Ratio Calculator

Simplify any ratio, scale it up or down, and turn it into a decimal or a percentage — in one step. Enter the two sides of the ratio, and the calculator shows the simplest form, the decimal value and the percentage straight away. It runs entirely in your browser: free, instant, no sign-in.

How the ratio calculator works

Simplifying a ratio means dividing both sides by the same number — their greatest common divisor (GCD), the largest number that divides both sides exactly. For 12:18, the GCD is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2:3. The simplified ratio means exactly the same thing as the original: 12 parts to 18 parts is the same relationship as 2 parts to 3 parts.

The decimal form is the first side divided by the second: decimal = a ÷ b. For 3:4 that is 3 ÷ 4 = 0.75. The percentage is the decimal times 100: percent = a ÷ b × 100, so 3:4 is 75%. Scaling a ratio multiplies both sides by the same factor: 2:3 scaled by 4 is 8:12, and the relationship stays the same — the scaled ratio still simplifies back to 2:3.

A ratio compares two amounts: 12:18 says there are 12 parts of one thing for every 18 parts of another. The Ratio Calculator takes that comparison and makes it easier to work with — it simplifies the ratio to its smallest whole-number form, turns it into a decimal, turns it into a percentage, and scales it up or down by any factor you choose. Enter the two sides, and the answers appear straight away. It runs entirely in your browser, so nothing you enter is uploaded anywhere, and there is no sign-in and no limit on how often you use it.

The three results answer three different questions about the same ratio. The simplified form — 12:18 becomes 2:3 — is the cleanest way to write it. The decimal — 0.75 for 3:4 — is the form you need for further maths. The percentage — 75% for 3:4 — is the form that is easiest to picture and to explain to someone else. The scale mode answers a fourth question: what does this ratio look like bigger or smaller, for example when a recipe or a mixture has to serve more people.

How to use the calculator, step by step

• Step 1 — Enter the first side. Type the first number of the ratio into the “First side (a)” box. For 12:18, enter 12. For a recipe with 2 cups of flour to 3 cups of sugar, enter 2.
• Step 2 — Enter the second side. Type the second number into the “Second side (b)” box. For 12:18, enter 18. The result updates as you type: the simplified ratio, the decimal and the percentage all appear at once.
• Step 3 — Read the three results. The big number is the simplified ratio. Under it, the calculator shows the decimal and the percentage, plus the working — which number both sides were divided by — so you can check the maths yourself.
• Step 4 — Scale the ratio (optional). If you need the ratio bigger or smaller, type a factor into the “Scale by” box. Scaling 2:3 by 4 gives 8:12; scaling 3:5 by 0.5 gives 1.5:2.5. Leave the box empty if you only want the simplified ratio, decimal and percentage.

How the maths works

Three small formulas do all the work:

• Simplify: divide both sides by their greatest common divisor (GCD). The GCD is the largest whole number that divides both sides exactly. For 12:18, the GCD is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2:3. For 15:25, the GCD is 5, so 15 ÷ 5 = 3 and 25 ÷ 5 = 5, giving 3:5.
• Decimal: divide the first side by the second. Decimal = a ÷ b. For 3:4, that is 3 ÷ 4 = 0.75. For 1:2, it is 1 ÷ 2 = 0.5.
• Percentage: multiply the decimal by 100. Percent = a ÷ b × 100. For 3:4, that is 0.75 × 100 = 75%. For 1:2, it is 0.5 × 100 = 50%.
• Scale: multiply both sides by the same factor. Scaled ratio = (a × factor):(b × factor). Scaling 2:3 by 4 gives (2 × 4):(3 × 4) = 8:12. Scaling 3:5 by 0.5 gives (3 × 0.5):(5 × 0.5) = 1.5:2.5. The relationship never changes — the scaled ratio always simplifies back to the original.

