Square–cube law

For geometrically similar objects, surface area scales with the square of a linear dimension, while volume scales with its cube. Consequently, larger similar objects have less surface area per unit volume.

Geometric similarity: A relation between figures with the same shape and proportional corresponding dimensions. The law applies when an object's shape stays fixed as its dimensions scale.
Metabolic scaling theory: A framework relating metabolic rate to organism size through resource transport and biological structure. It examines how geometric scaling contributes to size-dependent metabolism.
Cube: A regular solid with six equal square faces and equal edge lengths. Its area and volume are simple powers of one edge length.
Kleiber's law: An empirical relation stating that animal basal metabolic rate scales approximately as body mass to the three-quarter power. It predicts metabolic scaling rather than deriving it directly from surface-area-to-volume geometry.
Dimensional analysis: A method for checking physical relations by tracking the dimensions of quantities. Dimensions distinguish area's length-squared scaling from volume's length-cubed scaling.
Heat transfer: The movement of thermal energy by conduction, convection, or radiation. Heat exchange through a surface becomes less effective per unit volume as similar bodies grow.
Galileo Galilei: An Italian scientist whose work helped establish mathematical approaches to motion and material strength. His Two New Sciences discusses how structural strength changes with size.
Square–cube law in biology: Applications of geometric scaling to biological form, physiology, and organism size. Biological proportions and physiology complicate direct predictions from ideal geometric similarity.
Surface-area-to-volume ratio: The quotient of an object's surface area and its volume. For similar shapes, this ratio decreases inversely with linear size.
Bone scaling: The study of how bone dimensions and mechanical demands vary with body size. Larger animals require support structures that account for rapidly increasing body mass.

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Lanchester's lawsCompared with: Despite its similar name, it describes geometric scaling, not combat attrition.