Advanced Proportion Calculator

Two quantities are in direct proportion if they increase or decrease together. As one quantity goes up, the other goes up by the same ratio.

$$ \frac{A}{B} = \frac{C}{x} \implies x = \frac{B \cdot C}{A} $$

Two quantities are in inverse proportion when an increase in one leads to a proportional decrease in the other, and vice-versa.

$$ A \cdot B = C \cdot x \implies x = \frac{A \cdot B}{C} $$

This involves more than two ratios. The "chain rule" is used to find a single unknown value when multiple quantities are related. This calculator uses a common form where two causes relate to an effect.

$$ \frac{\text{Cause}_1}{\text{Effect}_1} = \frac{\text{Cause}_2}{\text{Effect}_2} \implies \frac{A \cdot B}{C} = \frac{D \cdot E}{x} \implies x = \frac{C \cdot D \cdot E}{A \cdot B} $$

Three quantities A, B, and C are in continued proportion if the ratio of the first to the second is equal to the ratio of the second to the third (A:B = B:C). B is the mean proportional, and C is the third proportional.

$$ \text{Third Proportional (x): } x = \frac{B^2}{A} $$

$$ \text{Mean Proportional (x): } x = \sqrt{A \cdot C} $$