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Ratio guide

The Ratio Calculator has three modes: simplify a ratio, solve a proportion (A:B = C:D), and scale a ratio by a factor. Each mode is a single-step operation.

Worked examples

Simplify the ratio 12:18

Select the "Simplify Ratio" tab.
Enter 12 as Term A and 18 as Term B.
Click Calculate.

Result: 12:18 = 2:3

The GCD of 12 and 18 is 6, so both terms are divided by 6.

Solve a proportion: 2:3 = 4:?

Select the "Ratio Proportion" tab.
Enter 2 as A, 3 as B, 4 as C, and leave D blank.
Click Calculate.

Result: D = 6

Cross-multiplication: 2 × D = 3 × 4, so D = 12 ÷ 2 = 6.

Scale the ratio 3:4 by a factor of 2

Select the "Scale Ratio" tab.
Enter 3 as A and 4 as B.
Choose Enlarge as the action.
Enter 2 as the scale factor.
Click Calculate.

Result: 3:4 scaled by 2 = 6:8

Both terms are multiplied by the same factor, so the proportion stays the same.

Tips

•A ratio is just a fraction written with a colon. 2:3 is the same as 2/3.
•The proportion solver requires exactly three of the four values.
•Scale factors can be fractions — 1/2 shrinks the ratio by half.

Frequently asked questions

What is a ratio?

A ratio compares two quantities and shows how many times one contains the other. 2:3 means for every 2 of the first item, there are 3 of the second.

How do I simplify a ratio?

Divide both terms by their greatest common divisor. For 12:18, the GCD is 6, so the ratio simplifies to 2:3.

Can ratios have decimals?

Yes, but they are usually clearer as whole numbers. Multiply both terms by a power of 10 to remove decimals, then simplify.

What is a proportion?

An equation stating that two ratios are equal. For example, 2:3 = 4:6 is a proportion.

How do I solve a proportion?

Cross-multiply: A × D = B × C. If you know three of the four values, you can find the fourth.

What does "scale a ratio" mean?

Multiply or divide both terms by the same factor. The relationship stays the same, but the numbers change. For a recipe ratio of 1:2, scaling by 3 gives 3:6 for a larger batch.

Can a ratio have a zero?

The first term can be zero (e.g., 0:5), but the second term cannot be zero because you cannot divide by zero.

What is the difference between a ratio and a fraction?

Mathematically they are very similar. A ratio compares two quantities (2:3), while a fraction represents a part of a whole (2/3).

How do I convert a ratio to a percentage?

Convert to a fraction first (2:3 → 2/3), then multiply by 100 (2/3 × 100 = 66.67%).

Why does the proportion solver reject my input?

You must provide exactly three of the four values. If you provide all four or fewer than three, the calculator shows an error.

What happens if I divide by a zero scale factor?

The calculator rejects it. A scale factor of zero would collapse the ratio to 0:0, which is meaningless.

Can I use negative ratios?

Yes. The calculator handles negative terms without issue.

How is a ratio used in real life?

Ratios describe recipes, map scales, aspect ratios (16:9), gear ratios, and financial ratios like debt-to-income.

What is the aspect ratio 16:9?

It means for every 16 units of width, the screen has 9 units of height. It’s the standard widescreen ratio for TVs and monitors.

How do I add ratios?

You cannot add ratios directly — convert them to fractions first, find a common denominator, and add the fractions. Then convert back.

What is the golden ratio?

Approximately 1.618:1. It appears in art, architecture, and biology, and is defined as (1 + √5) / 2.

Can I copy or save my ratio calculation?

Yes. Every result has a Copy button. Clicking "Save to History" stores it in your browser.

Does the ratio calculator work on mobile?

Yes. The layout is fully responsive and works on any screen size.

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