How do I simplify a ratio?

Divide both sides by their greatest common divisor. 12:18 divided by 6 becomes 2:3.

How do I share an amount in a ratio?

Add the parts, divide the total by that number, then multiply by each side. £450 in the ratio 4:5 gives £200 and £250.

Does 1:3 mean one third?

No. It means one part to three parts, four in total, so the first quantity is one quarter of the whole.

How do I compare two ratios?

Convert both to the same second term, or to decimals by dividing. 3:4 is 0.75 and 5:7 is about 0.71, so 3:4 is the larger.

Ratio Calculator - Simplify, Scale and Share

Ratio Calculator

Ratios compare quantities. This calculator simplifies them, scales them, and divides an amount between parts.

Formula

To split an amount in a:b, give each part amount × its share ÷ (a + b)

Simplify by dividing every term by their greatest common divisor
Equivalent ratios: a:b = c:d when ad = bc

£240 split 3:5: total parts 8, so £90 and £150

Simplifying and Scaling

Divide both sides by their greatest common divisor: 12:18 becomes 2:3 after dividing by 6.

To scale, multiply both sides by the same number. A 2:3 mix scaled by four becomes 8:12.

Whatever you do to one side, do to the other — that is the whole rule.

Sharing an Amount in a Ratio

The reliable method is to count the parts first:

Add the parts of the ratio.
Divide the total amount by that number to get the value of one part.
Multiply by each side of the ratio.

Sharing £450 in the ratio 4:5 gives 9 parts. 450 ÷ 9 = £50 per part, so the shares are £200 and £250.

Ratios Versus Fractions

A ratio of 1:3 does not mean one third. It means one part to three parts, so four parts in total — the first quantity is one quarter of the whole.

This catches people out constantly in mixing instructions. Squash diluted 1:4 means one part squash to four parts water, giving one fifth squash overall.

Quick Reference

Splitting by ratio, with each share as a percentage.
Ratio	Parts	Shares of £1,000	As percentages
1:1	2	£500, £500	50%, 50%
1:3	4	£250, £750	25%, 75%
2:3	5	£400, £600	40%, 60%
3:5	8	£375, £625	37.5%, 62.5%
2:3:5	10	£200, £300, £500	20%, 30%, 50%

Frequently Asked Questions

How do I simplify a ratio?: Divide both sides by their greatest common divisor. 12:18 divided by 6 becomes 2:3.
How do I share an amount in a ratio?: Add the parts, divide the total by that number, then multiply by each side. £450 in the ratio 4:5 gives £200 and £250.
Does 1:3 mean one third?: No. It means one part to three parts, four in total, so the first quantity is one quarter of the whole.
How do I compare two ratios?: Convert both to the same second term, or to decimals by dividing. 3:4 is 0.75 and 5:7 is about 0.71, so 3:4 is the larger.