Formeln

Formeln, or formulas, are symbolic representations of relationships used to compute quantities or describe laws. In mathematics, a formula expresses a rule relating variables and constants and provides a method to obtain a result by substitution. In science and engineering, formulas encode physical laws, geometric relationships, and chemical compositions, serving as compact expressions of underlying models.

Common examples include the Pythagorean theorem a^2 + b^2 = c^2, the area of a circle A = π r^2, Ohm’s law V = I R, and the ideal gas law PV = nRT. Chemical formulas such as H2O or CO2 denote composition and proportions of elements in compounds. Formulas can be manipulated to compute values, to solve for unknown quantities, or to express relationships in a concise way.

A key distinction is between formulas, equations, and expressions. A formula is often a rule intended for calculating a result, possibly after solving for a specific variable. An equation states that two expressions are equal and is typically solved for an unknown. An expression evaluates to a value without asserting an equality. Formulas may be rearranged to isolate a target variable, a process common in algebra and applied fields.

Notation, units, and dimensional analysis are important when using formulas. Correct application depends on the assumptions and domains for which the formula is valid, such as Euclidean geometry, Newtonian mechanics, or idealized gas behavior. Formulas play a central role in education and research, enabling concise communication of complex ideas and enabling rapid computation and prediction.