How to Calculate and Simplify Ratios: GCD, Proportions and Scaling Explained

You can simplify any ratio in seconds with the free Ratio Calculator: enter the first integer and the second integer, and the calculator divides both by their greatest common divisor. The ratio 24:36, for example, has a greatest common divisor of 12, so it simplifies to 24 ÷ 12 : 36 ÷ 12 = 2:3. The calculator also shows the proportion each term represents, so a simplified ratio and its meaning arrive together.

Ratios are the quiet workhorses of everyday numbers. A screen is 16:9, a recipe calls for flour and water in a stated proportion, a squash drink is diluted one part concentrate to a stated number of parts water, a map shrinks kilometres into centimetres at a fixed scale. In every case the ratio states a relationship, not an absolute quantity — and that is both its power and its trap. A ratio of 2:3 describes infinitely many pairs: 2 and 3, 20 and 30, 200 and 300. Simplifying strips a ratio to its smallest whole-number form so two ratios can be compared at a glance; scaling grows or shrinks it to fit a real quantity. This guide covers both directions, explains how ratios differ from fractions and percentages, and works examples from screen sizes to recipes. It deliberately stays on ratio ground: fraction arithmetic and percentage method have their own guides, linked at the end.

How Do You Use the Ratio Calculator, Step by Step?

1. Open the calculator. Go to the Ratio Calculator with the two quantities whose relationship you want to simplify or compare.
2. Enter the first integer. Type the first term of the ratio exactly as it stands — the width of a screen, the amount of the first ingredient, the count of the first thing being compared.
3. Enter the second integer. Type the second term, keeping the order the same as the source you took the figures from. Order matters: 2:3 and 3:2 are different relationships, the reverse of each other.
4. Read the simplified ratio. The calculator divides both terms by their greatest common divisor and shows the smallest whole-number form. If the two terms share no divisor larger than 1, the ratio is already in its simplest form and comes back unchanged.
5. Read the proportion alongside it. The proportion view relates the terms to each other and to the whole, which is the starting point for the scaling and percentage conversions explained below.

Simplifying Ratios: Divide Both Terms by the GCD

To simplify a ratio, find the greatest common divisor of its two terms — the largest whole number dividing exactly into both — then divide both terms by it. For 24:36, list the divisors if it helps: 24 divides by 1, 2, 3, 4, 6, 8, 12 and 24; 36 divides by 1, 2, 3, 4, 6, 9, 12, 18 and 36. The largest number on both lists is 12, so 24:36 becomes 2:3. Two checks guard the result. Both terms of the simplified ratio should be whole numbers, and they should share no common divisor larger than 1 — if they do, the simplification stopped early and there is a larger GCD still to divide by. Scaling runs the same relationship in reverse: multiply both terms by any number and the ratio is unchanged in meaning, larger in form, because the proportion between the terms is untouched.

Task	Method	Worked check
Simplify a ratio	Divide both terms by their GCD	24:36, GCD 12, becomes 2:3
Simplify a second ratio	Divide both terms by their GCD	18:27, GCD 9, becomes 2:3 — the same relationship
Simplify a ratio with a larger GCD	Divide both terms by their GCD	45:60, GCD 15, becomes 3:4
Scale a ratio up	Multiply both terms by the same number	2:3 scaled by 4 becomes 8:12
Scale a ratio to a total	Divide the total by the sum of terms, then multiply	2:3 into 50 parts: 50 ÷ 5 = 10, giving 20:30
Read a ratio as percentages	Each term divided by the sum of terms	2:3 gives 2 ÷ 5 = 40 percent and 3 ÷ 5 = 60 percent

The second row of the table carries an important insight: 18:27 and 24:36 simplify to the same 2:3, so they describe exactly the same relationship despite looking different. Simplification is what makes such comparisons possible. Two unsimplified ratios can only be compared with effort; two simplified ratios compare themselves. This is why simplified form is the standard way to state a ratio, and why the calculator returns it by default — it is the ratio with the noise removed, the relationship itself and nothing else.

