porcelain or glass, have a very low conductance (low number of siemens). The higher the conductance in siemens, the better suited is a substance to conduct electricity. The lower the conductance in siemens, the better suited is a substance to insulate from electricity.

The higher the conductance, the lower is the amount of power consumed by a conductor. High conductance is therefore very important for electric cables and networks to reduce the waste of electric power.

Named after the German electrical engineer and tycoon Werner von Siemens (1816–1892).

The name and the unit have been in use since 1933. Adopted by the 14th CGPM in 1971.

sievert [Sv] The sievert is the unit of radiation dose equivalent (also for ambient dose equivalent, directional dose equivalent, personal dose equivalent, organ equivalent dose).

Since each form of radiation (e.g. X-rays, gamma rays and neutrons) has a different effect on living tissue, the sievert is used to take into account the relative biological effectiveness of ionising radiation.

Whereas the unit gray measures only the radiation energy transferred into a body (in joule per kilogram), the sievert includes the harmfulness or biological effectiveness. The sievert is dimensionally equivalent to the gray (it also measures joules per kilogram), but includes a so-called quality factor. Absorbed radiation doses (in gray) are multiplied with the quality factor, depending on the type of radiation. Consequently, in order to measure or calculate radiation doses in sievert, the type of radiation must be known.

The following table lists commonly used quality factors for the effects of radiation on human tissue:

Type of radiation	Quality factor
Alpha radiation (helium nucleus radiation)	20	1 Gy = 20 Sv	1 Sv = 0.05 Gy
Beta radiation (electron radiation)	1	1 Gy = 1 Sv	1 Sv = 1 Gy
Gamma radiation (X-rays, electromagnetic radiation)	1	1 Gy = 1 Sv	1 Sv = 1 Gy
Neutron radiation	10	1 Gy = 10 Sv	1 Sv = 0.1 Gy

Accordingly, one sievert is generally defined as the amount of radiation roughly equivalent in biological effectiveness to one gray of gamma radiation. For example, one sievert is as harmful to the human body as 0.05 gray of alpha radiation, or as 0.1 gray of neutron radiation.

The sievert is quite large for many applications, and so the millisievert (mSv) is frequently used instead. One sievert corresponds to one joule of energy of gamma radiation transferred to one kilogram of living tissue; one millisievert corresponds to one microjoule of energy of gamma radiation transferred to one gram of living tissue.

Humans receive about 1 mSv to 2 mSv of radiation per year from natural sources (cosmic radiation, natural radiation in food, radiation from the ground, etc.) and roughly a further 1 mSv from artificial sources (x-rays, high altitude flights, radiation from nuclear tests, nuclear power stations, etc.). These radiation exposures can vary greatly from the averages, depending on where one lives and other individual factors.

It is named after the Swedish radiologist Rolf Maximilian Sievert (1896–1966).

The name and the unit have been in use since 1977. Adopted by the 16th CGPM in 1979.

Reference points for sievert (most commonly used as millisievert, sievert)

Dose equivalent of a chest X-ray 50 µSv

Dose equivalent of a skull X-ray 150 µSv

Annual natural radiation absorbed by humans 1 mSv to 2 mSv

Annual radiation limit for workers in the nuclear industry 20 mSv

Dose resulting in a 5% chance of fatal cancer 1 Sv

Dose considered deadly for humans 5 Sv

steradian [sr] The steradian is the unit of a solid angle.

The steradian is the sibling of the radian, the measurement for a plane (two-dimensional) angle. In contrast to the radian, the steradian measures solid (three-dimensional) angles. Neither the radian nor the steradian use degrees of arc or a similar measure, as one might expect. Instead, both measures are based on the circular number π (pi).

π is the ratio of the circumference of a circle to its diameter. This constant of nature is about 3.141 593 and is used in most calculations relating to circles.

One steradian is about 8 % of a sphere (or ball) and about 12.6 steradians cover a complete sphere, just as 360° cover a full circle. The exact numbers are: 1 steradian is 1 / (4 × π) of a sphere; one complete sphere contains 4 × π steradians.

This number of 4 × π steradians (about 12.566) in a sphere was chosen because of the formula for calculating the surface area of a sphere: area = 4 × π • radius².

Therefore, the surface area of a sphere with a radius of 1 meter is 4 × π square meters (about 12.566 m²). The surface area of a sphere with a radius of one centimeter is 4 × π square centimeters (about 12.566 cm²).

Using the steradian as measure for three-dimensional angles thus eliminates the number π from many calculations.

A solid angle in a sphere can be imagined as a cone, which extends from the centre in a ball to its surface. The angle between the sides of the cone is measured in steradians. If this angle is one steradian, the top of the cone covers about 8 % of the total surface of the ball; if the angle is about 3.1 steradians, the top of the cone covers 25 % of the ball.

An angle of 3 steradians in a sphere of one meter radius covers a surface area of 3 square meters.

Steradians are heavily used in physics whenever a flux through a three dimensional surface is involved. Many sources of light or other electromagnetic radiation radiate evenly in all directions. Such uniformly emitted radiation can be imagined as an ever-growing ball with the radiation source at its centre. That is why steradians are involved in measuring light emitted by a light source or in the engineering of antennas that are directed towards a source that emits evenly in all directions.

The name and the unit have been in use since around 1875.

Adopted by the 11th CGPM in 1960.

Reference points for steradian (most commonly used as steradian)

Sphere		Steradian
0 of a sphere	0 of a sphere	0 sr	0 sr
1 / (4 ∙ π) of a sphere	≈ 0.079 577 of a sphere	1 sr	1 sr
¼ of a sphere	0.25 of a sphere	π sr	≈ 3.142 sr
½ of a sphere	0.5 of a sphere	2 ∙ π sr	≈ 6.283 sr
¾ of a sphere	0.75 of a sphere	3 ∙ π sr	≈ 9.425 sr