Simplify Ratio Calculator
A simplify ratio calculator reduces a ratio to its lowest terms by dividing every part by the greatest common factor. The ratio 24:36 becomes 2:3, 45:60 becomes 3:4, and 100:150 becomes 2:3, and each reduced form says exactly the same thing as the original, in smaller numbers. The ratio calculator above simplifies two-part and three-part ratios instantly, and this page shows the hand method so you can check any result.
Simplifying matters because small numbers are easier to think with: 2:3 is easier to double, halve, or compare than 24:36, and a recipe written as 2:3 scales cleanly to any batch size. The rule is simple but strict: divide every part by the same number, and keep dividing until no common factor larger than 1 remains. This page works through five reductions, explains how to find the greatest common factor, and shows what to do when a ratio is already in its simplest form.
The Ratio Formulas: Simplify, Compare, and Convert
A ratio compares two or more quantities by division, and it is written with colons: 2:3 means for every 2 units of the first thing there are 3 units of the second. The ratio 12:18 says the same thing as 2:3, because both sides share a factor of 6, and simplifying a ratio means dividing every part by the greatest common factor until no further division is possible. The ratio 8:12:20 simplifies the same way: every part is divisible by 4, so it becomes 2:3:5. Ratios are the language of recipes, maps, mixtures, and money splits, anywhere that a fixed proportion must be kept while the total changes.
Converting a ratio to a percentage turns each part into a share of the whole. For the ratio 3:4, the whole is 3 + 4 = 7 parts, so the first part is 3 ÷ 7 = 42.86% and the second is 4 ÷ 7 = 57.14%. A proportion is an equation between two ratios, such as 3/4 = x/20, solved by cross-multiplication: 4x = 60, so x = 15. The calculator above handles all three jobs — simplifying, splitting a total by a ratio, and converting ratios to percentages — so you can move between these forms without redoing the arithmetic by hand.
Ratios are unit-free, which is why they travel so well between contexts. The same 2:3 can describe a classroom with 2 boys for every 3 girls, a paint mix of 2 parts blue to 3 parts white, or a budget split of $240 and $360 from $600. The National Institute of Standards and Technology uses ratios throughout its measurement guidance, because a ratio states a relationship that stays true no matter which units you measure in.
Step 1 — Write the Ratio With Colons
Put the quantities in the order that matters and join them with colons. A class with 12 boys and 18 girls is 12:18, and swapping the order to 18:12 would say the opposite, so the order is part of the answer. For three quantities, use two colons: 8 red, 12 blue, and 20 green marbles is 8:12:20.
Step 2 — Find the Greatest Common Factor
Find the largest number that divides every part exactly. For 12:18 that is 6; for 45:60 it is 15; for 18:24:30 it is 6. If no number larger than 1 divides all parts, the ratio is already in its simplest form, as 2:3 is.
Step 3 — Divide Every Part by That Factor
Divide each part by the common factor and write the result: 12:18 becomes 2:3, 45:60 becomes 3:4, and 18:24:30 becomes 3:4:5. Check by confirming no common factor remains, and by checking that the simplified ratio still describes the same relationship: 2:3 means the second quantity is one and a half times the first, exactly as 12:18 does.
Worked Examples: Simplifying Ratios
Each row shows the original ratio, the greatest common factor, and the reduced ratio. The last row is already simple, which is a valid answer.
| Original ratio | Greatest common factor | Simplified ratio |
|---|---|---|
| 24:36 | 12 | 2:3 |
| 45:60 | 15 | 3:4 |
| 100:150 | 50 | 2:3 |
| 7:21 | 7 | 1:3 |
| 18:24:30 | 6 | 3:4:5 |
The first row shows why the greatest common factor matters: 24 and 36 share the factors 2, 3, 4, 6, and 12, and dividing by 12 in one step gives 2:3 directly. Dividing by 2 first gives 12:18, which still needs dividing by 6, so using the greatest factor saves a step. The last row has three parts, and 6 divides 18, 24, and 30 exactly, giving 3:4:5, which has no common factor left.
How to Use the Ratio Calculator
Choose a mode, enter your numbers, and the calculator shows the simplified ratio, the split of a total, or the percentage form. It updates as you type, so you can test different totals against the same ratio in seconds.
- Pick a mode. Simplify a ratio, split an amount by a ratio, convert a ratio to a percentage, or solve a proportion — each mode asks only for the numbers it needs.
- Enter the ratio parts. Type the numbers separated by colons or commas, in the order that matches your real situation, because the order of the answer follows the order of the input.
- Enter a total when splitting. To divide $600 in the ratio 2:3, enter 600 as the total; the calculator gives $240 and $360, which add back to $600.
- Read the percentage form. The ratio 3:4 becomes 42.86% and 57.14%, which is the form most people find easiest to compare with other splits.
- Check the parts add up. In every mode, the parts of the answer should sum to the total you entered, or to 100% in percentage form. If they do not, recheck the order of your inputs.