Worked Examples: A Screen, a Recipe and a Mix

Example 1 — the shape of a screen. A screen measures 1920 by 1080 pixels. The greatest common divisor of 1920 and 1080 is 120, and dividing both terms by 120 gives 1920 ÷ 120 : 1080 ÷ 120 = 16:9. A smaller screen at 1280 by 720 has a GCD of 80, and 1280 ÷ 80 : 720 ÷ 80 is also 16:9. Two different sizes, one identical shape — which is exactly what an aspect ratio is for: it promises that content framed for one of these screens fits the other without distortion.

Example 2 — scaling a recipe ratio to a total. A recipe states an ingredient relationship of 2:3 — say, 2 parts of one ingredient to 3 parts of another, as an illustration — and you need 50 parts in total. The ratio has 2 + 3 = 5 parts. Divide the total by the parts: 50 ÷ 5 = 10 per part. Multiply each term by 10: 20:30. Check the sum: 20 + 30 = 50, and the relationship still simplifies back to 2:3. The same method scales to any total — a litre, a batch, a production run — because it never touches the proportion, only the unit size of a part.

Example 3 — simplifying a measured mix. A mix is made with 45 units of one component and 60 units of another in this example. The GCD of 45 and 60 is 15, so the ratio simplifies to 45 ÷ 15 : 60 ÷ 15 = 3:4. Stated that way, the next batch is easy at any size: 3 and 4 for a small batch, 30 and 40 for one ten times larger, each preserving the same relationship the original measurements happened to land on.

The chart converts ratios into shares of a whole, the view that makes ratios comparable with the percentage figures used everywhere else. In a 2:3 ratio the first share is 40 percent and the second is 60 percent; in a 3:4 ratio the first share is 3 of 7 parts, which is about 42.86 percent; and a 1:1 ratio is the familiar half-and-half. Notice that converting to percentages always runs through the total of the parts — 5 parts, 7 parts, 2 parts — never through the other term alone. That single step is where ratios and fractions part company, and the next section is devoted to it.

Ratios vs Fractions vs Percentages: Three Views of Related Ideas

A ratio compares two quantities with each other. A fraction compares one quantity with a whole. A percentage compares one quantity with a whole scaled to 100. The three are close relatives and constant sources of confusion, because the same two numbers can appear in all three while meaning different things. Take 2 and 3. As a ratio, 2:3 means 2 parts of one thing alongside 3 parts of another — 5 parts in total. As a fraction, 2/3 means 2 out of 3 equal parts of one whole, which is about 66.67 percent. As shares of the ratio's whole, the first quantity is 2 of 5 parts, which is 40 percent. Three different answers — 2:3, 66.67 percent and 40 percent — from the same pair of digits, each correct for its own question. The question decides which view is right: comparing two ingredients with each other is ratio work; asking what share of the finished whole one ingredient forms is fraction and percentage work.

The practical rule is to ask what the whole is. If there is no whole in the question — just two things standing in relation — you are working with a ratio, and simplifying by the GCD is the whole technique. If a whole enters the question — a total weight, a finished mixture, 100 percent — convert through the sum of the terms first, as the table shows, and only then speak in fractions or percentages. Guides devoted to those views go deeper: the fraction and percentage tools linked in the conclusion handle their arithmetic, and the percentage guide linked there explains its method. This guide's claim is only the boundary: ratios compare part with part, fractions compare part with whole, and mixing the two views mid-calculation is the error to avoid.

Where Ratio Calculations Show Up

Situation	Typical ratio work	Watch for
Screens, video and photography	Simplifying width to height, such as 1920:1080 to 16:9	Keeping width first and height second — order is the meaning
Recipes and baking	Scaling a stated proportion to a bigger or smaller batch	Scaling both terms together; changing one changes the dish
Mixes, dilutions and concentrates	Simplifying measured amounts, then scaling to the container in hand	Whether the stated ratio is concentrate to water, or concentrate to finished mix — different wholes
Maps and scale models	Reading a scale as a ratio between drawing and reality	Keeping units consistent on both sides before simplifying
Sharing and dividing quantities	Splitting a total in a stated ratio using the parts method	Dividing the total by the sum of terms, not by one term
Comparing two groups	Simplifying both ratios, then comparing like with like	Unsimplified ratios that look different but simplify to the same form

