Ratio Calculator

How this ratio is calculated

You type a first value A and a second value B. B cannot be 0. The page stops and warns you, because the decimal is A ÷ B. If both values are whole numbers, including negatives, the simplified ratio divides both by their greatest common divisor. The divisor is computed on the absolute values, and the signs stay on the sides where you typed them. So 1920 and 1080 become 16:9, and −8 and 12 become −2:3. If either value is not a whole number, the page does not hunt for a common factor. It prints both numbers to four decimal places. 1.5 and 2.5 stay 1.5:2.5. They are not rewritten as 3:5.

The decimal line is A ÷ B, to six decimal places. The percent line is (A ÷ B) × 100, to four decimal places. That percent means "A as a percent of B." It does not mean "A's share of A+B." For 16 and 9 the decimal displays as 1.777778 and the percent as 177.7778%. Sixteen is 177.7778 percent of 9. Sixteen is not 177 percent of the whole 25. The share of the whole would be 16 ÷ 25, and this page does not compute that.

The scale boxes are optional. If "scale first to" has a number, the factor is that number ÷ A, and the scaled ratio is the number you typed, then B × factor. If the first scale box is empty and "scale second to" has a number, the factor is that number ÷ B, and the scaled ratio is A × factor, then the number you typed. If both scale boxes have numbers, the first one wins and the second is ignored. The scaled numbers are not run through the simplifier again. 3:5 scaled so the first side is 12 displays as 12:20, while the simplified line above it still says 3:5. Scaling when A is 0 and you use the first scale box divides by zero.

Worked examples

Example 1: 1920 and 1080

Both are whole numbers. Their greatest common divisor is 120. 1920 ÷ 120 = 16 and 1080 ÷ 120 = 9, so the simplified ratio is 16:9. Decimal 1.777778. Percent 177.7778%. Put 1280 in "scale first to" and leave the other scale box empty. The factor is 1280 ÷ 1920 = 2 ÷ 3, and the second side is 1080 × 2 ÷ 3 = 720. The scaled line displays 1280:720. It does not reduce that further to 16:9. The simplified line already did.

Example 2: 3 and 5, scaled, and what the percent is not

3 and 5 are already simplified, since the greatest common divisor is 1. Decimal 0.6. Percent 60%, because 3 is 60 percent of 5. That is not "3 parts out of 8." The page never adds 3+5. Scale the first side to 12: the factor is 4, and the scaled line is 12:20. If you needed each side's share of a sum, you would be doing different arithmetic from the percent line. A $90 bill split 3:2 is not a result this form produces. The Tip Calculator splits a bill into equal shares after a tip percent. It also does not apply a 3:2 ratio.

Example 3: 50 and 1, scaled to 2.5

50 and 1 simplify to 50:1. Decimal 50. Percent 5000%, because 50 is 5,000 percent of 1. Scale the first side to 2.5. The factor is 2.5 ÷ 50 = 0.05, and the scaled line displays 2.5:0.05. If both numbers are liters, the second number is 0.05 liters. Turning 0.05 liters into 50 milliliters is a unit change this page does not do. The Volume Converter does. Leave the ratio in one unit until you have read the scaled pair.

When to use this

Use it to reduce a pair of whole numbers, to see A as a multiple of B, or to scale one side to a length or a volume you already chose. Screen sizes are the first example: 1920:1080 and 1280:720 are the same simplified ratio and different scaled pairs. A recipe that should grow by servings, ingredient by ingredient, is the Recipe Scaler, which multiplies a list. This page multiplies one pair. A fraction you want written as a percent of one, rather than as a ratio of two, is the Fraction to Decimal to Percent converter.

Order, decimals, and the map-scale rounding

2:1 and 1:2 are different. The decimal of 2 and 1 is 2. The decimal of 1 and 2 is 0.5. The percent flips the same way, 200% versus 50%. Fuel-mix directions that say which liquid is first are describing A and B. Reversing the boxes reverses the ratio. The page will not infer oil versus gasoline from the size of the number.

Decimals skip the greatest-common-divisor step on purpose. If you want 1.5:2.5 reduced, multiply both by 2 yourself and type 3 and 5. The page will not do that multiplication for you. Very small ratios show the six-decimal limit on the decimal line. 1 and 24000 simplify to 1:24000, and the decimal 1 ÷ 24000 displays as 0.000042, because six places round 0.000041666… upward. The simplified ratio is the exact pair. The decimal line is the rounded quotient. For a map scale, keep the simplified ratio and convert a measured length with the Length Converter. Do not treat 0.000042 as the scale factor if you still have 1:24000 on the line above.

Common mistakes

• Reading the percent as a share of the total. 3:5 displays as 60%, which is 3 ÷ 5, not 3 ÷ 8.
• Expecting 1.5:2.5 to become 3:5. Non-integers are printed to four decimals. They are not scaled up to whole numbers.
• Filling both scale boxes. The first scale box wins. The second is ignored until you clear the first.
• Expecting the scaled line to simplify. 3:5 scaled to 12 displays as 12:20. Simplifying already happened on the other line.
• Reversing the mix. 50:1 and 1:50 are different ratios, different decimals, and different percents.
• Using the rounded decimal of a huge ratio as the working factor. 1:24000 displays a decimal of 0.000042. The simplified line is the exact ratio.

Limitations

Two numbers only. No third part, no "split this dollar total" field, and no unit conversion inside the ratio. Zero is rejected on the second value. Zero on the first value simplifies, for whole numbers, but scaling the first side then divides by zero. Negatives are allowed and keep their signs. The greatest common divisor runs only when both values are integers. Output rounding is four decimals on a non-integer simplified pair and on each scaled number, six decimals on the quotient, and four decimals on the percent.

FAQ

Is the percent A's share of the whole?

No. The percent is (A ÷ B) × 100. For 16 and 9 that displays as 177.7778%, meaning 16 as a percent of 9. The page does not divide by A+B.

Why doesn't 1.5 to 2.5 simplify to 3 to 5?

The greatest-common-divisor step runs only when both values are whole numbers. 1.5 and 2.5 display as 1.5:2.5. Type 3 and 5 if you want the reduced whole-number ratio.

What happens if I fill in both scale boxes?

The first scale box is used. Its factor is that number divided by A. The second scale box is ignored until the first one is empty.

Does the scaled ratio get simplified?

No. 1920 and 1080 simplify to 16:9 on the first line. Scaling the first side to 1280 displays 1280:720 on the scaled line, unreduced.

Can this split $90 in the ratio 3:2?

No. There is no total to share. The percent line would show 3 as a percent of 2, which is 150%, not two dollar shares. Equal splits of a restaurant bill are the tip calculator, and that split is equal, not 3:2.

Why is the decimal of 1:24000 shown as 0.000042?

1 ÷ 24000 is 0.000041666…, and the decimal line keeps six places, which rounds to 0.000042. The simplified ratio still shows 1:24000.

Does order matter?

Yes. 2 and 1 display as 2:1, decimal 2, percent 200%. 1 and 2 display as 1:2, decimal 0.5, percent 50%. The page does not sort them.

Related calculators

• Fraction to Decimal to Percent
• Tip Calculator for an equal split of a bill
• Recipe Scaler
• Volume Converter after a scaled ratio is still in mixed units
• Length Converter
• Percent Change Calculator