Ratio Calculator
Three tools in one: simplify a ratio to its lowest terms, solve for a missing value in a proportion (A:B = C:?), or scale a ratio by any factor. Full working shown for each mode.
How It Works
A ratio compares two or more quantities. This calculator covers three common ratio tasks.
Mode 1 — Simplify:
Divide both parts by their GCD (Greatest Common Divisor).
Example: 12:18 → GCD(12,18) = 6 → 12÷6 : 18÷6 = 2:3
Mode 2 — Proportion (solve for missing value):
A proportion states that two ratios are equal: A:B = C:D
To solve for the missing value, use cross-multiplication:
If D is unknown: D = B × C ÷ A
If A is unknown: A = B × C ÷ D
If B is unknown: B = A × D ÷ C
If C is unknown: C = A × D ÷ B
Example: 3:4 = 9:?
Cross-multiply: 3 × ? = 4 × 9
? = 36 ÷ 3 = 12
Mode 3 — Scale:
Multiply both parts of a ratio by a scale factor.
Example: 3:4 scaled by 2.5 → 7.5:10 → simplify → 3:4 (same ratio, but 7.5:10 shows the scaled values)
Frequently Asked Questions
What is a ratio?
A ratio expresses the relative size of two or more values. The ratio 3:4 means for every 3 of one thing there are 4 of another. Ratios can also be expressed as fractions (3/4) or decimals (0.75).
What is a proportion?
A proportion is a statement that two ratios are equal: A/B = C/D. Cross-multiplication (A×D = B×C) is the standard method to solve for an unknown value in a proportion.
Why does simplification use GCD?
The GCD (Greatest Common Divisor) is the largest number that divides evenly into both parts of the ratio. Dividing by the GCD reduces the ratio to its simplest form without changing the proportional relationship.
Can ratios have decimal values?
Yes. The calculator handles decimal inputs. The simplified form may also contain decimals if the inputs are not whole multiples of each other.