Ratio Calculator
Simplify a two-part ratio A:B to lowest terms, or find an equivalent ratio when one new term is known. A ratio compares two quantities with the same unit. 54:24 and 9:4 describe the same relationship because both parts were divided by 6.
Ratio Calculator tool
About the Ratio Calculator
Simplify mode prints A:B in lowest terms, the GCF, A ÷ B, and each part as a share of |A| + |B|. Equivalent mode scales the reduced ratio so one term matches the value you type — 3:4 = x:20 gives x = 15.
This is part-to-part, not “what percent is X of Y.” That question is the percentage calculator’s second mode. A 0:0 ratio is undefined and rejected.
How the Ratio Calculator works
Divide both terms by GCF(A, B). For an equivalent ratio, multiply or divide both terms by the same nonzero scale. If B′ is known, A′ = A × (B′ ÷ B) using the reduced A:B.
A:B in lowest terms = (A ÷ g):(B ÷ g), g = GCF(A, B)
A:B = A′:B′ ⇒ A′ = A × B′ ÷ B (B ≠ 0)
Example
54:24 simplifies to 9:4. 3:4 = x:20 has x = 15.
How to Use the Ratio Calculator
- Enter whole numbers A and B.
- Choose simplify, or equivalent if you already know one new term.
- For equivalent, pick whether the new left or new right term is known.
- Read the reduced A:B and, in equivalent mode, the missing term.
- Use the percentage calculator if the sentence is “X is what percent of Y.”
Ratio Calculator Examples
Simplify
54:24 ÷ 6 = 9:4. 9 ÷ 4 = 2.25, so A is 2.25 times B.
Equivalent with known B
3:4 = x:20 → x = 15. Scale factor 20/4 = 5.
Equivalent with known A
3:4 = 12:y → y = 16.
Shares
In 9:4 the parts are 9/13 ≈ 69.23% and 4/13 ≈ 30.77% of the combined size.
How to Simplify a Ratio
Find the GCF of the two parts and divide both. 54 and 24 share 6, so 54:24 = 9:4. If the GCF is 1, the ratio is already in lowest terms. That is the same reduction used for fractions; the GCF calculator will show 6 if you only want the divisor. Recipes that say “2 parts oil to 1 part vinegar” are already simplified 2:1.
Equivalent ratios
Multiply or divide both terms by the same nonzero number. 3:4, 6:8, 9:12 and 15:20 are equivalent. If a worksheet gives 3:4 = x:20, the scale is 20/4 = 5 and x = 15. That is the equivalent mode on this page. Map scales, similar triangles and mixing problems all use that proportion. For similar-triangle side lengths you may also want the triangle calculator, which solves SSS/SAS rather than a two-term ratio.
Ratio versus percentage
“What percent is 9 of 4?” is 225% — percentage mode “X is what % of Y.” “What share of the total is 9 in 9:4?” is 9/13 ≈ 69%. Those are different questions. Tip, discount and sales tax have their own money tools. Use this ratio calculator when the sentence uses a colon or the word “to” between two like quantities.
| Input | Mode | Result |
|---|---|---|
| 54:24 | Simplify | 9:4 |
| 3:4 = x:20 | Equivalent, B known | 15:20 |
| 3:4 = 12:y | Equivalent, A known | 12:16 |
| 7:3 | Simplify (already lowest) | 7:3 |
| 0:5 | Simplify | 0:1 |
Units must match
A ratio of 3 cups to 4 cups is 3:4. A ratio of 3 cups to 4 pints is not 3:4 until you convert. This calculator does not convert units. Use the length, weight or volume tools first, then simplify the two numbers that share a unit.
Frequently Asked Questions
Is a ratio the same as a fraction?
A:B matches the fraction A/B when B ≠ 0, but ratio language is part-to-part. The fraction calculator operates on numerators and denominators, including mixed numbers.
Can the result have decimals?
Lowest terms of whole A and B stay whole. An equivalent missing term can be a decimal if the known value is not a multiple of the reduced part.
What about 0:5?
That simplifies to 0:1. 0:0 is rejected.
Does this do 3-part ratios?
No. Only two terms. Reduce A:B:C by GCF of all three by hand, or GCF them in pairs with the GCF calculator.
How is the percent share computed?
Each part divided by |A| + |B|, times 100. That is not “A is what percent of B.”
Can I enter negatives?
Yes, as whole numbers. The GCF uses absolute values; signs stay on the reduced terms.
Guides that use this calculator
- How to Simplify a Ratio (and Find Equivalents)
A ratio is part-to-part. Divide by the GCF to simplify, or scale both terms for an equivalent. The free ratio calculator does both.
- How to Find GCF (Greatest Common Factor)
GCF is the largest integer that divides every input. Euclid’s algorithm, a 48-18-30 example and the free GCF calculator.