Ratio Calculator

How this is calculated

To simplify, both numbers are divided by their greatest common factor. To solve for a missing value in an equivalent ratio, the two ratios are cross-multiplied and solved algebraically.

Working with ratios

A ratio compares two quantities and stays the same when both numbers are multiplied or divided by the same amount — that's what makes simplifying and scaling possible.

Formulas

Example: simplifying 12:18 (GCF 6) gives 2:3. Solving 2:5 = 10:x gives x = (5 × 10) ÷ 2 = 25.

Quick reference table

Common pitfalls

• Only dividing one side — both numbers in the ratio must be divided (or multiplied) by the same value to keep it equivalent.
• Mixing up the order — a ratio of 3:4 is not the same as 4:3, so keep track of which quantity comes first.
• Treating a 3-part ratio as two separate 2-part ratios incorrectly — when scaling a ratio like 2:3:5, the same scale factor must apply to all three parts.

Tips

• Any ratio can be converted to a "for every 1" form by dividing both sides by the first number — useful for unit-rate comparisons.
• Cross-multiplication works for any two equivalent ratios, not just when solving for x.

Frequently asked questions

How do you simplify a ratio? Divide both numbers in the ratio by their greatest common factor (GCF). For 12:18, the GCF is 6, so the simplified ratio is 2:3.

How do you solve a ratio with a missing value? Cross-multiply the two ratios and solve for the unknown. For 2:5 = 10:x, cross-multiplying gives 2x = 50, so x = 25.

What does a ratio like 3:4 mean? A ratio of 3:4 means that for every 3 units of the first quantity, there are 4 units of the second — the actual amounts can be any multiple of 3 and 4, such as 6:8 or 30:40.

What's the difference between a ratio and a fraction? A ratio compares two separate quantities (like boys to girls), while a fraction represents a part of a whole — though a ratio can be written as a fraction and manipulated the same way.

How do I scale a recipe using ratios? Keep the ratio between ingredients constant. If a recipe uses a 2:1 ratio of flour to sugar and you want 6 cups of flour, solve 2:1 = 6:x to get 3 cups of sugar.

Worked examples

Example 1 — Simplifying: 12:18 → GCF is 6 → simplified to 2:3.

Example 2 — Solving for a missing value: 2:5 = 10:x → x = 25.

Example 3 — Recipe scaling: a 3:2 ratio of water to rice, scaled to 9 cups of water, needs x in 3:2 = 9:x → x = 6 cups of rice.