Measurement
Measurement is the estimation or determination of
extent,
dimension or
capacity, usually in relation to some
standard or
unit of measurement. The measurement is expressed as a number of units of the standard (a
real number times a unit), such as distance being indicated by a number of
miles or
kilometers.
In more technical terms, the process of measuring involves estimating the
ratio of the magnitude of a
quantity to the magnitude of a unit of the same type (length, time, mass, etc.). A measurement is the result of such a process, expressed as the product of a
real number and a unit, where the real number is the estimated ratio. An example is 9 metres, which is an estimate of an object's length relative to a unit of length, the
metre. Unlike a count, or integer quantity of items that is known exactly, every measurement is an estimate that has some
uncertainty.
A measurement is a comparison to a standard. --
William ShockleyBy number we understand not so much a multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same kind, which we take for Unity. --
Sir Isaac Newton (1728)
In the
natural sciences, the act of measuring an object normally involves comparing the magnitude of a quantity possessed by an
object with a standard unit by using an instrument under controlled conditions. Examples of measuring instruments include the
thermometer,
speedometer,
weighing scale and
voltmeter. In order to measure accurately, measuring instruments must be carefully constructed and
calibrated. However, all measurements have some degree of uncertainty associated with them, which is usually expressed as a
standard error of measurement. This means that while a measurement is usually given as a number followed by a unit, every measurement has three components; the estimate, an error bound, and a probability that the actual magnitude lies within the error bound of the estimate. For example, a measurement of a plank might result in a measurement of 9 meters plus or minus 0.01 meters, with a probability of 0.95.
A measurement is usually distinguished from a count. A measurement is a real number, and is never exact. A count is a
natural number and may be exact. For example, we can determine that there are exactly 12 eggs in a carton by counting them. However some groups are not so easily counted, and estimating their numbers can involve similar issues to physical measurement. For example, figures for the
number of people with HIV or the number of stars in the
Milky Way will have associated standard errors, and can be viewed as estimates rather than exact counts.
Measurement is fundamental to most fields of science, including physics, chemistry and biology. Measurement is also essential to a diverse range of industries and commercial applications such as in engineering, construction, manufacturing, pharmaceutical production and electronics.
Other uses of the term
In addition to the definition of
measurement given above, the term is also often used in a looser fashion to refer to any process which numbers are assigned to entities to represent increasing amount or degree in some sense. For example, counts of raw scores on tests are sometimes referred to as measurements. Other examples include
consumer confidence and the rate of increase in the price of a good or service.
Laws to regulate measurement were originally developed to prevent
fraud. However, units of measurement are now generally defined on a scientific basis, and are established by international treaties. In the
United States, commercial measurements are regulated by the National Institute of Standards and Technology
NIST, a division of the
United States Department of Commerce.
The history of measurements is a topic within the
history of science and technology. The
metre (us: meter) was standardized as the unit for length after the
French revolution, and has since been adopted throughout most of the world. The United States and the UK are in the process of converting to the SI system. This process is known as
metrication.
Because measurement involves the estimation of magnitudes of quantities relative to particular quantities, called units, the specification of units is of fundamental importance to measurement. The definition or specification of precise standards of measurement involves two key features, which are evident in the
International System of Units (SI). Specifically, in this system the definition of each of the
base units makes reference to specific
empirical conditions and, with the exception of the kilogram, also to other quantitative attributes. Each
derived SI unit is defined purely in terms of a relationship involving itself and other units; for example, the unit of velocity is 1 m/s. Due to the fact that derived units make reference to base units, the specification of empirical conditions is an implied component of the definition of all units.
The measurement of a specific entity or relation results in at least two
numbers for the relationship between the entity or relation under study and the referenced unit of measurement, where at least one number estimates the
statistical uncertainty in the measurement, also referred to as
measurement error.
Measuring instruments are used to estimate ratios of magnitudes to units. Prior comparisons underlie the
calibration, in terms of standard units, of commonly used instruments constructed to measure physical quantities.
