Proportion Calculator

How it works

A proportion says two ratios are equal: A/B = C/D. Multiplying both sides by B × D clears the fractions and leaves A × D = B × C, the cross products. That equation has one unknown when three terms are known, so the missing term is the product of the two terms diagonally opposite it, divided by the term it sits across from.

In the language of means and extremes, A and D are the extremes and B and C are the means: the product of the means equals the product of the extremes. A missing extreme is the product of the means over the other extreme; a missing mean is the product of the extremes over the other mean.

The worked step shows exactly that multiplication and division with your numbers, and the completed proportion lets you check it: both sides should reduce to the same fraction, and the cross product is the same whichever pair you multiply.

Formula

A/B = C/D  ⇔  A × D = B × C
A = B × C ÷ D
B = A × D ÷ C
C = A × D ÷ B
D = B × C ÷ A

Example

2/3 = 8/D: D = 3 × 8 ÷ 2 = 12, so 2/3 = 8/12 and both cross products are 24.

A/63 = 4/7: A = 63 × 4 ÷ 7 = 36.

A map scale of 1 inch to 50 miles with 3.5 inches measured: 1/50 = 3.5/D gives D = 50 × 3.5 ÷ 1 = 175 miles.

Assumptions and limitations

• A proportion with a zero term either has no solution, has infinitely many, or forces the other numerator to zero, so this calculator requires all three known terms to be non-zero.
• Negative terms are allowed and the signs follow through the cross products.
• The field for the missing term is ignored entirely; whatever it holds has no effect on the result.
• Results are rounded to four decimal places for display only.

Frequently asked questions