How do I simplify a ratio by hand?

Find the greatest common divisor (GCD) of both numbers, then divide each number by it. For example, to simplify 18:24 — the GCD is 6, so 18÷6=3 and 24÷6=4, giving you 3:4.

What is the formula for solving a proportion?

Use cross-multiplication: if a:b = c:x, then x = (b × c) ÷ a. For example, if 2:5 = 6:x, then x = (5 × 6) ÷ 2 = 15.

How do I find the GCD of two numbers?

List the factors of each number and pick the largest one they share. Alternatively, use the Euclidean algorithm: divide the larger number by the smaller, take the remainder, and repeat until the remainder is zero — the last non-zero remainder is the GCD.

Can I use decimal numbers in a ratio?

Yes, the calculator accepts decimals. If you prefer whole numbers, multiply both sides by the same value to clear the decimals first — for example, 1.5:2 becomes 3:4 when you multiply both by 2.

Is my data saved or uploaded anywhere?

No. All calculations happen directly in your browser. Nothing you type is sent to any server or stored anywhere.

How do I split an amount in a given ratio?

Add all parts of the ratio together to get the total number of parts. Divide your amount by that total to find one part's value, then multiply by each share. For example, split £300 in ratio 2:3 — total parts = 5, one part = £60, shares are £120 and £180.

What is the difference between a ratio and a proportion?

A ratio compares two quantities, like 3:4. A proportion is a statement that two ratios are equal, like 3:4 = 9:12. The ratio calculator handles both — simplifying a ratio and solving for a missing value in a proportion.

Is this ratio calculator free to use?

Yes, completely free. There is no sign-up, no account, and no usage limit.

Ratio Calculator - Simplify & Solve Ratios Free

Work Out Any Ratio in Seconds

This ratio calculator does two things: it simplifies a ratio to its lowest terms (like turning 18:24 into 3:4), and it solves a missing value in a proportion (like finding x in 3:4 = 9:x). Type in your numbers and the result appears immediately.

How to Use the Ratio Calculator

Simplify a ratio — Enter both values (for example, 18 and 24) and click Simplify. The calculator divides both numbers by their greatest common divisor (GCD) and shows the simplest form.
Solve a proportion — Enter three of the four values in a:b = c:x format and click Solve. The missing value is calculated instantly.
Copy or note the result. Everything runs in your browser — nothing is sent to any server.

Worked Example: Simplify 18:24

Suppose a recipe calls for 18 ml of oil and 24 ml of vinegar. You want to know the simplest ratio so you can scale it up or down easily.

Find the GCD of 18 and 24. The factors of 18 are 1, 2, 3, 6, 9, 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The greatest one they share is 6.
Divide both numbers by 6: 18 ÷ 6 = 3, 24 ÷ 6 = 4.
Result: 3:4. The simplified ratio tells you to use 3 parts oil for every 4 parts vinegar.

You can scale this up freely — 6:8, 9:12, 30:40 — because the underlying proportion never changes.

Worked Example: Solve a Proportion (Find the Missing Value)

You know a car travels 3 km for every 4 minutes. How far does it travel in 20 minutes?

Set up the proportion: 3:4 = x:20
Cross-multiply: 3 × 20 = 4 × x → 60 = 4x
Divide both sides by 4: x = 15
Result: the car travels 15 km in 20 minutes.

How It Is Calculated

There are two core operations under the hood:

Simplifying a ratio

Divide both parts by their greatest common divisor (GCD) — the largest whole number that divides into both values evenly. The result is the ratio in its lowest terms.

Simplified ratio = (A ÷ GCD) : (B ÷ GCD)

Example: 18:24 → GCD(18,24) = 6 → (18÷6):(24÷6) = 3:4

Solving a proportion

Use cross-multiplication. Given a:b = c:x, multiply the diagonals and divide to isolate the unknown.

a:b = c:x
a × x = b × c
x = (b × c) ÷ a

Example: 3:4 = 9:x → x = (4 × 9) ÷ 3 = 36 ÷ 3 = 12

Common ratio equivalents at a glance

Original ratio	Simplified	GCD used
2:4	1:2	2
6:9	2:3	3
18:24	3:4	6
25:100	1:4	25
50:75	2:3	25
120:180	2:3	60

Different Ways People Phrase Ratio Problems

Ratio questions show up in many forms. Here is when to reach for each approach:

'Simplify the ratio X:Y' — Use the simplify mode. Handy for recipes, mixing paint or chemicals, map scales, and financial comparisons.
'Share an amount in a given ratio' — For example, split £200 in the ratio 3:2. First add the parts (3+2=5), divide the total by 5 (£40 each part), then multiply: 3×40=£120 and 2×40=£80.
'Find the missing number in a proportion' — Use the solve mode. Common in unit-rate problems, scale drawings, ingredient scaling, and speed/distance/time.
'Express as a fraction or percentage' — A ratio of 3:4 means 3 out of every 7 parts (3/7 ≈ 43%). Divide the first number by the total of both parts.

Quick Tips and Common Mistakes

Keep units consistent. Mixing metres and centimetres gives a wrong ratio. Convert everything to the same unit first.
Zero is not allowed. A ratio like 5:0 is undefined — you cannot have zero parts of something in a proportion.
Order matters. The ratio 3:4 is not the same as 4:3. Always double-check which quantity comes first in your problem.
Decimal inputs work too. If you have 1.5:2.5, the calculator handles decimals. But whole-number ratios are easier to work with — multiply both sides by 2 to get 3:5 first if you prefer.
Check your cross-multiplication. The most common manual error is multiplying the wrong diagonal. In a:b = c:x, it is a×x = b×c — not a×b = c×x.
Equivalent ratios are still the same ratio. 2:3, 4:6, and 8:12 all mean the same thing — they just look different. Simplify to confirm two ratios are equal.

Everything is calculated locally in your browser. Your numbers are never uploaded, stored, or shared.

Nail any ratio problem in a few clicks — use the calculator above to simplify or solve right now.

Ratio Calculator - Simplify & Solve Ratios Instantly

Ratio

How it is calculated