Imperial system
Before
SI units were widely adopted around the world, the British systems of
English units and later
Imperial units were used in Britian, the
Commonwealth and the United States. The system came to be known as
U.S. customary units in the United States and is still in use there and in a few
Caribbean countries. These various systems of measurement have at times been called
foot-pound-second systems after the Imperial units for distance, weight and time. It is interesting to note that a few Imperial units remain in use in Britain despite the fact that it has mostly switched to the SI system; road signs are still in
miles per hour, and beer is sold in
pints. For information on differences between the U.S. and Imperial systems, see
Comparison of the Imperial and U.S. customary systems.
Metric system
The
metric system is a decimalised
system of measurement based on the
metre and the
gram. It exists in several variations, with different choices of
base units, though these do not affect its day-to-day use. Since the 1960s the , explained further below, is the internationally recognised standard metric system. Metric units of mass, length, and electricity are widely used around the world for both everyday and scientific purposes.
The main advantage of the metric system is that is has a single base unit for each physical quanitity. All other units are
powers of ten or multiples of ten of this base unit. Unit conversions are always simple because they will be in the ratio of ten, one hundred, one thousand, etc. All lengths and distances, for example, are measured in metres, or thousandths of a metre (millimetres), or thousands of metres (kilometres), and so on. There is no profusion of different units with different conversion factors as in the Imperial system (e.g.
inches,
feet,
yards,
fathoms,
rods). Multiples and submultiples are related to the fundamental unit by factors of powers of ten, so that one can convert by simply moving the decimal place: 1.234 metres is 1234 millimetres or 0.001234 kilometres. The use of
fractions, such as 2/5 of a metre, is not prohibited, but uncommon.
SI
The
International System of Units (abbreviated
SI from the
French language name
Système International d'Unités) is the modern form of the
metric system. It is the world's most widely used
system of units, both in everyday
commerce and in
science. The SI was developed in 1960 from the
metre-
kilogram-
second (MKS) system, rather than the
centimetre-gram-second (CGS) system, which, in turn, had many variants. At its development the SI also introduced several newly named units that were previously not a part of the metric system.
Measuring devices are the means by which a measurement is made, referencing an object to a standard unit.
Length
|
A 2 metre carpenter's rule |
;RulerA
ruler or rule is an
instrument used in
geometry,
technical drawing and engineering/building to measure distances and/or to rule straight lines. Strictly speaking, the
ruler is the instrument used to
rule lines and the calibrated instrument used for determining measurement is called a
measure. However, common usage is that a ruler is calibrated so that it can measure.
Several different designs of flexible instruments are used to determine length, such as the carpenter's rule, the ribbon-like tape measure used by tailors, and the retractable rule used especially in the construction trades and by home handyman, also known as a
tape measure. As can be seen by the photos on this page, a 2
metre carpenter's rule can be folded down to a length of only 20
centimetres to easily fit in a pocket, and the 5 metre long tape easily retracts to fit within a small-sized housing.
Practical rulers have distance markings along their edges.
;Tape measureA
tape measure or measuring tape is a ribbon of cloth, plastic, or metal withlinear-measure markings, often in both
imperial and .
Surveyors use tape measures in lengths on the order of
hectometres. It is a convenient measuring tool. Its flexibility allows for a measure of great length to be easily carried in pocket or toolkit and permits one to measure around curves or corners.
Time
The most common devices for measuring time are the
clock, for periods less than a day, and the
calendar, for periods longer than a day. Clocks can range from
watches, to more exotic varieties such as the
Clock of the Long Now. They can be driven by a variety of means, including a
pendulum. There are also a variety of different
calendars, for example the
Lunar calendar and the
Solar calendar, although the
Gregorian calendar is the most commonly used.
A
chronometer is a timekeeper precise enough to be used as a portable time standard, usually in order to determine
longitude by means of
celestial navigation.