The table below shows the simplified form, decimal and percentage for the most common ratios:

• 1:2 — already simplest, decimal 0.5, 50%
• 1:3 — already simplest, decimal 0.3333, 33.33%
• 1:4 — already simplest, decimal 0.25, 25%
• 2:3 — already simplest, decimal 0.6667, 66.67%
• 2:5 — already simplest, decimal 0.4, 40%
• 3:4 — already simplest, decimal 0.75, 75%
• 3:5 — already simplest, decimal 0.6, 60%
• 4:5 — already simplest, decimal 0.8, 80%
• 5:8 — already simplest, decimal 0.625, 62.5%
• 7:10 — already simplest, decimal 0.7, 70%

A ratio is already in its simplest form when the two sides share no common factor other than 1 — the calculator tells you this, so you know there is nothing left to simplify. If the GCD is 1, the ratio is already simple: 7:13 stays 7:13, and 2:3 stays 2:3.

Worked examples

Example 1 — simplify 12:18. Find the GCD of 12 and 18. The factors of 12 are 1, 2, 3, 4, 6 and 12; the factors of 18 are 1, 2, 3, 6, 9 and 18. The largest number in both lists is 6. Divide both sides by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 12:18 simplifies to 2:3.

Example 2 — simplify 15:25. The GCD of 15 and 25 is 5. Divide both sides by 5: 15 ÷ 5 = 3 and 25 ÷ 5 = 5, so 15:25 simplifies to 3:5. As a decimal, 3 ÷ 5 = 0.6; as a percentage, 0.6 × 100 = 60%.

Example 3 — scale 2:3 by 4. Multiply both sides by 4: 2 × 4 = 8 and 3 × 4 = 12, so 2:3 scaled by 4 is 8:12. The scaled ratio means the same thing — divide both sides of 8:12 by 4 and you are back to 2:3. This is how a recipe is doubled or quadrupled without changing the balance of ingredients.

Example 4 — scale 3:5 by 0.5. Multiply both sides by 0.5: 3 × 0.5 = 1.5 and 5 × 0.5 = 2.5, so 3:5 scaled by 0.5 is 1.5:2.5. A factor below 1 shrinks the ratio; a factor above 1 grows it. Halving a recipe uses a factor of 0.5, just like this example.

Example 5 — 3:4 as a decimal and a percentage. Divide the first side by the second: 3 ÷ 4 = 0.75. Multiply by 100 for the percentage: 0.75 × 100 = 75%. A ratio of 3:4 means the first amount is three quarters of the second — the decimal and the percentage say the same thing in two different forms.

Example 6 — 1:2 as a decimal and a percentage. Divide 1 by 2: 1 ÷ 2 = 0.5. Multiply by 100: 0.5 × 100 = 50%. A 1:2 ratio means the first amount is exactly half of the second, which is why the answer is a clean 50%.

Common mistakes

• Dividing only one side. Simplifying means dividing BOTH sides by the same number. Dividing only the first side of 12:18 by 6 gives 2:18, which is a different ratio entirely. The calculator divides both sides by the GCD, so the relationship is preserved.
• Simplifying by the wrong number. Dividing 12:18 by 2 gives 6:9, which is correct but not finished — 6 and 9 still share a factor of 3, so 6:9 simplifies further to 2:3. Always divide by the greatest common divisor, not just any common factor.
• Reading the decimal the wrong way round. The decimal for a:b is a ÷ b, not b ÷ a. For 3:4 the decimal is 3 ÷ 4 = 0.75, not 4 ÷ 3 = 1.3333. If your answer is bigger than 1 when the first side is smaller than the second, the division is backwards.
• Confusing a ratio with a fraction of the total. In a 3:4 ratio, the first part is 3 out of 7 total parts (3 ÷ (3 + 4) = 42.86%), not 75% of the total. The 75% in this calculator is the first side as a percentage of the second side — 3 is 75% of 4 — which is a different question from “what share of the whole is it?”
• Scaling only one side. Scaling a recipe by 2 means doubling every ingredient. Doubling only the flour in a 2:3 flour-to-sugar mix gives 4:3, which is a different recipe — sweeter flour, less sugar in proportion. The scale factor must multiply both sides.
• Using a ratio with a zero side. A ratio of 0:4 or 4:0 does not describe a comparison — the first would mean “none of this, some of that”, and the second cannot even be divided. The calculator shows an error instead of a result when either side is 0, so enter a number above 0 for both sides.