Five Mistakes That Spoil Ratio Calculations

• Dividing only one term when simplifying. Dividing 24 by 12 but leaving 36 untouched turns 24:36 into 2:36, a different relationship entirely. The GCD divides both terms, always, or the ratio has been changed rather than simplified.
• Stopping before the greatest common divisor. Dividing 24:36 by 6 gives 4:6, which still shares a divisor of 2. A simplified ratio whose terms share any divisor larger than 1 is not finished — divide again, or use the true GCD in one step.
• Reading a ratio as a fraction of the whole. In 2:3, the first quantity is not two thirds of anything. It is 2 of 5 total parts, or 40 percent. The fraction view needs the sum of terms as its whole.
• Reversing the order of the terms. 16:9 describes a wide screen; 9:16 describes a tall one. Ratios carry direction, and swapping terms describes the opposite relationship.
• Scaling one term to fit a total. Needing 50 parts of a 2:3 mix does not mean 50 of the first ingredient. Divide the total by the sum of terms — 5 — to find the size of one part, then multiply both terms by it.

Conclusion: Simplify to See the Relationship

A ratio is a relationship stated in numbers: divide both terms by their greatest common divisor to see it clearly, multiply both terms by the same number to scale it to the quantity in front of you, and convert through the sum of the terms when a share of the whole is what you need. The Ratio Calculator simplifies from two integers and shows the proportion in one step. Its neighbours cover the related views: the Fraction Calculator for part-to-whole work and the Percentage Calculator for shares out of 100, and our guide to how to calculate percentages — with the percentage method set out in full — pairs with this one wherever a ratio needs expressing as percentages.

Frequently Asked Questions

How do I simplify a ratio?

Divide both terms by their greatest common divisor — the largest number that divides into both exactly. For 24 to 36, the greatest common divisor is 12, and dividing both terms by 12 gives 2 to 3. The calculator on this page performs the division and reports the simplified ratio and the proportion.

What is a greatest common divisor?

The greatest common divisor, or GCD, of two numbers is the largest whole number that divides into both of them with nothing left over. The GCD of 24 and 36 is 12: 12 divides into both, and no larger number does. Simplifying a ratio is exactly the act of dividing both terms by their GCD.

How do I scale a ratio up or down?

Multiply or divide both terms by the same number. The ratio 2 to 3 scaled by 4 becomes 8 to 12; scaled to make 50 parts in total, since 2 plus 3 is 5 parts and 50 divided by 5 is 10, it becomes 20 to 30. Changing only one term changes the ratio itself — both terms must always move together.

What is the difference between a ratio and a fraction?

A ratio compares two quantities to each other — 2 to 3 means 2 parts of one thing for every 3 parts of another. A fraction compares a part to a whole — 2 over 5 means 2 of 5 equal parts. In a 2 to 3 ratio, the first quantity is 2 of 5 total parts, which is 40 percent of the whole, not the 66.67 percent that the fraction 2 over 3 would give.

How do I turn a ratio into percentages?

Add the terms to get the total number of parts, then express each term as a share of that total. For 2 to 3, the total is 5 parts: the first share is 2 divided by 5, which is 40 percent, and the second is 3 divided by 5, which is 60 percent. The shares always add back up to 100 percent.

Why are screens described as 16 to 9?

Because their width and height stand in that ratio. A 1920 by 1080 screen divides by 120 on both sides to give exactly 16 to 9, and a 1280 by 720 screen divides by 80 to give the same simplified ratio. The ratio describes the shape, not the size — screens of many sizes share it, which is why videos framed for it fit all of them.

Can a ratio have more than two terms?

Yes. Three-way ratios appear in recipes, mixes and sharing plans, such as a mix described with three components in proportion. The simplification rule is unchanged: divide every term by the greatest common divisor of all the terms. The two-term calculator in this guide covers the commonest case; the method extends directly.