Direct proportionality

Two quantities a and b are said to be directly proportional, if the quotient <math>\frac{a}{b}</math> is constant. This is written as <math>a \propto b</math>.

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Constant of Proportionality

The constant <math>c = \frac{a}{b}</math> is called constant of proportionality. Therefore, a proportionality can be written as:

<math>a = c \times b</math>

Famous Proportionality

• The circumference C of a circle is proportional to its radius r:

<math>C \propto r</math>

Here, the constant is <math>2 \pi</math>

• Mass–energy equivalence: The energy E of a body is proportional to its mass m:

<math>E \propto m</math>

Here, the constant is c², the square of the speed of light.

Misunderstandings

The role of the quantities and of the constant are not interchangeable. It would be wrong to say in the examples above that <math>C \propto 2 \pi</math> or <math>E \propto c^2</math>.

Sources

Weisstein, Eric W. "Proportional." From MathWorld--A Wolfram Web Resource.