# Dictionary Definition

mensuration n : the act or process of measuring;
"the measurements were carefully done"; "his mental measurings
proved remarkably accurate" [syn: measurement, measuring, measure]

# User Contributed Dictionary

## English

### Noun

- The branch of mathematics that deals with measurement, especially the derivation and use of algebraic formulae to measure the areas and volumes of geometric figures.

#### Related terms

# Extensive Definition

Measurement is the estimation of the magnitude of
some attribute of an object, such as its length or weight, relative
to a unit of measurement. Measurement usually involves using a
measuring instrument, such as a ruler or scale, which is calibrated
to compare the object to some standard, such as a meter or a
kilogram. In science, however, where accurate measurement is
crucial, a measurement is understood to have three parts: first,
the measurement itself, second, the margin of error, and third, the
confidence level -- that is, the probability that the actual
property of the physical object is within the margin of error. For
example, we might measure the length of an object as 2.34 meters
plus or minus 0.01 meter, with a 95% level of confidence.

Metrology is the
scientific study of measurement. In measurement theory a
measurement is an observation that reduces an uncertainty expressed
as a quantity. As a verb, measurement is making such observations.
It includes the estimation of a physical quantity such as distance,
energy, temperature, or time. It could also include such things as
assessment of attitudes, values and perception in surveys or the
testing of aptitudes of individuals.

In the physical sciences, measurement is most
commonly thought of as the ratio of some physical quantity to a
standard quantity of the same type, thus a measurement of length is
the ratio of a physical length to some standard length, such as a
standard meter. Measurements are usually given in terms of a real
number times a unit of measurement, for example 2.53 meters, but
sometimes measurements use complex numbers, as in measurements of
electrical
impedance.

## Observations and error

The act of measuring often requires an instrument
designed and calibrated for that purpose, such as a thermometer, speedometer, weighing
scale, or voltmeter. Surveys and tests
are also referred to as "measurement instruments" in academic
testing, aptitude testing, voter polls, etc.

Measurements always have errors and therefore
uncertainties. In fact, the reduction—not necessarily the
elimination—of uncertainty is central to the concept of
measurement. Measurement
errors are often assumed to be normally
distributed about the true value of the measured quantity.
Under this assumption, every measurement has three components: the
estimate, the error bound, and the probability that the actual
magnitude lies within the error bound of the estimate. For example,
a measurement of the length of a plank might result in a
measurement of 2.53 meters plus or minus 0.01 meter, with a
probability of 99%.

The initial state of uncertainty, prior to any
observations, is necessary to assess when using statistical methods
that rely on prior knowledge (Bayesian
methods). This can be done with
calibrated probability assessment.

Measurement is fundamental in science; it is one
of the things that distinguishes science from pseudoscience. It is
easy to come up with a theory about nature, hard to come up with a
scientific theory that predicts measurements with great accuracy.
Measurement is also essential in industry, commerce, engineering,
construction, manufacturing, pharmaceutical production, and
electronics.

## History

The word measurement comes from the Greek
"metron", meaning limited proportion. This also has a common root
with the word "moon" and "month" possibly since the moon and other
astronomical objects were among the first measurement methods of
time.

The history of measurements is a topic within the
history of science and technology. The metre (U.S.:
meter) was standardized as the unit for length after the French
revolution, and has since been adopted throughout most of the
world.

## Standards

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.

## Units and systems

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.### Imperial system

Before SI units were
widely adopted around the world, the British systems of English
units and later Imperial
units were used in Britain, 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. Many Imperial units remain in use in
Britain despite the fact that it has officially switched to the SI
system. Road signs are still in miles, yards, miles per
hour, and so on, people tend to measure their own height in
feet and inches and milk
is sold in pints, to give
just a few examples. Imperial units are used in many other places,
for example, in many Commonwealth countries which are considered
metricated, land area is measured in acres and floor space in
square feet, particularly for commercial transactions (rather than
government statistics). Similarly, the imperial gallon is used in
many countries that are considered metricated at gas/petrol
stations, an example being the United
Arab Emirates.

### 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 International System of
Units (SI), explained further below, is the internationally
recognized 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 it has a single base unit for each physical quantity. 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 meters, or thousandths of a metre (millimeters), or
thousands of meters (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 meter, 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,
revised 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.

There are two types of SI units, base and derived
units. Base units are the simple measurements for time, length,
mass, temperature, amount of substance, electric current, and light
intensity. Derived units are made up of base units, for example
density is kg/m3.

