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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^[1]. 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.

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 almost always have an error and therefore uncertainty. 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,Applied Information Economics). 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.

When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of science. —LORD KELVIN

Main article: History of measurement

The word measurement comes from the Greek word 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.

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.

Main articles: Units of measurement and Systems of measurement

A baby bottle that measures in all three measurement systems—Imperial (U.K.), U.S. Customary, and metric.

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.

Main article: Imperial Unit