⚖️ Ratio Calculator
Find the missing value in a proportion A : B = C : D, or reduce any ratio to its simplest form.
Quick answer: To solve 3 : 4 = 12 : D, cross-multiply: D = 4 × 12 ÷ 3 = 16, so 3 : 4 = 12 : 16. Both ratios simplify to 3 : 4 (0.75).
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Ratio Calculator inputs
Result
3 : 4 = 12 : 16
D = 16
- Simplified ratio
- 3 : 4
- Ratio as a decimal
- 0.75
Step by step
- Write the proportion as fractions: A/B = C/D
- Cross-multiply: A × D = B × C
- D = B × C ÷ A = 4 × 12 ÷ 3 = 16
- Check: 3 ÷ 4 = 0.75 and 12 ÷ 16 = 0.75
What a ratio means
A ratio compares two quantities. 3 : 4 means “3 of the first for every 4 of the second.” Two ratios that describe the same relationship are called equivalent, and an equation stating that two ratios are equal is a proportion.
Solving a proportion
Write the ratios as fractions and cross-multiply. The product of the outer terms always equals the product of the inner terms:
A : B = C : D ⇔ A × D = B × C ⇒ D = B × C ÷ A
Example: 3 : 4 = 12 : D. Cross-multiplying gives 3 × D = 4 × 12 = 48, so D = 16. Check: 3 ÷ 4 = 0.75 and 12 ÷ 16 = 0.75.
Simplifying a ratio
Divide both terms by their greatest common divisor (GCD). For decimals, first scale both terms by the same power of ten so they become whole numbers.
| Ratio | GCD | Simplest form |
|---|---|---|
| 18 : 24 | 6 | 3 : 4 |
| 1920 : 1080 | 120 | 16 : 9 |
| 1.5 : 2.25 (→ 150 : 225) | 75 | 2 : 3 |
| 45 : 60 | 15 | 3 : 4 |
Everyday uses
- Cooking: scale ingredient quantities up or down for a different number of servings.
- Screens and photos: keep an aspect ratio such as 16 : 9 when resizing.
- Maps and models: convert between scale distance and real distance.
- Mixing: concrete, paint, fertiliser or fuel mixtures are given as ratios.
Tips
- Keep the order consistent – if A is flour and B is servings on the left, C must be flour and D servings on the right.
- Use the same units for both quantities before comparing them.
Frequently asked questions
How do you solve a proportion?
Write it as two equal fractions, A/B = C/D, and cross-multiply so that A × D = B × C. Then divide to isolate the unknown. For 2 : 5 = x : 20, x = 2 × 20 ÷ 5 = 8.
How do I simplify a ratio?
Divide both terms by their greatest common divisor. 18 : 24 has a GCD of 6, so it simplifies to 3 : 4. If the terms are decimals, multiply both by 10, 100 and so on until they are whole numbers first.
Can I use the ratio calculator to scale a recipe?
Yes. If a recipe needs 3 cups of flour for 4 servings and you want 10 servings, enter 3 : 4 = C : 10 and leave C blank – you need 7.5 cups.
What is the difference between a ratio and a fraction?
A ratio compares two quantities (part to part, like 3 boys to 4 girls), while a fraction usually compares a part to the whole (3 boys out of 7 children, or 3/7).