Proportion Calculator

A proportion calculator solves equations between two ratios, such as 3/4 = x/20, where one value is unknown. The method is cross-multiplication: multiply the numerator of one side by the denominator of the other, set the products equal, and solve. For 3/4 = x/20, cross-multiplication gives 4x = 60, so x = 15. The ratio calculator above solves proportions in its proportion mode, and this page teaches the method with four worked examples.

Proportions are the arithmetic of scaling: recipes, maps, currency, and unit conversions all run on them. If 3 litres of paint cover 4 square metres, a proportion tells you how much paint covers 20 square metres, and the answer, 15 litres, comes from the same cross-multiplication. This page shows the method on four problems, explains how to set a proportion up correctly, and warns about the one error that ruins most proportion work: matching the wrong quantities across the equals sign.

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: Solving Proportions

Each row shows the proportion, the cross-multiplication, and the solution, with a check that the two ratios are equal.

The second row shows the unknown in the denominator, which is the case people find hardest: 2/5 = 8/x cross-multiplies to 2x = 40, so x = 20, and the check is 8/20 = 2/5, which is correct. The fourth row is a map scale: 1:50 means 1 cm on the model is 50 cm in reality, so a 3 cm model wall represents 3 × 50 = 150 cm in reality. Always check a proportion answer by substituting it back and confirming the two ratios are equal.

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.

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.

Setting Up a Proportion Correctly

A proportion is only as good as its setup. The quantities must match across the equals sign: the same kind of thing on top on both sides, and the same kind of thing on the bottom on both sides. This table shows correct and incorrect setups for the same problem.

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.

Direct and Inverse Proportion

Most proportions are direct: more of one thing means more of the other, and the ratio stays constant. A few are inverse: more workers means fewer days, and more speed means less travel time. Inverse proportions cannot be solved by cross-multiplication in the ordinary way; instead, the product stays constant, so 2 workers × 5 days = 10 worker-days, and 8 workers take 10 ÷ 8 = 1.25 days. Recognising which kind you have, before you calculate, is the skill that separates a right answer from a confident wrong one.

Tips for Accurate Results

Small habits keep ratio work exact, whether you are mixing paint or dividing a bill.

1. Always match units first. Convert hours to minutes, or miles to feet, before forming the ratio, or the comparison is meaningless.
2. Simplify before scaling. A simplified ratio is easier to scale mentally: 2:3 is easier to double than 12:18.
3. 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.
4. 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.
5. 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.

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 solve a proportion?

Cross-multiply and solve: for 3/4 = x/20, multiply 3 by 20 and 4 by x to get 60 = 4x, then divide by 4 to get x = 15. Check the answer by substituting it back: 15/20 simplifies to 3/4, which matches.

What is x in 2/5 = 8/x?

Cross-multiplication gives 2x = 40, so x = 20. The check is 8/20 = 2/5, which is correct. When the unknown is in the denominator, the cross-multiplication still works the same way.

How do proportions work with maps?

A map scale such as 1:50 is a proportion: 1 cm on the map equals 50 cm in reality. A 3 cm line on the map represents 3 × 50 = 150 cm in reality, which you find by solving 1/50 = 3/x.

What is the difference between direct and inverse proportion?

In a direct proportion, both quantities grow together and their ratio stays constant. In an inverse proportion, one grows while the other shrinks and their product stays constant, as with workers and days to finish a job.

Why is my proportion answer wrong?

The most common cause is mismatched quantities: litres over area on one side and area over litres on the other. Set the proportion so the same kind of quantity is on top on both sides, and the same kind on the bottom.

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.