physical measurement

Physical measurement

Quantitative information on physical conditions, properties, or relations essential for coordination of activities, efficiency of communication, and understanding of the nature of things in science and engineering and in much of everyday life. Time, distance, mass, temperature, force, power, and all other physical quantities (or parameters or variables), as well as the properties of matter, materials, and devices, must be described and measured in terms which have the same meaning for everyone. The measuring device or instrument is calibrated (that is, the functional relationship between its indication and the magnitude of the measured quantity is determined) by direct or indirect comparison with a standard which embodies, possesses, or generates a fixed or reproducible magnitude of the physical quantity which is taken as the unit or some multiple or fraction of the unit. Any measured quantity may thus be expressed by a number (the magnitude ratio) and the name of the unit, for example, a length of 1.54 meters. The general area of scientific activity relating to standards and units and the accuracy of measurement is called metrology. See Units of measurement

Metric system

The basic unit of length in the decimal metric system was defined as one ten-millionth of the Earth's polar quadrant (as determined from latitude surveys), and is termed the meter. The basic unit for mass was defined as the mass of a cubic decimeter of water, to be called the kilogram.

The United States has adopted the Metric Conversion Act, declaring that “the policy of the U.S. shall be to coordinate and plan the increasing use of the metric system in the United States,” and established the U.S. Metric Board “to coordinate the voluntary conversion to the metric system.” However, English units have become almost universal in some worldwide industries—for example, dimensions of oil-drilling equipment, or altitude measurement in aviation. Thus it is likely that there will always be exceptions to uniformity, requiring special knowledge of special units for at least some people even as the whole world “goes metric” in principle.

International System of Units (SI)

At present the International System of Units (abbreviated SI, from the French Système International d'Unit és) is constructed from seven base units for independent quantities (Table 1). Units for all other quantities are derived from these seven units. In Table 2 are listed 22 SI derived units with special names. These units are derived from the base units in a coherent manner, which means they are expressed as products and quotients of the seven base units without numerical factors. All other SI derived units are similarly derived in a coherent manner from the 29 base and special-name SI units. For use with the SI units, there is a set of 20 prefixes (Table 3) to form multiples and submultiples of these units. For mass, the prefixes are to be applied to the gram instead of to the SI unit, the kilogram. See Dimensional analysis

SI base units
Quantity* Unit name Symbol
Length meter m
Mass kilogram kg
Time second s
Electric current ampere A
Thermodynamic temperature kelvin K
Amount of substance mole mol
Luminous intensity candela cd
*Quantity here and in Table 2 means a measurable attribute.

The SI units together with the SI prefixes provide a logical and interconnected framework for measurements in science, industry, and commerce.

In some cases, quantities are commonly expressed in terms of fundamental constants of nature, and use of these constants or “natural units” is acceptable. See Fundamental constants

SI derived units with special names
in terms of Expression in terms of
Quantity Unit name Symbol other units SI base units
Plane angle radian rad m · m-1 = 1
Solid angle steradian sr m2 · m-2 = 1
Frequency hertz Hz s-1
Force newton N m · kg · s-2
Pressure, stress pascal Pa N/m2 m-1 · kg · s-2
Energy, work, quantity of heat joule J N · m m2 · kg · s-2
Power, radiant flux watt W J/s m2 · kg · s-3
Quantity of electricity,
electric charge coulomb C A · s s · A
Electric potential difference,
electromotive force, voltage volt V W/A m2 · kg · s-3 · A-1
Capacitance farad F C/V m-2 · kg-1 · s4 · A2
Electric resistance ohm &OHgr; V/A m2 · kg · s-3 · A-2
Electric conductance siemens S A/V m-2 · kg-1 · s3 · A2
Magnetic flux weber Wb V · s m2 · kg · s-2 · A-1
Magnetic flux density tesla T Wb/m2 kg · s-2 · A-1
Inductance henry H Wb/A m2 · kg · s-2 · A-2
Celsius temperature degree Celsius °C K
Luminous flux lumen Im cd · sr m2 · m-2 · cd = cd
Illuminance lux Ix lm/m2 m2 · m-4 · cd = m-2 · cd
Activity (of a radionuclide) becquerel Bq s-1
Absorbed dose, specific
energy imparted, kerma gray Gy J/kg m2 · s-2
Dose equivalent sievert Sv J/kg m2 · s-2
Catalytic activity katal kat s-1 · mol

Typical examples of natural units, with their symbols, are:

Certain units which are not part of the SI are used so widely that it is impractical to abandon them. The units that are accepted for continued use with the International System are listed in Table 4. It is likewise necessary to recognize, outside the International System, the following units which are used in specialized fields: Logarithmic measures such as pH, dB (decibel), and Np (neper) are acceptable. See Atomic mass unit, Decibel, Electronvolt

