Calculation

Calculation is the process of determining a numerical result by performing operations on numbers or quantities. It covers arithmetic operations such as addition, subtraction, multiplication, and division, as well as more advanced mathematical procedures, including solving equations, evaluating functions, and performing measurements and conversions. Calculations can be exact, using symbolic reasoning, or approximate, using numerical methods to achieve a desired tolerance.

Calculations can be performed by hand, with tools such as the abacus or slide rule, or by machines and computers. Over time, devices evolved from mechanical calculators to electronic calculators and general-purpose computers, which can execute algorithms to perform routine calculations rapidly and with high precision. Algorithms underpin calculation in many fields, from basic arithmetic to numerical analysis and simulations.

Calculations may be arithmetic, algebraic, geometric, or statistical, among others. In numerical work, issues of precision and rounding arise, leading to concepts such as significant figures and error propagation. Exact calculations produce precise results, while numerical methods provide approximations that converge to the true result as computation continues. Symbolic calculation preserves exact forms using algebraic rules, whereas numeric calculation uses floating-point or other representations.

Calculation is central to science, engineering, finance, data analysis, and daily decision making. It underpins measurements, modeling, simulations, and decision support. The study of calculation intersects with computer science, mathematics, and applied disciplines, and it continues to evolve with advances in algorithms, hardware, and numerical methods.