DOI: 10.1615/AtoZ.s.si_units


When expressing the magnitude of a physical quantity, we use a number followed by a unit, e.g., M = 6 kg. The number represents the ratio of the magnitude of the quantity (mass M) to that of the unit (kilogram, kg). Over past centuries several different systems of units have been used by engineers and scientists, necessitating a large number of conversion factors and often leading to confusion.

In 1948, following a resolution of the Ninth Conference of Weights and Measures (CGPM) an international committee was established to formulate a new international system of units. Système Internationale d'Unités, or SI Units, was the outcome.

For a complete detailed account of SI units and their proper usage the chapter in the Heat Exchanger Design Handbook entitled "Conventions and nomenclature for physical quantities, units numbers and mathematics" by Y. R. Mayhew is recommended.

In the SI system there are seven base units, from which others are derived by combination, and two supplementary units that are angles.

Base Units in SI

These are:

  1. meter, m, the standard of length;

  2. kilogram, kg, the standard of mass;

  3. second, s, the standard of time;

  4. amper, A, the standard of electric current;

  5. kelvin, K, the standard of temperature;

  6. candela, cd, the standard of luminar intensity;

  7. mole, mol, the standard of amount of substance.

The meter, m, (from the Latin metrum—measure) was introduced in France at the time of the revolution. In an era of idealism it was designed to relate neatly to the size of the earth, designated as one part in forty million of the earth's circumference. In other words, the shortest distance from equator to pole was to be exactly 107 m. This proved an inexact measure, so for a while an actual bar of platinum-iridium at Sèvres became the standard meter. Today with the need for greater precision, the meter is defined as 1,650,763.73 times the wavelength, in vacuum, of the orange light emitted by in the transition 2 p10 to 5 d5. Alternatively a meter is the distance travelled by light in vacuum in 1/299,792,458 of a second.

The kilogram, kg, was originally defined as the mass of a liter (10−3 m3) of pure water at its maximum density. A platinum-iridium cylinder at Sèvres, intended to have exactly this mass, was made oversize by 28 parts per million, so for a while prior to 1964, the liter was defined at 1.000028 × 10−3 m3 to avoid this anomaly. The Sèvres cylinder is still the standard kilogram.

The second, s, is the time taken for 9,192,631,770 cycles of the radiation from the hyperfine transition in Caesium 133 when unperturbed by external fields. Alternatively, the ephemeris second is defined as 1/31,556,925.974 7 of the tropical year for 1900.

The ampere, A, is that constant current which, if maintained in each of two infinitely long straight parallel wires of negligible crosssection, placed one meter apart in vacuum, will produce between the wires a force of 2 × 10−7 newtons per meter length.

The kelvin, K, unit of thermodynamic temperature is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

The candela, cd, is the luminous intensity, in the perpendicular direction, of a surface 1/600,000 square meter of a full radiator at the temperature of freezing platinum under a pressure of 101,325 newtons per square meter. (Alternatively, a candela is the luminous intensity of a source that emits, in a given direction, monochromatic radiation of frequency 540 × 1012 hertz and has a radiant intensity in the same direction of 1/683 watt per steradian.)

The mole, mol, is the amount of substance which contains as many elementary entities as there are atoms in 0.012 kilogram of the carbon isotope . The entities must be specified, as atoms, molecules, ions, electrons or other particles or groups of particles.

Supplementary Units in SI

Supplementary units in SI are the radian and the steradian. The radian, rad, is the plane angle between two radii of a circle, which cut off in the circumference an arc equal in length to the radius.

The steradian, sr, is the solid angle which, having its vertex in the center of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere.

Derived SI Units

There are several units obtained by combining SI base units, which have special names, e.g. watt for power which is equivalent to kg m2/s2 or Nm/s or J/s. These named units are listed in Table 1 and defined below. There are also many more units derived from SI base units, which do not have special names (that is to say the unit does not have a special name although of course the quantity does). For example, the unit of acceleration is m/s2.