Related tools

The ratio calculator sits in the Math group, and two companion tools cover the percentage and purity maths that ratios often lead into.

• Percentage Calculator — work out percentages, percentage change and what percentage one number is of another, once a ratio has given you the decimal or percent to start from.
• Gold Purity Percentage Converter — convert between purity percentage and karat, the same kind of part-to-whole maths as a ratio expressed as a percentage.

The Proportion Calculator and the LCM & GCF Calculator are companion maths tools being built for ToolZana — the Proportion Calculator solves for an unknown in an equation like a/b = c/d, and the LCM & GCF Calculator finds the greatest common factor used to simplify ratios. For all of ToolZana’s free tools, start at the ToolZana home page.

Tips for working with ratios

• Simplify first, calculate second. A simplified ratio makes every later step easier: 2:3 is far easier to scale or compare than 12:18, and it is the same relationship. Always reduce before you scale.
• Use the decimal for further maths. If you need to multiply a ratio by a quantity, use the decimal form — 0.75 times a weight is one multiplication, while 3:4 needs a division and a multiplication. Convert to a decimal, then calculate.
• Use the percentage to explain it. Percentages are the easiest form for other people to picture: “the first part is 75% of the second” is clearer than “the ratio is 3:4” for most readers. Use the percentage when you are writing the answer down for someone else.
• Check a scaled ratio by simplifying it back. After scaling 2:3 by 4 to get 8:12, divide 8 and 12 by their GCD (4) — you should land back on 2:3. If you do not, one side was multiplied by the wrong factor.
• Keep the order the same. In a ratio, order matters: 3:4 and 4:3 are different relationships. When you scale, write the scaled numbers in the same order as the original, so the first side still refers to the same thing.

The short version

The Ratio Calculator simplifies any ratio by dividing both sides by their greatest common divisor — 12:18 becomes 2:3 (GCD 6) and 15:25 becomes 3:5 (GCD 5) — and it also gives the decimal and the percentage: 3:4 is 0.75 and 75%, and 1:2 is 0.5 and 50%. The scale mode multiplies both sides by the same factor: 2:3 scaled by 4 is 8:12, and 3:5 scaled by 0.5 is 1.5:2.5. The decimal is always a ÷ b, the percentage is a ÷ b × 100, and the simplified ratio means exactly the same thing as the original. A ratio with a zero side is not meaningful, so the calculator asks for numbers above 0 on both sides. The tool is free, runs entirely in your browser, and needs no sign-in.

Frequently Asked Questions

What is a ratio calculator?

A ratio calculator takes a ratio like 12:18 and works out its simplest form, its decimal value and its percentage. For 12:18 it gives the simplified ratio 2:3, the decimal 0.6667 and the percentage 66.67%. It also scales ratios: enter a factor and it multiplies both sides, so 2:3 scaled by 4 becomes 8:12. It runs entirely in your browser, with no sign-in and no limits.

How do I simplify a ratio?

Divide both sides of the ratio by their greatest common divisor (GCD) — the largest whole number that divides both sides exactly. For 12:18, the GCD is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2:3. For 15:25, the GCD is 5, so 15 ÷ 5 = 3 and 25 ÷ 5 = 5, giving 3:5. Enter the two sides in the calculator and it finds the GCD and divides both sides for you.

How do I scale a ratio up or down?

Multiply both sides of the ratio by the same factor. To scale 2:3 by 4, multiply 2 × 4 = 8 and 3 × 4 = 12, giving 8:12. To scale 3:5 down by 0.5, multiply 3 × 0.5 = 1.5 and 5 × 0.5 = 2.5, giving 1.5:2.5. A factor above 1 grows the ratio and a factor below 1 shrinks it, but the relationship never changes — the scaled ratio always simplifies back to the original. Enter the factor in the “Scale by” box and the calculator does the multiplication for you.