#### Converting prefixes

The SI allows easy multiplication when switching among units having the same base but different prefixes. To convert from meters to centimeters it is only necessary to multiply the number of meters by 100, since there are 100 centimeters in a meter. Inversely, to switch from centimeters to meters one multiplies the number of centimeters by .01.### Length

A ruler
or rule is a tool used in, for example, geometry, technical
drawing, engineering, and carpentry, to measure distances or to
draw straight lines. Strictly speaking, the ruler is the instrument
used to rule straight lines and the calibrated instrument used for
determining length is called a measure, however common usage calls
both instruments rulers and the special name straightedge is used
for an unmarked rule. The use of the word measure, in the sense of
a measuring instrument, only survives in the phrase tape measure,
an instrument that can be used to measure but cannot be used to
draw straight lines. As can be seen in the photographs on this
page, a two metre carpenter's rule can be folded down to a length
of only 20 centimetres, to easily fit in a pocket, and a five metre
long tape measure easily retracts to fit within a small
housing.

### Time

The most common devices for measuring time are
the clock or watch. A chronometer is a timekeeping
instrument precise enough to be used as a portable time standard.
Historically, the invention of chronometers was a major advance in
determining longitude
and an aid in celestial
navigation. The most accurate device for the measurement of
time is the atomic
clock.

Before the invention of the clock, people
measured time using the hourglass, the sundial, and the water
clock.

### Mass

Mass refers to the intrinsic property of all
material objects to resist changes in their momentum. Weight, on
the other hand, refers to the downward force produced when a mass
is in a gravitational field. In free fall,
objects lack weight but retain their mass. The Imperial units of
mass include the ounce,
pound, and
ton. The metric units
gram and kilogram are units
of mass.

A unit for measuring weight or mass is called a
weighing scale or, often, simply a scale. A spring scale measures
force but not mass, a balance compares masses, but requires a
gravitational field to operate. The most accurate instrument for
measuring weight or mass is the digital scale, but it also requires
a gravitational field, and would not work in free fall.
=Economics=== The measures used in
economics are physical measures, nominal price value measures and
fixed price value measures. These measures differ from one another
by the variables they measure and by the variables excluded from
measurements. The measurable variables in economics are quantity,
quality and distribution. By excluding variables from measurement
makes it possible to better focus the measurement on a given
variable, yet, this means a more narrow approach.

## Difficulties

Since accurate measurement is essential in many
fields, and since all measurements are necessarily approximations,
a great deal of effort must be taken to make measurements as
accurate as possible. For example, consider the problem of
measuring the time it takes for an object to fall a distance of one
meter (39 in). Using physics, it
can be shown that, in the gravitational field of the Earth, it
should take any object about 0.45 seconds to fall one meter.
However, the following are just some of the sources of error that
arise. First, this computation used for the acceleration of gravity
9.8 meters per second per second (32.2 ft/s²). But this
measurement is not exact, but only accurate to two significant
digits. Also, the Earth's gravitational field varies slightly
depending on height above sea level and other factors. Next, the
computation of .45 seconds involved extracting a square root, a
mathematical operation that required rounding off to some number of
significant digits, in this case two significant digits.

So far, we have only considered scientific
sources of error. In actual practice, dropping an object from a
height of a meter stick and using a stop watch to time its fall, we
have other sources of error. First, and most common, is simple
carelessness. Then there is the problem of determining the exact
time at which the object is released and the exact time it hits the
ground. There is also the problem that the measurement of the
height and the measurement of the time both involve some error.
Finally, there is the problem of air resistance.

Scientific measurements must be carried out with
great care to eliminate as much error as possible, and to keep
error estimates realistic.

## Definitions and theories

### Classical definition

In the classical definition, which is standard throughout the physical sciences, measurement is the determination or estimation of ratios of quantities. Quantity and measurement are mutually defined: quantitative attributes are those which it is possible to measure, at least in principle. The classical concept of quantity can be traced back to John Wallis and Isaac Newton, and was foreshadowed in Euclid's Elements (Michell, 1993).### Representational theory

In the representational theory, measurement is defined as "the correlation of numbers with entities that are not numbers" (Nagel, 1932). The strongest form of representational theory is also known as additive conjoint measurement. In this form of representational theory, numbers are assigned on the basis of correspondences or similarities between the structure of number systems and the structure of qualitative systems. A property is quantitative if such structural similarities can be established. In weaker forms of representational theory, such as that implicit within the work of Stanley Smith Stevens, numbers need only be assigned according to a rule.The concept of measurement is often misunderstood
as merely the assignment of a value, but it is possible to assign a
value in a way that is not a measurement in terms of the
requirements of additive conjoint measurement. One may assign a
value to a person's height, but unless it can be established that
there is a correlation between measurements of height and empirical
relations, it is not a measurement according to additive conjoint
measurement theory. Likewise, computing and assigning arbitrary
values, like the "book value" of an asset in accounting, is not a
measurement because it does not satisfy the necessary
criteria.