The most accurate type of measuring devices for time is the
atomic clock. More archaic devices include the
hourglass, the
sundial, the
tempometer and the
water clock.
Mass
A weighing scale is a device for measuring the weight of an object. Until digital scales, the most accurate means of measuring the weight or mass of an object was using a balance. In its conventional form, this class of measuring instrument compares the sample, placed in a weighing pan (weighing basin) and suspended from one end of a beam with a standard mass or combination of standard masses in a scale pan (scale basin) suspended from the other end. To weigh an object in the measuring pan, standard
weights are added to the scale pan until the beam is in
equilibrium as closely as possible. Less accurate, but very versitile is the spring-based scale which has a calibrated spring that deforms linearly as more weight is put on it.
Metrology is the study of measurement. In general, a
metric is a scale of measurement defined in terms of a standard: i.e. in terms of well-defined unit. The quantification of phenomena through the process of measurement relies on the existence of an explicit or implicit metric, which is the standard to which measurements are referenced. If one says
I am 5, that person is indicating a measurement without supplying an applicable standard. He could mean
I am 5 years old or
I am 5 feet high, however the implicit metric is that he is 5 years old.
Measurement is not limited to physical quantities and relations but can extend to the quantification of a magnitude of any kind. In the social sciences and other fields such as health, biology and market research, probabilistic models such as the
Rasch model for measurement are applied in order to measure using instruments such as questionnaires and assessments which enable comparisons between persons. The field of
psychometrics is concerned with the theory and technique of measurement of psychological and mental phenomena.
Measurement of many quantities is very difficult and prone to large
error. Part of the difficulty is due to
uncertainty, and part of it is due to the limited
time available in which to make the measurement.
Examples of things that are very difficult to measure in some respects and for some purposes include social related items such as:
* A person's
knowledge (as in
testing, see also
assessment)
* A person's
feelings,
emotions, or beliefs
* A person's senses (
qualia)
Even for physical quantities gaining accurate measurement can be difficult. It is not possible to be exact; instead, repeated measurements will vary due to various factors affecting the quantity such as
temperature, time,
electromagnetic fields, and especially measurement method. As an example in the measurement of the
speed of light, the quantity is now known to a high degree of precision due to modern methods, but even with those methods there is some variability in the measurement.
Statistical techniques are applied to the measurement samples to estimate the speed. In earlier sets of measurements, the variability was greater, and comparing the results shows that the variability and bias in the measurement methods was not properly taken into account. Proof of this is that when various group's measurements are plotted with the estimated speed and error bars showing the expected variability of the estimated speed from the actual number, the error bars from each of the experiments did not all overlap. This means a number of groups incorrectly accounted for the true sources of error and overestimated the accuracy of their methods.
Measuring the ratios between physical quantities is an important sub-field of
physics.
Some important physical quantities include:
*
Speed of light*
Planck's constant*
Gravitational constant*
Elementary charge (
electric charge of
electrons,
protons, etc.)
*
Fine-structure constant*
Conversion of units*
Dimensional analysis*
Dimensionless number*
Econometrics*
History of measurement*
Instrumentation*
Levels of measurement*
Measurement in quantum mechanics*
Orders of magnitude*
Statistics*
Systems of measurement*
Timeline of temperature and pressure measurement technology*
Timeline of time measurement technology*
Units of measurement*
Uncertainty principle*
Uncertainty in measurement
*
Virtual instrumentation*
Weights and measuresNewton, I. (1728/1967). Universal Arithmetic: Or, a Treatise of Arithmetical Composition and Resolution. In D.T. Whiteside (Ed.),
The mathematical Works of Isaac Newton, Vol. 2 (pp. 3-134). New York: Johnson Reprint Corp.
*
A Dictionary of Units of Measurement*
'Metrology In Short', 2nd Edition*
Metric conversions*
Euromet.
zh-yue:量度
