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A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or ''results''. The term is used in a variety of senses, from the very definite
arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19t ...
al calculation of using an
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
, to the vague
heuristic A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, ...
s of calculating a strategy in a competition, or calculating the chance of a successful relationship between two people. For example, multiplying 7 by 6 is a simple algorithmic calculation. Extracting the
square root In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or  ⋅ ) is . For example, 4 and −4 are square roots of 16, because . E ...
or the cube root of a number using mathematical models is a more complex algorithmic calculation. Statistical estimations of the likely election results from opinion polls also involve algorithmic calculations, but produces ranges of possibilities rather than exact answers. To ''calculate'' means to determine mathematically in the case of a number or amount, or in the case of an abstract problem to deduce the answer using
logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...
,
reason Reason is the capacity of consciously applying logic by drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, la ...
or common sense. The English word derives from the
Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of ...
''calculus'', which originally meant a small stone in the gall-bladder (from Latin ''calx''). It also meant a pebble used for calculating, or a small stone used as a counter in an
abacus The abacus (''plural'' abaci or abacuses), also called a counting frame, is a calculating tool which has been used since ancient times. It was used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the Hin ...
(Latin ''abacus'', Greek ''abax''). The abacus was an instrument used by Greeks and Romans for arithmetic calculations, preceding the slide-rule and the electronic calculator, and consisted of perforated pebbles sliding on iron bars. Calculation is a prerequisite for
computation Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. An esp ...
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* Calculus (disambiguation) — list of general methods of calculation by application area * Complexity class — theoretical notion to categorize calculability * Cost accounting — business application of calculation *
List of algorithms The following is a list of well-known algorithms along with one-line descriptions for each. Automated planning Combinatorial algorithms General combinatorial algorithms * Brent's algorithm: finds a cycle in function value iterations using on ...
— fully formalized, computer-executable methods of calculation *
Mental calculation Mental calculation consists of arithmetical calculations using only the human brain, with no help from any supplies (such as pencil and paper) or devices such as a calculator. People may use mental calculation when computing tools are not availa ...
— performing arithmetics using one's brain only