Units in use with the International System
Name Symbol Value in SI unit
Minute min 1 min = 60 s
Hour h 1 h = 60 min = 3600 s
Day d 1 d = 24 h = 86,400 s
Degree ° 1° = (&pgr;/180) rad
Minute 1 = (1/60)° = (&pgr;/10,800) rad
Second 1 = (1/60) = (&pgr;/648,000) rad
Liter L* 1 L = 1 dm3 = 10-3 m3
Metric ton t 1 t = 103 kg
Nepera Np 1 Np = 1
Belb B 1 B = (1/2) In 10 (Np)
*An alternate symbol for liter is “ l.” Since “ l” can be easily confused with the numeral 1, the symbol “L” is recommended for United States use. aThe neper is used to express values of various logarithmic quantities. Natural logarithms are used to obtain the numerical values of quantities expressed in nepers. The neper is coherent with the SI, but is not yet adopted as an SI unit. bThe bel is used to express values of various logarithmic quantities. Logarithms to base ten are used to obtain the numerical values of quantities expressed in bels.

The internationally accepted definitions for the seven base units follow:


The kilogram (kg) is equal to the mass of the International Prototype Kilogram. The International Prototype is a platinum-iridium cylinder preserved at the International Bureau of Weights and Measures at Sèvres, France.

Mass is the only one of the base quantities for which the standard is an arbitrarily defined object. No basic property of matter involving mass can be measured with more precision than is possible in comparing kilogram masses by weighing, about 1 part in 108. See Mass


The meter is defined in terms of time and the speed of light: “The meter is the length of the path traveled by light in a vacuum during a time interval of 1/299 792 458 of a second.” This definition defines the speed of light to be exactly 299 792 458 m/s and defines the meter in terms of the most accurately known quantity, the second. See Light

The most accurate method of realizing the meter is by means of an interferometrically measured distance by fringe counting in which each vacuum fringe is a half wavelength from the next one. This wavelength, λ, is obtained from the measured frequency, f, using the relation λ = c/f, where c is the value of the speed of light in vacuum. To this end, major standards laboratories have measured the frequencies of several lasers stabilized to narrow molecular absorptions in the visible and near-infrared spectral regions. These stabilized lasers now serve as standards of length. See Interferometry, Wavelength standards

Time interval

The second (s) is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. In the best equipments the stability and accuracy of the cesium frequency generator correspond to an uncertainty of a few parts in 1015.

The second was long defined, for physical measurements as well as for civil affairs, as 1/86,400 of the time required for an average complete rotation of the Earth on its axis with respect to the Sun. Because of the slight slowing of the Earth's rotation rate, now averaging about 1 second per year (that is, 3 parts in 108) but with erratic and unexplained fluctuations, the universal second thus defined is not a constant. A time scale called Coordinated Universal Time (UTC) recommended by the General Conference of Weights and Measures (CGPM) in 1975 is defined in such a manner that it differs from international atomic time (TAI) by an exact whole number of seconds. This difference is adjusted occasionally by the use of a positive or negative leap second at the end of certain months to keep UTC in agreement with the time defined by the rotation of the Earth with an approximation better than 9/10 second. See Atomic clock, Frequency measurement, Time


The kelvin (K), the unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. The unit kelvin and its symbol K should also be used to express an interval or differences of temp-erature.

To provide convenient and adequately accurate means for practical realization and measurement of temperature, the International Temperature Scale is used, based on the assigned values of the temperatures of a number of reproducible equilibrium states (defining fixed points), on standard instruments calibrated at those temperatures, and on vapor-pressure temperature relationships. Interpolation between the fixed-point temperatures is provided by formulas used to establish the relation between indications of the standard instruments and values of International Temperature. An extensive revision, which came into effect in 1990, is called the ITS-90. See Temperature, Temperature measurement

Electric current

The ampere (A) is that constant current which, if maintained in two straight parallel conductors of infinite length and of negligible circular sections, and placed 1 meter apart in a vacuum, would produce between these conductors a force equal to 2 × 10-7 newton per meter of length. See Electrical units and standards

Luminous intensity

The CGPM, in 1979, redefined the base SI unit candela as the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and of which the radiant intensity in that direction is 1/683 watt per steradian. See Light, Luminous efficacy, Luminous efficiency, Luminous intensity, Photometry, Radiometry

Amount of substance

The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. When the mole is used, the elementary entities must be specified, and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

physical measurement

[′fiz·ə·kəl ′mezh·ər·mənt]
Quantitative information on a physical condition, property, or relation, generally in the form of the ratio of the measured quantity to a standard quantity, or to some fixed multiple or fraction thereof.
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