TeXipedia

propto

Denotes proportionality between mathematical quantities, indicating that one value varies directly with another by some constant factor.

Overview

Essential in scientific and mathematical writing to express relationships between variables without specifying exact equality. Common applications include:

  • Physics equations showing relationships between physical quantities (e.g., force proportional to acceleration)
  • Statistical analysis when describing correlations
  • Engineering contexts for approximate relationships
  • Chemical equations indicating reaction rates

Particularly valuable when the exact constant of proportionality is unknown or unnecessary for the discussion at hand.

Examples

Expressing that energy is proportional to frequency in quantum mechanics.

E∝fE \propto f 
E \propto f

Showing the relationship between force and acceleration in Newton's Second Law.

F∝aF \propto a 
F \propto a

Stating that the gravitational force is proportional to the inverse square of distance.

Fg∝1r2F_g \propto \frac{1}{r^2} 
F_g \propto \frac{1}{r^2}