Ratio Calculator
Simplify a ratio to lowest terms, or solve a proportion (A:B = C:D) for the one value you don't know.
Simplify a ratio
Solve a proportion (A:B = C:D)
How ratios work
Proportion A:B = C:D → A × D = B × C (cross-multiply)
Simplify 18:24 → divide by GCD 6 → 3:4.
Solve 3:4 = 9:? → 3 × ? = 4 × 9 → ? = 36 ÷ 3 = 12.
Two business partners agree to split a $10,000 bonus in a 3:2 ratio based on their ownership stakes. Add the terms: 3 + 2 = 5 total shares.
One share = $10,000 ÷ 5 = $2,000. Partner A (3 shares) receives 3 × $2,000 = $6,000; Partner B (2 shares) receives 2 × $2,000 = $4,000. Check: $6,000 + $4,000 = $10,000. ✓
Ratios in the real world
Ratios scale things while keeping proportions fixed — recipes, map distances, mixing paint or concrete, aspect ratios, and financial ratios all rely on them. The core trick is cross-multiplication: any proportion with one unknown solves in a single step. To turn a ratio into parts of a whole (like splitting a bill or a batch), add the terms — a 2:3 ratio is 2/5 and 3/5 of the total. Related: the fraction calculator for the same relationships as fractions, and the concrete and paint calculators for mix ratios in practice.
Common aspect ratios and mix ratios
| Use case | Common ratio |
|---|---|
| Widescreen video (16:9) | 16:9 |
| Standard photo print | 3:2 |
| Concrete mix (cement:sand:gravel) | 1:2:3 |
| Simple syrup (sugar:water) | 1:1 |
| Golden ratio | 1.618:1 |
Common ratio mistakes
- Dividing by the number of terms instead of their sum. Splitting $10,000 in a 3:2 ratio uses 5 total shares (3 + 2), not 2 shares — dividing by the wrong number understates or overstates each party's amount.
- Simplifying a ratio when the original units matter. A 4:6 mix ratio simplifies to 2:3 mathematically, but if a recipe specifies exact cup measurements, scaling down can leave awkward fractional amounts to measure.
- Cross-multiplying with the terms in the wrong position. For A:B = C:D, the correct relationship is A × D = B × C — mixing up which terms multiply together gives a wrong answer.
Frequently asked questions
How do I simplify a ratio?
Divide both terms by their GCD. 18:24 → 3:4.
How do I solve a proportion?
Cross-multiply. 3:4 = 9:x → x = 12.
How do I scale a recipe?
Set up a proportion. 2:3 = x:9 → x = 6.
What's the difference between a ratio and a fraction?
A ratio compares two separate quantities (2 cups flour to 3 eggs), while a fraction represents a part of a single whole (2/5 of a pizza). Ratios can be converted to fractions of a total by adding the terms together as the denominator.
How do I split a bonus using a ratio?
Add the terms for total shares, divide the amount by that number, then multiply by each party's term. $10,000 split 3:2 = 5 shares of $2,000: $6,000 and $4,000.
What is the golden ratio?
Approximately 1.618:1 — a proportion where the whole to the larger part equals the larger part to the smaller part, often cited in art and design.
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Last reviewed: September 2026.