Ratio Calculator
Simplify ratios, solve proportions, and scale recipes or plans to any size — ratio, decimal and percent together.
Calculate
Solve a:b = c:? — enter three numbers.
How to Use the Ratio Calculator
Pick the mode that matches your question. Simplify reduces any ratio to lowest terms — type it with colons, like 12:18, and slashes or the word "to" work too. Missing value solves proportions: if 2:3 = 10:?, enter 2, 3, 10 and get 15, with the cross-multiplication steps shown. Scale grows or shrinks a ratio to a target total: enter 1:4 and 200 to split 200 into the 1:4 proportion (40:160). Recipe presets halve, double, or triple in one tap.
Every answer shows three forms at once — the simplified ratio, its decimal, and its percentage — so follow-up questions answer themselves.
Simplifying Ratios
A ratio is in lowest terms when its parts share no common divisor bigger than 1. The method mirrors fraction simplification:
For 12:18, the GCD of 12 and 18 is 6. Divide: 12 ÷ 6 = 2, 18 ÷ 6 = 3 → 2:3. Three-part ratios work the same way: 2:4:6 has GCD 2, so it simplifies to 1:2:3. A zero part is fine (0:5 stays 0:5 — it means "none of the first, five of the second"), but all zeros is meaningless and the calculator will say so.
Finding a Missing Value in a Proportion
A proportion states that two ratios are equal: a:b = c:d. Cross-multiplication turns it into solvable arithmetic:
Example: a map uses 2 cm for every 3 km, and two cities are 10 cm apart on the map. Real distance: d = (3 × 10) ÷ 2 = 15 km. The calculator shows both steps so you can reuse the method on paper. This single pattern powers unit conversions, map scales, dosage math, and currency estimates.
Worked Example: Scaling a Recipe
Double a 1:4 vinaigrette to serve a crowd
Your vinaigrette is 1 part vinegar to 4 parts oil, and you need 250 ml total.
Step 1: Total parts = 1 + 4 = 5.
Step 2: One part = 250 ÷ 5 = 50 ml.
Step 3: Vinegar = 1 × 50 = 50 ml; oil = 4 × 50 = 200 ml.
Check: 50 + 200 = 250 ✓, and 50:200 simplifies to 1:4 ✓.
The relationship never changes when you scale — doubling gives 2:8, which is still 1:4 in lowest terms. That's the whole point of ratios: they describe the relationship, not the amounts, so they scale cleanly to any batch size.
Ratios in Real Life
- Cooking: bread dough is often a 5:3 flour-to-water ratio by weight — scale it to any loaf size.
- Finance: a 1:3 risk-reward ratio means risking $1 to make $3; traders live by these.
- Mixing: concrete, paint, and fertilizer all specify ratios — getting them wrong wastes material or weakens the result.
- Photography: aspect ratios (3:2, 16:9) describe frame shape; scaling a 16:9 video to any screen keeps the picture undistorted.
- Fitness: work-to-rest ratios (like 2:1 in interval training) structure workouts independent of your speed.
Whenever you see "for every X there are Y," you're looking at a ratio — and now you can simplify it, solve it, or scale it in seconds.
My saved numbers reuse them in any calculator
Save a number once — like your rent or hourly rate — then just type its name instead of the number, in any calculator here. You can also type formulas like 5000 * 1.1 right into any box.
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Frequently Asked Questions
How do you simplify a ratio?
Divide every part by their greatest common divisor. For 12:18, the GCD is 6: 12÷6=2, 18÷6=3, so 12:18 simplifies to 2:3.
What is 3:4 as a percentage?
3:4 means 3 out of 4 parts: 3 ÷ 4 = 0.75 = 75%. As a ratio it compares two quantities; as a percentage it expresses the first as a share of the total.
How do I find a missing value in a ratio?
Use cross-multiplication: if a:b = c:d, then d = (b × c) ÷ a. For 2:3 = 10:?, d = (3 × 10) ÷ 2 = 15. The Missing value mode shows these steps.
What is the difference between a ratio and a fraction?
A ratio like 3:4 compares two quantities and both orders matter; the fraction 3/4 is the value of the first part relative to the second. Every ratio a:b can be written as the fraction a/b, but ratios can also have three or more parts (1:2:3), which fractions cannot.
How do you scale a ratio up or down?
Multiply or divide every part by the same factor. To double a 1:4 recipe ratio, multiply both parts: 2:8 (which simplifies back to 1:4 — the relationship is unchanged). To scale 1:4 to a total of 200, each part is 200 ÷ 5 = 40, giving 40:160.