Ratio Calculator
Solve a proportion a : b = c : d for the unknown term and simplify ratios.
Solve for d in the proportion a : b = c : d
a : b = c : d
Simplified ratio a : b = 2 : 3
Full proportion: 2 : 3 = 10 : 15
Formula
About this calculator
A ratio compares two quantities, and a proportion states that two ratios are equal. When three of the four terms in a : b = c : d are known, the fourth can be found by cross multiplication: d = (b × c) / a.
This calculator solves for the missing fourth term and also reduces the given ratio a : b to lowest terms using the greatest common divisor. Proportions are widely used for scaling recipes, converting units, reading maps, and resizing images.
Frequently asked questions
In a : b = c : d the cross products are equal, so a × d = b × c. Solving for the unknown d gives d = (b × c) / a.
Divide both numbers by their greatest common divisor. For example 8 : 12 simplifies to 2 : 3 because the GCD of 8 and 12 is 4.
Yes. The proportion still holds with decimal terms; the simplified form is shown when both leading terms are whole numbers.
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