3.14 is a standard measurement used by man in all
history although they did not realize it. When building the
piramids in Egypt or other projects they used a wheel rolling it to
mark the boundrys, therefor almost all projects in the past will
confirm to no matter the size of the wheel, one revolution equals
3.14

## Types proposed by Stevens

The definition of measurement was purportedly broadened by Stanley S. Stevens. He defined types of measurements to include nominal, ordinal, interval, and ratio. In practice, this scheme is used mainly in the social sciences but even there its use is controversial because it includes definitions that do not meet the more strict requirements of the classical theory and additive conjoint measurement. However, the classifications of interval and ratio level measurement are not controversial.- Nominal

- Discrete data which represent group membership to a category which does not have an underlying numerical value. Examples include ethnicity, color, pattern, soil type, media type, license plate numbers, football jersey numbers, etc. May also be dichotomous such as present/absent, male/female, live/dead

- Ordinal

- Includes variables that can be ordered but for which there is no zero point and no exact numerical value. Examples: preference ranks (Thurstone rating scale), Mohs hardness scale, movie ratings, shirt sizes (S,M,L,XL), and college rankings. Also includes the Likert scale used in surveys – strongly agree, agree, undecided, disagree, strongly disagree. Distances between each ordered category are not necessarily the same (a four star movie isn't necessarily just "twice" as good as a two star movie).

- Interval

- Describes the distance between two values but a ratio is not relevant. A numerical scale with an arbitrary zero point. Most common examples Celsius and Fahrenheit. Some consider indexes such as IQ to be interval measurements whereas others consider them only counts. Interval-level measurements can be obtained through application of the Rasch model.

- Ratio

- This is what is most commonly associated with measurements in the physical sciences. The zero value is not arbitrary and units are uniform. This is the only measurement type where ratio comparisons are meaningful. Examples include weight, speed, volume, etc.

The concept of measurement is often confused with
counting, which implies an exact mapping of integers to clearly
separate objects.

## Citations

## Miscellanea

Measuring the ratios between physical quantities
is an important sub-field of physics.

Some important physical quantities include:

## See also

- Conversion of units
- Detection limit
- Detection Limits
- Differential linearity
- Dimensional analysis
- Dimensionless number
- Econometrics
- History of measurement
- Instrumentation
- Levels of measurement
- Measurement in quantum mechanics
- Orders of magnitude
- Psychometrics
- Statistics
- Systems of measurement
- Test method
- Timeline of temperature and pressure measurement technology
- Timeline of time measurement technology
- Units of measurement
- Uncertainty principle
- Uncertainty in measurement
- Virtual instrumentation
- Weights and measures

## External links

mensuration in Afrikaans: Mate

mensuration in Arabic: علم القياس

mensuration in Bengali: পরিমাপ

mensuration in Breton: Muzul

mensuration in Catalan: Mesura

mensuration in Czech: Měření

mensuration in German: Messung

mensuration in Spanish: Medición

mensuration in Esperanto: Mezuro

mensuration in Basque: Neurketa

mensuration in French: Mesure physique

mensuration in Hebrew: מדידה

mensuration in Hindi: मापन

mensuration in Indonesian: Pengukuran

mensuration in Icelandic: Mæling

mensuration in Italian: Misura

mensuration in Swahili (macrolanguage):
upimaji

mensuration in Latin: Mensura

mensuration in Lingala: Lomeko

mensuration in Hungarian: Mérés

mensuration in Japanese: 測定

mensuration in Dutch: Meten

mensuration in Norwegian: Måling

mensuration in Narom: M'suthe

mensuration in Polish: Pomiar

mensuration in Portuguese: Medição

mensuration in Russian: Измерение

mensuration in Simple English: Unit of
measurement

mensuration in Slovenian: meritev

mensuration in Swedish: Mätning

mensuration in Tamil: அளவியல்

mensuration in Ukrainian: Вимірювання

mensuration in Vietnamese: Đo lường

mensuration in Turkish: Ölçüm

mensuration in Volapük: Mafam

mensuration in Yiddish: מאס

mensuration in Contenese: 量度

mensuration in Chinese: 量度

# Synonyms, Antonyms and Related Words

altimetry, appraisal, appraisement, approximation, assessment, assize, assizement, bathymetry, biometrics, biometry, cadastration, calculation, cartography, chorography, computation, correction, craniometry, determination, estimate, estimation, evaluation, gauging, geodesy, geodetics, goniometry, hypsography, hypsometry, instrumentation,
measure, measurement, measuring, metric system,
metrology, oceanography, planimetry, psychometrics, psychometry, quantification, quantization, rating, stereometry, survey, surveying, telemetering, telemetry, topography, triangulation, valuation