Finding the Greatest Common Factor
The greatest common factor is the key step, and there are two reliable ways to find it. This table shows both on the same numbers.
| Numbers | Method 1: list factors | Method 2: divide by primes |
|---|---|---|
| 24, 36 | Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 | Divide by 2, then 2, then 3: 2 × 2 × 3 = 12 |
| 45, 60 | Common factors: 1, 3, 5, 15 | Divide by 3, then 5: 3 × 5 = 15 |
| 18, 24, 30 | Common factors: 1, 2, 3, 6 | Divide by 2, then 3: 2 × 3 = 6 |
| 100, 150 | Common factors: 1, 2, 5, 10, 25, 50 | Divide by 2, then 5, then 5: 50 |
| 7, 21 | Common factors: 1, 7 | 7 is prime and divides 21: 7 |
Common Mistakes With Ratios
Ratios are simple, but a few habits produce wrong answers again and again. Watch for these.
- Mixing up the order. A ratio of 2:3 is not the same as 3:2. Always write the parts in the order the question asks for them.
- Simplifying only one side. Dividing just the first number changes the relationship. Every part must be divided by the same factor.
- Adding ratios directly. Ratios with different totals cannot be added part by part: 1:2 and 1:3 do not combine into 2:5. Convert to fractions of a common whole first.
- Confusing a ratio with a fraction. In the ratio 3:4, the first part is 3/7 of the whole, not 3/4. The denominator is the sum of the parts, not the second part.
- Forgetting units. A ratio of 2 hours to 30 minutes is 4:1, not 2:30, because the units must match before you compare.
Where You Will Use Ratios
Ratios show up wherever a fixed relationship must scale up or down: cooking, building, money, and maps all run on them.
- Cooking and recipes. A rice-to-water ratio of 1:2 doubles cleanly for a crowd: 2 cups of rice need 4 cups of water, and the dish tastes the same.
- Paint and concrete mixes. A 1:2:4 cement, sand, and gravel mix keeps its strength at any batch size because the ratio, not the absolute amounts, defines the mix.
- Splitting money. Business partners, roommates, and prize winners divide totals in agreed ratios, and the split must add back to the original amount.
- Maps and scale models. A scale of 1:50 means 1 cm on the model is 50 cm in reality, so a 3 cm model wall represents a 150 cm real wall.
- Classrooms and surveys. A student-teacher ratio of 20:1, or a survey result of 3:2 in favour, summarises a whole group in two small numbers.
When a Ratio Is Already Simple
A ratio with no common factor larger than 1 is already in its simplest form, and the correct answer is the ratio itself. The ratio 2:3 is simple, 3:5 is simple, and 5:7 is simple. If you divide by 1, nothing changes, which is the sign that you are done. A ratio such as 14:21 is not simple, because 7 divides both parts, giving 2:3, so always test the small primes 2, 3, 5, and 7 before concluding a ratio is finished.
Tips for Accurate Results
Small habits keep ratio work exact, whether you are mixing paint or dividing a bill.
- Always match units first. Convert hours to minutes, or miles to feet, before forming the ratio, or the comparison is meaningless.
- Simplify before scaling. A simplified ratio is easier to scale mentally: 2:3 is easier to double than 12:18.
- Keep the total visible. When splitting an amount, write the total next to the ratio so you can check that the shares add back to it.
- Use decimals only at the end. Keep ratios as whole numbers while you simplify, and convert to percentages or decimals only for the final answer.
- Label each part. Write “boys:girls” or “blue:white” next to the numbers so nobody, including you tomorrow, reads the ratio backwards.
Ratio Quick Answers
These are the ratio answers people look up most often, each one verified against the calculator above.
| Question | Answer |
|---|---|
| 12:18 simplified | 2:3 |
| 45:60 simplified | 3:4 |
| 3:4 as percentages | 42.86% and 57.14% |
| $600 split in the ratio 2:3 | $240 and $360 |
| Solve 3/4 = x/20 | x = 15 |
Related tools on this site: the main ratio calculator, fraction calculator, percentage calculator, basic calculator, and the ratio calculator again whenever you need a fresh check.
Frequently Asked Questions
How do I simplify a ratio?
Divide every part by the greatest common factor. For 24:36, the greatest common factor is 12, so dividing both parts by 12 gives 2:3. Keep dividing until no number larger than 1 divides all the parts.
What is 24:36 simplified?
The ratio 24:36 simplifies to 2:3, because 12 is the greatest common factor of 24 and 36. Dividing both parts by 12 gives 2 and 3, and 2 and 3 share no common factor.
How do I simplify a ratio with three parts?
Find the greatest common factor of all three parts and divide each one by it. For 18:24:30, the common factor is 6, so the simplified ratio is 3:4:5. All three parts must be divided, not just two.
What if the ratio is already in simplest form?
Then the answer is the ratio itself. The ratio 2:3 has no common factor larger than 1, so it cannot be reduced further, and the calculator will return 2:3 unchanged.
Can a ratio be simplified to decimals?
Ratios are normally kept as whole numbers, because whole numbers are exact. A ratio such as 1:1.5 can be doubled to 2:3 to remove the decimal, which is the cleaner form for recipes, mixes, and splits.
Disclaimer: This calculator is for general information only. Ratios describe proportions; always confirm mix proportions, dosages, and financial splits against the authoritative instructions or agreement that governs them.