How do I turn a ratio into a decimal?

Divide the first side by the second side: decimal = a ÷ b. For 3:4, divide 3 by 4 to get 0.75. For 1:2, divide 1 by 2 to get 0.5. For 2:3, divide 2 by 3 to get 0.6667. The calculator shows the decimal rounded to four places, so a repeating decimal like 2 ÷ 3 appears as 0.6667 rather than going on forever.

How do I turn a ratio into a percentage?

Divide the first side by the second side and multiply by 100: percent = a ÷ b × 100. For 3:4, 3 ÷ 4 = 0.75, and 0.75 × 100 = 75%. For 1:2, 1 ÷ 2 = 0.5, and 0.5 × 100 = 50%. For 2:5, 2 ÷ 5 = 0.4, and 0.4 × 100 = 40%. The percentage tells you how big the first side is compared with the second side, which is the easiest form to picture and to explain.

What is the greatest common divisor (GCD)?

The greatest common divisor is the largest whole number that divides two numbers exactly, with no remainder. The GCD of 12 and 18 is 6, because 6 divides both 12 and 18 and no larger number does. The GCD of 15 and 25 is 5, and the GCD of 100 and 80 is 20. When two numbers share no factor other than 1 — like 7 and 13 — their GCD is 1, and the ratio is already in its simplest form. Simplifying a ratio means dividing both sides by their GCD.

What is the simplest form of 12:18?

The simplest form of 12:18 is 2:3. The greatest common divisor of 12 and 18 is 6: dividing 12 by 6 gives 2, and dividing 18 by 6 gives 3. The ratio 2:3 means exactly the same thing as 12:18 — 12 parts to 18 parts is the same relationship as 2 parts to 3 parts — it is just written with the smallest whole numbers possible.

How do I use a ratio calculator for recipes?

Enter the amounts of two ingredients as the two sides of the ratio, then use the scale factor to resize the recipe. A recipe with 2 cups of flour to 3 cups of sugar is a 2:3 ratio. To make four times as much, scale by 4: 2 × 4 = 8 cups of flour and 3 × 4 = 12 cups of sugar, giving 8:12. To make half as much, scale by 0.5: 2 × 0.5 = 1 cup of flour and 3 × 0.5 = 1.5 cups of sugar, giving 1:1.5. Scale both sides by the same factor and the balance of flavours stays the same.

Can a ratio have a zero in it?

No — a ratio with a zero side is not meaningful for this calculator. A ratio of 0:4 would mean “none of the first thing and some of the second”, which is not a comparison, and a ratio of 4:0 cannot be turned into a decimal because dividing by zero is impossible. The calculator shows a friendly error when either side is 0 or empty, and asks for a number above 0 on both sides.

What is the difference between a ratio and a proportion?

A ratio compares two amounts, like 2:3. A proportion is an equation saying two ratios are equal, like 2/3 = 4/6, and it is usually used to solve for an unknown — for example, finding the missing number in a/b = c/d. This tool works with single ratios only: it simplifies, scales and converts them to decimals and percentages. Solving for an unknown in a proportion belongs to the Proportion Calculator, a separate ToolZana tool.

What is the difference between a ratio and a fraction?

A ratio and a fraction describe the same comparison in different ways. The ratio 3:4 says there are 3 parts of one thing for every 4 parts of another, while the fraction 3/4 says the first amount is three quarters of the second. The decimal for both is the same: 3 ÷ 4 = 0.75. The difference shows up when you ask about the whole: in a 3:4 mix there are 7 parts in total, so the first part is 3 out of 7 (about 42.86%) of the whole — not 75%, which is the first part as a percentage of the second part only.

Is the ratio calculator free?

Yes — the Ratio Calculator is completely free, with no sign-in and no limits. It runs entirely in your browser, so nothing you enter is uploaded anywhere, and you can use it as often as you like, for recipes, mixtures, scaling, homework or any other ratio.