How to Simplify a Ratio (and Find Equivalents)
Published 2026-11-03
Ratio calculator is a top math query because colons show up in recipes, maps and worksheets: simplify 54:24, or solve 3:4 = x:20. A ratio compares two like quantities. It is not “what percent is X of Y” — that is the percentage calculator.
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Run these formulas with your own numbers. Math stays in your browser.
Open Ratio Calculator →Our ratio calculator simplifies A:B with the GCF and can find an equivalent when one new term is known. 0:0 is undefined. Three-part ratios are not supported.
Open the ratio calculator
Enter A and B. Simplify 54:24 should read 9:4. Switch to equivalent, keep 3:4, set new B = 20, and the missing A is 15.
Simplify by the GCF
GCF(54, 24) = 6, so 54:24 = 9:4. If the GCF is 1, you are done. The GCF calculator reports only the divisor; this page applies it.
A:B = (A ÷ g):(B ÷ g), g = GCF(A, B)
A:B = A′:B′ ⇒ A′ = A × B′ ÷ B
Equivalent ratios
3:4, 6:8, 15:20 are the same comparison. Scale factor 20/4 = 5 sends 3 to 15.
| Input | Result |
|---|---|
| 54:24 | 9:4 |
| 3:4 = x:20 | 15:20 |
| 3:4 = 12:y | 12:16 |
| 7:3 | 7:3 |
Ratio versus percent
9 is 225% of 4, but 9 is about 69% of the combined 9+4. Those sentences are different. Use the percentage calculator for “of / is / change,” and this ratio calculator when the problem uses a colon or “to.” Convert units first if the parts are cups versus pints.
- Make the units the same.
- Simplify by the GCF, or scale to the known term.
- If the sentence is a percent, switch tools.
Recipes, maps and similar figures
A dressing that is 2 parts oil to 1 part vinegar is already 2:1. Doubling a recipe is the equivalent-ratio mode: 2:1 = 6:3 when you need six parts oil. Map scales such as 1:50,000 are ratios of like lengths; convert both to meters before you simplify if one side was written in centimeters. Similar triangles use the same proportion — 3:4 = x:20 is the missing-side problem the ratio calculator solves — but three sides of a specific triangle (SSS) still belong on the triangle calculator. Keep the units matched. 3 cups to 4 pints is not 3:4 until you convert. The percentage calculator is the wrong tool for a colon; it is the right tool for “what percent is 9 of 13.”
Use the free tool
Run these formulas with your own numbers. Math stays in your browser.
Open Ratio Calculator →Frequently Asked Questions
Is a ratio a fraction?
A:B matches A/B when B ≠ 0, but the language is part-to-part.
Can the missing term be a decimal?
Yes, if the known value is not a multiple of the reduced part.
What about 0:5?
It simplifies to 0:1. 0:0 is rejected.
Three-part recipes?
Not on this tool. GCF all three, then divide each part.
Does this convert units?
No. Use a converter, then simplify the two numbers.
Related calculators
Ratio Calculator
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GCF Calculator
Greatest common factor (GCD/HCF) of two or more whole numbers.