Ratio and Proportion Calculator: Simplify, Scale and Compare

Write the two numbers as A:B, then divide both by their greatest common divisor to get the simplest form. For 14 and 21 the divisor is 7, so the ratio is 2:3. To see the size of one against the other, divide: 14 ÷ 21 is about 0.667. The calculator does both steps in Simplify.

18 to 6 is 3 to 1 (3:1), because both numbers divide by 6. The decimal 18 ÷ 6 = 3 shows that the first number is three times the second.

14 to 21 simplifies to 2 to 3 (2:3), because both numbers divide by 7. As a decimal, 14 ÷ 21 is about 0.667, so the first number is two thirds of the second.

It does the arithmetic of ratios for you: it reduces a ratio to lowest terms, finds the missing number in A:B = C:D, tells you whether two ratios are equal or which one is larger, and splits a total in a ratio. You enter the numbers and it shows the result with the steps.

It treats a ratio like a fraction. To simplify, it divides both numbers by their greatest common divisor. To find a missing number, it multiplies the known number by the ratio of the other two terms. To compare, it cross-multiplies. To split a total, it divides the total by the sum of the terms and multiplies by each term.

This one takes two numbers at a time. A ratio of three numbers follows the same rules: 12:18:30 divides by 6 to give 2:3:5, and a total split three ways uses the sum of the terms (2 + 3 + 5 = 10), so 100 becomes 20, 30 and 50.

A fraction compares a part with the whole (3/4 means 3 of 4 equal parts), while a ratio compares any two quantities, including part with part. In the ratio 3:1 the parts are 3 and 1, the whole is 4, and the fractions are 3/4 and 1/4. The ratio A:B equals the fraction A/B, which is why the same rules apply. For fraction arithmetic, use the fraction calculator.

A ratio compares two numbers, such as 3:4. A proportion is a statement that two ratios are equal, such as 3:4 = 9:12. Solving a proportion means finding a missing number, which is what Scale does.

Cross-multiply. For 3:4 = 9:x, multiply 4 × 9 = 36 and divide by 3 to get x = 12. In Scale, enter 3 and 4, choose that you know the first number of the new ratio, and enter 9. If you know the second number instead, as in 3:4 = x:20, choose Second number and enter 20 to get x = 15.

Equal (equivalent) ratios have the same value: multiply or divide both terms by the same number, and 2:3 = 4:6 = 6:9. The table under the calculator lists the first ten multiples of your ratio in whole numbers.

Enter the decimals as they are. The calculator finds the largest number that divides both exactly, and with decimals that number is a decimal too: 0.5 for 1.5 and 2.5, so 1.5 ÷ 0.5 = 3, 2.5 ÷ 0.5 = 5 and the ratio is 3:5. For 2.05 and 1.23 it is 0.41, which gives 5:3. The result row “Both numbers divided by” shows this number for the numbers as you typed them. The calculator reads up to six decimal places.

Divide each term by the sum of both terms and multiply by 100. The ratio 3:1 gives 3 ÷ 4 = 75% and 1 ÷ 4 = 25%. The calculator shows these as Share of A and Share of B in Simplify and in Split a total. For a percent of a number or a percent change, use the percentage calculator.

A 3:1 ratio means 3 parts of the first thing for every 1 part of the second, 4 parts in all, so 75% and 25%. A 2:1 ratio is 2 parts to 1 part, about 66.7% and 33.3%. The same reading works for 4:1, 3:4, 4:5 and any other pair.

A 50:1 ratio means 50 parts of one ingredient to 1 part of the other, 51 parts in all. In Split a total, enter 50 and 1 and your total: 102 ounces in all gives 100 ounces and 2 ounces. Follow the instructions of your equipment or product, because makers sometimes define a mix ratio differently.

Mixes for mortar, concrete and grout are given as ratios of parts by volume, such as 1:4 cement to sand. In Split a total, enter the ratio and the amount: 10 buckets in all at 1:4 is 2 buckets of cement and 8 of sand. For a three-part mix such as 1:2:3, add the parts (6) and divide the total by 6: 12 buckets give 2, 4 and 6. A roof pitch of 4:12 simplifies to 1:3. Follow the mix on the product or in your plans.

Enter the width as A and the height as B in Simplify. 1920 × 1080 pixels reduces to 16:9 and 1024 × 768 reduces to 4:3. To resize while keeping the shape, use Scale: 16:9 with a width of 1280 gives a height of 720.

The current ratio is current assets divided by current liabilities. Enter current assets as A and current liabilities as B in Simplify and read A ÷ B: 150,000 and 100,000 give 1.5, the same as 3:2 in whole numbers. The quick ratio is the same division with inventory and prepaid expenses taken out of the assets. These are definitions, not advice; how a ratio is judged depends on the business.

Ratios resize recipes, set map and model scales, describe screen shapes such as 16:9, give the mix for paint, concrete and fuel, express odds such as 3 to 1 and compare money figures such as assets to liabilities. Anywhere two quantities are compared by division, a ratio is at work.

Ratios let you compare quantities of different sizes and resize plans, recipes and mixtures without changing their proportions. Because a ratio does not change when both terms are scaled, 2 cups to 3 cups is the same mix as 20 cups to 30 cups.