Ratio Calculator
A ratio compares two quantities, and a proportion says two ratios are equal. If a recipe uses 2 cups of flour for every 3 cups of milk, how much milk goes with 10 cups of flour? This tool solves A : B = C : x by cross-multiplication and also simplifies the A : B ratio.
How to use the ratio calculator
- Enter A and B, the known pair.
- Enter C, the new amount that matches A.
- Read x, the amount that matches B, along with the simplified ratio and decimal form.
Formula
If A : B = C : x, then A × x = B × C, so x = B × C ÷ A. To simplify a ratio of whole numbers, divide both by their GCF.
Worked examples
Recipe scaling
2 : 3 = 10 : x gives x = 3 × 10 ÷ 2 = 15 cups of milk.
Map scale
If 1 cm on a map is 5 km, then 1 : 5 = 7.5 : x gives x = 37.5 km.
Ratios and proportions in real life
Ratios turn up wherever things are scaled: recipes, maps, mixing paint, currency, gear systems and drug doses. The key idea is that scaling multiplies both parts by the same factor. If a smoothie uses 2 parts fruit to 3 parts yoghurt, then 10 parts of fruit needs 15 parts of yoghurt, because both parts were multiplied by 5.
Types of ratio
| Type | Example | Meaning |
|---|---|---|
| Part to part | 2 : 3 | Two cups flour for three cups milk |
| Part to whole | 2 : 5 | Two out of every five items in total |
| Rate | 60 km : 1 h | A ratio of different units |
Solving by unit rate
Another way to solve proportions is to find the unit rate. If 3 kg of apples cost $9, then 1 kg costs $3, and 7 kg costs $21. The cross-multiplication used by this calculator gives the same answer and is faster for awkward numbers.
Direct and inverse proportion
In a direct proportion, when one quantity doubles the other doubles too (price and weight). In an inverse proportion, when one doubles the other halves (speed and travel time for a fixed distance). This tool solves the direct kind.
Practice problems
Try these yourself first, then check your answer. The answers come from the calculator above.
- A recipe uses 3 eggs for 5 cups of flour. How many eggs for 20 cups?
Show answer
5 : 3 = 20 : x, so x =: 12
- A map scale is 2 cm : 30 km. How many km is 7 cm?
Show answer
2 : 30 = 7 : x, so x =: 105
Common mistakes to avoid
- Putting values in the wrong order. Keep matching quantities in the same position: flour with flour.
- Adding instead of scaling. Increasing both sides by the same number changes the ratio; multiplying by the same number keeps it.
Frequently asked questions
What is a ratio?
A comparison of two quantities, written A : B, A/B or “A to B”.
How do you simplify a ratio?
Divide both numbers by their greatest common factor. 4 : 6 becomes 2 : 3.
What is a proportion?
A statement that two ratios are equal, such as 2/3 = 10/15.
How do ratios relate to percentages?
A part-to-whole ratio times 100 is a percentage. 3 out of 4 is 3/4 = 75%.
Reviewed September 26, 2026 by the SolveCalcPro editorial team. Found a mistake? Tell us; see our editorial policy.