proportionalitet

Proportionalitet, or proportionality, is a relationship between two quantities in which a change in one quantity corresponds to a constant multiple of the other. If y is proportional to x, there exists a constant k such that y = kx. Inverse proportionality occurs when y is inversely proportional to x, so y = k/x. More generally, a proportional relationship is one in which the ratio y/x is constant for all measured values.

Graphically, direct proportionality yields a straight line through the origin with slope k. Inverse proportionality produces a hyperbola, where the product xy remains constant. The constant of proportionality k carries the units needed to balance the equation, so it reflects the dimensional relationship between the quantities involved.

Direct proportionality appears in many contexts, such as Ohm’s law (current proportional to voltage in a fixed resistance) and Hooke’s law (force proportional to displacement in a spring). Proportional relationships are also central to scaling in geometry, where similar figures have corresponding linear dimensions in fixed ratios. Inverse proportionality is common in problems involving reciprocal effects, such as certain physical laws where a quantity decreases as another increases, or in situations where a product of two quantities remains constant.

In law and policy, the principle of proportionality requires that measures taken to achieve a public objective be proportionate to the aim, balancing effectiveness with burden and rights. Proportionality is a foundational idea across mathematics, science, design, and governance.