(1) The difference (unsigned) between a specified value of a particular quantity and a value that has been accepted as correct for that quantity. When this difference is known and has a sign, it may be called a correction or an error, depending on the viewpoint of the user. When the difference is known only very approximately, it is usually referred to merely as high accuracy if small and low accuracy if large, without stating numerical values.

(2) A measure of the closeness of a set of values, measured or calculated, to the true value. Also called outer accuracy or external accuracy by some European writers. Accuracy is sharply distinguished, in English, from precision, which is a measure of the closeness of the measurements to each other. So a very precise set of measurements can be much less accurate than a different set which is more accurate but less precise. For example, some early geodesists using a few poor measurements were able to find values of the Earth's flattening quite close to the value now accepted as correct, while later geodesists using more precise data obtained values considerably farther from the present value. The history of measurements of the speed of light provides another example of many, presumably very precise, measurements gave quite erroneous values for the speed. Several different kinds of measure are in use. (a) The square root of the average value of the sum of squares of the differences between the values in a set and the corresponding correct or standard values. This is the most common measure and is usually referred to as the accuracy of the set of values. It is also referred to as the outer accuracy or external accuracy if the precision is referred to as the inner accuracy. (This latter terminology is rare in American usage. ) If (x_i) is the set of values (measured of calculated) and if s is + √( S (x_i - x_io )²)/M then s is a measure of the accuracy if (x_io) is a set of correct or standard values and M = I (the number of values in the set). It is the precision if x_io = x, the average value of the (x_io ) and if M = I 1. (b) The average of the sum of the absolute values of the differences between the measured or calculated values and the correct or standard values. (c) The reciprocal of the s defined in (a). Accuracy cannot be calculated solely from the measured or calculated values. A standard (correct) value or set of such values must be used for comparison. The standard may be (a) an exact value, such as the sum of the three angles of a plane triangle; (b) the value of a conventional unit, such as the length of the International Meter, defined from the speed of light in a vacuum; (c) a value determined by refined methods and deemed sufficiently near the correct value that it can be used as such: e.g., the adjusted elevation of a permanent bench mark or the graticule of a map projection.

(3) The standard deviation. This is a measure of precision. It should never be used as a measure of accuracy.

(4) The root mean square error. This is approximately the same as the standard deviation and, like it, should not be used as a measure of accuracy.

(5) When the set (x_i ) consists of calculated numbers (e.g. those in a mathematical table), the term accuracy may mean (a) the number of significant digits in the numbers; (b) the magnitude of the least significant digit; or (c) the number of correct places in the numbers.