proportionality

Proportionality refers to a relation between two quantities in which one quantity changes in a fixed ratio to the other. When one quantity is directly proportional to the other, it satisfies y = kx, where k is the constant of proportionality. In inverse proportionality, y is proportional to the reciprocal of x, expressed as y = k/x; here y decreases as x increases.

Graphically, directly proportional relationships form a straight line through the origin, while inversely proportional relationships trace a hyperbola. The constant of proportionality, k, carries units that reflect the relation between the variables and measures the strength of the link.

Common examples include distance traveled being proportional to time at constant speed, and force in a spring being proportional to displacement (Hooke’s law: F = kx). Proportionality is a fundamental concept across science, engineering, and everyday reasoning, supporting scaling, unit analysis, and modeling of relationships.

In law and ethics, the principle of proportionality requires that measures taken are appropriate, necessary, and balanced with the pursued aims. It is a core idea in constitutional law and international humanitarian law, guiding assessments of whether actions or policies are justified given their effects and the legitimate objective.

Overall, proportionality provides a framework for understanding how changing one quantity affects another, and it supports judgement about efficiency, fairness, and consistency in both scientific and normative contexts.