Various meters

Measurement is the estimation of a physical quantity such as length, temperature, or time. Measurements find 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. Measurements always involve some error, and so in science measurements are often accompanied by error bounds, as in 2.53 meters plus or minus .01 meters. The study of measurement is called metrology. An old fashioned word for measurement is mensuration.

Two distinctly different kinds of measurement are the marker and the span. 3:05 P.M. GMT, 3 June 2001 is a marker. 15 minutes is a span. Both must be given in reference to some standard, and both involve some necessary error. A count, as distinct from a measurement, may be exact. I have exactly two ears. There are exactly 60 seconds in one minute (by definition). On the other hand large counts, such as the number of people in a crowd, often use estimation, even which an exact count is theoretically possible.

Overview

In the natural sciences, the act of measuring often requires an instrument designed and calibrated for that purpose, such as a thermometer, speedometer, weighing scale or voltmeter. Measurements are usually assumed to be normally distributed. 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 meters, with a probability of 99%.

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.

Other uses of the term

In addition to the standard use of the word measurement, the word is often loosely used to mean any number assigned to a physical object. Thus the wind chill factor, which has no scientific validity, or IQ, which is just a count of correct answers on a test, are loosely called measurements. Measurements carried out by surveys or questionaires are, strictly speaking, counts rather than measurements, but may be converted to measurements by the use of statistics, usually with some assumption about the distribution of such data. The field of psychometrics is concerned with the theory and technique of measurement of psychological and mental phenomena.

History

Main article: History of measurement

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, though there is considerable resistance to the change. This process is known as metrication.

Units and systems of measurement

Main articles: Units of measurement 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.

Imperial system

Main article: Imperial Unit

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 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 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

Main article: 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 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

Main article: International System of Units

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. 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 2 metre carpenter's rule

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

Main article: 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

Main article: Weighing scale

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 ounce, pound, and tonne are units of weight. 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 weight 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.

Difficulties in measurement

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. Using physics, it can be showns that, in the gravitational field of the Earth, it should take any object about .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. But this measurement is not exact, but only accurate to two significant digits. Also, the Earth's gravitational field varies slightly depending of hight 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, droping an object from a hieght 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.

Miscellaneous

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
• Quantity

See also

• Conversion of units
• Dimensional analysis
• Dimensionless number
• Econometrics
• History of measurement
• Instrumentation
• Levels of measurement
• Measurement in quantum mechanics
• Orders of magnitude
• Psychometrics
• 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 measures

External links

• A Dictionary of Units of Measurement
• 'Metrology In Short', 2nd Edition
• Metric conversions
• Euromet.