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

Original ratio	Simplified
12:18	2:3
10:4	5:2
100:25	4:1

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.

Using ratios in everyday situations

Keeping a shape in proportion

Screens and photos keep their shape when width and height stay in the same ratio. If a 16:9 video is 1,920 pixels wide, its height is 1,920 × 9 ÷ 16 = 1,080 pixels. Solving for the missing value in an equivalent ratio gives you the right size for any width you choose.

Where ratios appear

Area	Example
Cooking	Rice to water at 1:2, scaled for any number of servings.
Maps and models	A 1:50,000 scale means 1 cm on the map equals 50,000 cm on the ground.
Mixtures	Concentrate to water ratios on cleaning or garden products.
Finance	Debt-to-income and price-to-earnings ratios.

Avoiding ratio mistakes

• Keep the order consistent: 3:4 is not the same as 4:3.
• Use the same units on both sides before comparing.
• Simplify by dividing both numbers by the same factor, such as 12:18 to 2:3.

More questions

Can a ratio have more than two parts? Yes. A ratio like 2:3:5 compares three quantities, and you scale or simplify every part in the same way.

How do I share a total in a given ratio? Add the parts, divide the total by that sum to get one part, then multiply by each ratio number. To split 100 in the ratio 2:3, one part is 20, giving 40 and 60.