Quick answer: A ratio compares two quantities, written a to b, and simplifies by dividing both by their greatest common divisor, like 12:18 becoming 2:3. In a proportion, cross-multiplication solves the unknown: if a/b equals c/d, then a times d equals b times c. Ratios scale recipes, maps, mixtures and financial comparisons.
Last reviewed: September 2026
Key facts
- Solves any proportion A : B = C : X — enter three values, get the fourth.
- Uses cross-multiplication: X = B × C ÷ A.
- Powers recipes, maps, scale models, mixing ratios and similar-triangle problems.
- Ratios can be simplified like fractions: 10:15 is the same as 2:3.
A ratio compares two quantities — and when two ratios are equal, you have a proportion you can solve. This free ratio calculator finds the missing value in A : B = C : X: enter any three numbers and it computes the fourth by cross-multiplication.
Use it for recipes (scaling servings), maps and scale models, mixing paint or concrete, and any “if this much gives that much, how much gives…” question.
How to use
- Enter A and B — the known ratio.
- Enter C — the known side of the new ratio.
- The missing value X appears instantly.
- Read the full proportion underneath to double-check.
Solving a proportion
| Term | Meaning |
|---|---|
| A : B | The known ratio (e.g. 2 cups flour : 3 cups sugar). |
| C | The new known quantity on the same side as A. |
| X | The unknown quantity — what you are solving for. |
Cross-multiplication: A × X = B × C, so X = B × C ÷ A. A cannot be zero.
Worked examples
Scaling a recipe
2 : 3 = 10 : X — a recipe with ratio 2:3 flour-to-sugar, scaled to 10 cups of flour.
X = 3 × 10 ÷ 2 = 15 cups of sugar. The proportion 2:3 = 10:15 checks out.
Mixing paint
5 : 8 = X : 40 — paint mixed 5:8 (colour:white), making 40 litres total of white.
X = 5 × 40 ÷ 8 = 25 litres of colour. (Equivalently, total parts = 13, and 40 ÷ 8 = 5 litres per part.)
Ratio in everyday life
| Situation | Ratio idea | Example |
|---|---|---|
| Cooking | Scale ingredients proportionally | 2:3 flour:sugar → 10:15 |
| Maps | 1 cm represents real distance | 1:50,000 — 1 cm = 0.5 km |
| Scale models | Model : real size | 1:72 — 1 cm model = 72 cm real |
| Finance | Debt-to-income, price ratios | Keep housing under 28% of income |
| Mixing | Parts of each ingredient | Concrete 1:2:4 cement:sand:gravel |
Frequently asked questions
How do you solve A:B = C:X?
Cross-multiply: A × X = B × C, so X = B × C ÷ A. The calculator does this instantly.
What is the difference between a ratio and a fraction?
A ratio compares two quantities (2:3); a fraction is one number divided by another (2/3). Every ratio a:b can be written as the fraction a/b.
Can ratios be simplified?
Yes, by dividing both sides by their greatest common divisor: 10:15 simplifies to 2:3, exactly like reducing a fraction.
What if A is zero?
Then the proportion is undefined — you cannot divide by zero — and the calculator asks you to check the input.
How do map scales work?
A 1:50,000 map means 1 unit on the map = 50,000 units in reality, so 1 cm represents 0.5 km. Measure, then multiply.
Sources
- Khan Academy — Ratios and proportions
- Maths is Fun — Ratios with worked examples
Key takeaways
- Enter any three of A, B, C to find X via cross-multiplication.
- Ratios scale recipes, maps, models and mixtures — anywhere “in proportion” applies.
- Like fractions, ratios simplify by dividing both sides by their GCD.
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