Table 1. SI derived units with special names

Derived units of force and energy (involving only kg, m and s)

The newton, N, is the derived unit of force. One newton is the force that produces an acceleration of one meter per second per second when applied to a mass of one kilogram, i.e. N = kg m/s2. (A mass of 1 kg exerts a force of 9.80 newtons in New York, 9.81 newtons in London, and 9.83 newtons at the North pole.)

The pascal, Pa, is the derived unit of pressure. It is the pressure exerted by one newton acting uniformly over one square meter, i.e., Pa = N/m2.

The joule, J, is the derived unit of energy or work. One joule is the work done by a force of one newton exerted over a distance of one meter, i.e. J = N m = kg m2/s2.

The watt, W, is the derived unit of power or energy per unit time. One watt is one joule per second, i.e., W = J/s = N m/s = kg m2/s3.

Derived SI units involving electricity and magnetism

The only additional SI base unit involved in both electrical and magnetic quantities is the ampere, A. This is because of the fundamental relationship between electricity and magnetism.

The coulomb, C, is the derived unit of electric charge. It is the quantity of electricity transported per second by a current of one ampere, i.e., C = A s.

The volt, V, is the derived unit of electrical potential, or potential difference. It is that difference in potential which generates one watt of energy per ampere of current, i.e., V = W/A = kg m2/A s3.

The ohm, Ω is the derived unit of electrical resistance. It is the resistance between two points that produces a potential difference of one volt when a current of one ampere flows between them, i.e., Ω = V/A = kg m2/A2 s3.

The siemens, S, is the derived unit of electrical conductance. It is the conductance between two points that produces a potential difference of one volt when a current of one ampere flows between them, i.e., S = 1/R = A/V = A2 s3/kg m2.

The henry, H, is the derived unit of inductance. It is the inductance of a closed circuit in which a potential difference of one volt is produced when the current in the circuit varies uniformly at the rate of one ampere per second, i.e., H = V s/A = kg m2/A2 s2.

The farad, F, is the derived unit of capacitance. It is the capacitance of two plates which hold a charge of one coulomb when there is a potential difference between them of one volt, i.e., F = C/V = A2 s4kg m2.

The weber, Wb, is the derived unit of magnetic flux. Wb = HA = V s = kg m2/A s2.

The tesla, T, is the derived unit of magnetic flux density. T = Wb/m2 = kg/A s2.

Equivalence of mechanical and electrical units of power

The SI base units are so defined that power, in the derived unit watt, can be obtained from force × displacement/time or ampere × volt, i.e.,


Derived SI optical units

These are combinations of the SI unit of luminous intensity, the candela (cd), with other SI units.

The lumen, lm, is the light energy emitted per second within unit solid angle by a point source of unit luminous intensity, i.e., lm = cd sr.

The lux, lx, is the unit of illuminance defined as the flux reaching the surface per unit area, i.e., lx = cd sr/m2.

Fractions and Multiples of SI Units

SI units can be multiplied or divided by powers of ten by attaching the appropriate prefix, as listed in Table 2, to the name of the unit and putting the corresponding letter before the standard symbol. For example, a force may be expressed as millions of newtons, or meganewtons, the symbol for which is MN, e.g.,

The prefix symbol may also be used with derived units, either named or unnamed, e.g.,


Some units which are decimally related to SI units have specific names. These are listed in Table 3. Other units are directly related to SI units, but not decimally; these are listed in Table 4.

Table 2. Decimal multiples or fractions of SI units

Table 3. Units having special names decimally related to SI units

Note. From Heat Exchanger Design Handbook, Hemisphere Publishing Corporation

Table 4. Units having special names not decimally related to SI units

Note. From Heat Exchanger Design Handbook, Hemisphere Publishing Corporation

Fundamental Constants in SI Units

Some of the fundamental constants are listed in Table 5. Because SI is a consistent system of units the relationships between fundamental constants apply without conversion factors, e.g.,


Table 5. Fundamental constants in SI units


Mayhew, Y. R. (1989) Conventions and nomenclature for physical quantities, units, numbers and mathematics, Heat Exhangers Design Handbook, Hemisphere Publishing Corp.

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