# Measurement

### 2007 Schools Wikipedia Selection. Related subjects: Mathematics

**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.

The process of measuring involves estimating the ratio of the magnitude of a quantity to the magnitude of a unit of the same type (e.g. 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.

## Overview

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.

## History

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.

## Units and systems of measurement

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 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. It is interesting to note that many 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, yards, miles per hour, etc, people tend to measure their own height in feet and inches and beer 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 meter 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 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 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/m^{3}.

#### Converting Prefixes

The SI allows easy multiplication when switching among units having the same base but different prefixes. If you are working with meters and want to convert to centimeters, you only need to multiply the number of meters by 100 because there are 100 centimeters in a meter. Inversely, to switch from centimeters to meters you multiply the number of centimeters by .01.

### Length

A ruler or rule is a tool 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.

### 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. Mass can also refer to how much inertia an object has.

## Metrology

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.

## Probabilistic measurement

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.

## Difficulties in measurement

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.