This ratio calculator simplifies ratios to their lowest terms and scales them to any total. Enter two terms to simplify — or add a target total to split a quantity in that ratio (recipes, mixtures, screen sizes, map scales).
What Is a Ratio?
A ratio compares two quantities — 4:15 means “for every 4 of the first, there are 15 of the second.” Ratios run recipes (2:1 flour to sugar), construction (1:3 cement mixes), screens (16:9), maps (1:50,000) and finances (debt-to-income). Simplifying a ratio means dividing both terms by their greatest common factor — the same engine as our GCF Calculator. This calculator is part of our Math Calculators collection.
Worked Examples (Verified)
- Simplify 48 : 180 — GCF is 12, so divide both by 12: 4 : 15. As a share: 4/19 ≈ 21.1% of the combined total.
- Split $228 in the ratio 48:180 — the parts are 48/228 and 180/228 of the total: 48 : 180 (the example is already scaled to that total — try splitting 4:15 into a total of 190 to get 40:150).
- Scale a recipe: a 2:3 ratio for 5 servings must become 20 servings — multiply both terms by 4: 8:12.
Ratios, Fractions and Proportions
- A ratio A:B is the fraction A/(A+B) of the whole, but A/B against the other term — keep the two straight: “1:4 dilution” means 1 part concentrate to 4 parts water (5 parts total, 20% strength), a distinction our chemistry readers meet in the Dilution Calculator.
- Proportions set two ratios equal (a/b = c/d) and solve by cross-multiplication — the method behind map scales and similar triangles.
- Percentages are ratios standardized to 100: 4:15 ≈ 21.1 : 78.9 per hundred of total.
- Fraction skills in general live in our Fraction Calculator.
Related Tools
- GCF Calculator — the simplification engine
- Fraction Calculator
- Math Calculators — the full collection
Frequently Asked Questions
How do I simplify a ratio?
Divide both terms by their greatest common factor. 48:180 ÷ 12 = 4:15.
How do I split an amount in a given ratio?
Add the ratio terms (4 + 15 = 19), divide the amount by that sum to get one “part,” then multiply each term by it. Enter your total in the calculator and it does this for you.
What is the difference between a ratio and a fraction?
A fraction compares a part to the whole; a ratio compares part to part. 4:15 as a fraction of the whole is 4/19.
Can ratios have more than two terms?
Yes — concrete mixes (1:2:4 cement:sand:aggregate) and alloy recipes use three or more. Simplify them by the GCF of all terms together.
How do I scale a ratio up?
Multiply both terms by the same factor — the relationship is unchanged, only the quantities grow.
Is this ratio calculator free?
Yes — free, instant, no sign-up.