Ratio Calculator
Simplify ratios and solve proportions (A : B = C : ?).
Simplify a ratio to its lowest whole-number terms, or solve a proportion to find a missing value when two ratios are equal. Results update instantly.
Ratios compare quantities; proportions say two ratios are equal. This tool handles both — from reducing 8 : 12 to scaling a recipe.
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Formula
Simplify a ratio
a : b ÷ gcd(a, b)
Divide both sides by their greatest common divisor. Example: 8 : 12 → 2 : 3.
Solve a proportion
a : b = c : x → x = (b × c) ÷ a
Cross-multiply to find the missing term. Example: 2 : 3 = 10 : x → x = 15.
How to use the ratio calculator
- 1Choose a mode: simplify a ratio, or solve a proportion.
- 2Enter the known values.
- 3Read the simplified ratio or the missing term; copy the result.
Examples
| Example | Input | Result |
|---|---|---|
| Simplify | 8 : 12 | 2 : 3 |
| Decimal ratio | 1.5 : 3 | 1 : 2 |
| Proportion | 2 : 3 = 10 : ? | 15 |
Simplifying ratios
A ratio is in simplest form when its terms share no common factor other than 1. To simplify, divide both numbers by their greatest common divisor (GCD). For 8 : 12, the GCD is 4, so the ratio reduces to 2 : 3. Decimal ratios are scaled to whole numbers first, so 1.5 : 3 also reduces to 1 : 2.
Solving proportions
A proportion states that two ratios are equal, like a : b = c : x. To find the unknown, cross-multiply: x = (b × c) ÷ a. Proportions are everywhere — scaling recipes, converting units, working out map distances, and resizing images while keeping their aspect ratio.
Frequently asked questions
How do I simplify a ratio?
Divide both terms by their greatest common divisor. 8 : 12 has a GCD of 4, so it simplifies to 2 : 3.
How do I solve a proportion?
For a : b = c : x, cross-multiply to get x = (b × c) ÷ a. So 2 : 3 = 10 : x gives x = 15.
Can it handle decimal ratios?
Yes. Decimals are scaled to whole numbers before simplifying, so 1.5 : 3 becomes 1 : 2.
Is my data private?
Yes. Everything is calculated in your browser.
Embed this calculator
Add the Ratio Calculator to your own website — free. Copy and paste this snippet:
<iframe src="https://numvella.com/embed/ratio-calculator" width="100%" height="460" style="border:1px solid #e2e8f0;border-radius:12px" title="Ratio Calculator — Numvella" loading="lazy"></iframe>