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
Ratio
2 : 3a
40%
b
60%
Simplified ratio a : b = 2 : 3
Full proportion: 2 : 3 = 10 : 15
- 1
Cross product b × c
3 × 10 = 30 - 2
Solve for d: (b × c) ÷ a
30 ÷ 2 = 15
Formula
How this is calculated
You enter three terms of a proportion written as a : b = c : d, and the calculator solves for the fourth, d. The core idea is that a proportion asserts two ratios are equal, so their cross products are equal: a × d = b × c. Rearranging gives d = (b × c) ÷ a, which is exactly the value reported.
The terms are pure numbers, so they can be whole numbers or decimals and carry no units of their own — any units cancel as long as a and c describe the same quantity and b and d describe the same quantity. The only restriction is that a cannot be zero, since dividing by zero is undefined; that case is flagged as an error.
Separately, the input ratio a : b is reduced to lowest terms by dividing both numbers by their greatest common divisor (GCD). This simplification is only shown when a and b are both integers; with decimal inputs the ratio is displayed as entered. The proportion itself still holds for decimals, and results are rounded for display to a handful of fractional digits.
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.
Also known as
TG we-Calculate Editorial Team. (2026). Ratio Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/ratio-calculator
TG we-Calculate Editorial Team. "Ratio Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/ratio-calculator.
TG we-Calculate Editorial Team, "Ratio Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/ratio-calculator
@misc{wecalculate_ratio_calculator, title = {Ratio Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/ratio-calculator}}, year = {2026}, note = {TG we-Calculate} }
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