Ratio Calculator
Simplify ratios, scale them up or down, and solve proportions for a missing value — three ratio tools in one place, with the working shown every time.
Result
How It Works
A ratio compares two quantities: 12:18 says that for every 12 of one thing there are 18 of the other. Ratios can be simplified exactly like fractions, by dividing both sides by their greatest common divisor (GCD). The GCD of 12 and 18 is 6, so 12:18 simplifies to 2:3 — the same relationship, in the smallest whole numbers.
Scaling a ratio multiplies both sides by the same factor, which keeps the relationship identical while changing the size — this is how recipes are doubled and map scales are applied. Solving a proportion finds a missing value: if a:b = c:x, then x = (b × c) / a, because the two ratios must be equal.
Worked examples: Simplify 12:18 → divide both sides by 6 → 2:3. Scale 2:3 by 5 → 10:15. Solve 2:3 = 4:x → x = (3 × 4) / 2 = 6, and indeed 4:6 simplifies back to 2:3.
How to Use This Calculator
Choose power or root from the dropdown, enter your numbers, and the result appears live with the working underneath.
- Simplify a ratio — enter both numbers (for example 12 and 18) to get the ratio in lowest terms (2:3).
- Scale a ratio — enter a ratio and a factor (for example 2:3 scaled by 5 gives 10:15), handy for resizing recipes or batches.
- Find a missing value — enter a, b and c for a:b = c:x (for example 2:3 = 4:x gives x = 6), useful for unit prices and scale drawings.
Decimals are accepted in every field. The Reset button restores the examples so you can start over.
Tips and Practical Advice
Ratios are everywhere once you look for them — recipes, mixing paint, currency exchange, screen sizes, and gear ratios all run on the same idea. A few habits keep them straight.
- Keep the units the same. A ratio of 2 metres to 30 centimetres is not 2:30 — convert first (200 cm to 30 cm), then simplify to 20:3.
- Order matters. 2:3 is not the same as 3:2 — the first number always belongs to the first quantity, so double-check which value you entered where.
- Scale recipes by ratio, not by feel. Doubling a 2:3 mix means multiplying both parts by 2 (4:6); adding 2 to each part instead would change the flavour.
- Use proportions for unit prices. If 3 kg costs $12, the proportion 3:12 = 5:x gives x = $20 for 5 kg — quicker and more reliable than mental division.
Frequently Asked Questions
How do you simplify a ratio?
Divide both numbers by their greatest common divisor. For 12:18, the GCD is 6, so dividing both sides by 6 gives 2:3.
How do you scale a ratio?
Multiply both sides by the same factor. Scaling 2:3 by 5 gives 10:15 — the relationship is unchanged, only the size changes.
How do you find a missing value in a proportion?
If a:b = c:x, then x = (b × c) / a. For 2:3 = 4:x, x = (3 × 4) / 2 = 6.
What is the difference between a ratio and a fraction?
A ratio compares two quantities (2:3), while a fraction is one quantity as a part of a whole (2/5). In a 2:3 ratio, the first part is 2/5 of the total.
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