How do I simplify a ratio?

Divide every term by the greatest common divisor of all of them. For 18:24 the GCD is 6, giving 3:4. The tool shows the divisor it used and the scale factor to get back, so you can check the reduction rather than trust it. Ratios of three or more terms reduce the same way, so 12:18:30 becomes 2:3:5.

What about ratios with decimals?

They are scaled to integers first. 1.5:2 is multiplied by 10 to give 15:20, which reduces to 3:4. This matters because a greatest common divisor is only defined for integers: a calculator that runs GCD directly on 1.5 and 2 returns the input unchanged and looks like it worked, which is the most common wrong answer in this category.

How do I solve a proportion?

Choose Solve for x and enter 3:4 in the first box and 9:x in the second. Cross-multiplication gives x = (4 × 9) ÷ 3 = 12. Fractional terms work too: 1/2:3/4 = 2:x gives x = 3. You may put the whole proportion in the first box if the second is empty. Multiple distinct unknowns can be solved when a known matching pair fixes the scale: 3:4:5 = 9:x:y gives x = 12 and y = 15. A repeated unknown or an unknown on both sides of the same position needs algebra this page does not solve.

Can I use / or the word 'to' instead of a colon?

A lone slash separates a ratio: 16/9, 16:9 and 16 to 9 mean the same thing. When a colon or the word to separates the ratio terms, a slash within a term is a fraction bar: 1/2:3/4 or 1/2 to 3/4 means two fractional terms and reduces to 2:3. Use this explicit form for fractions; mixed numbers such as 1 1/2 must first be written as 3/2 or 1.5.

What does the percentage split mean?

Each term expressed as a share of the whole. For 3:4 that is 42.86% and 57.14%, which is the form you want when the ratio describes how something is divided rather than how two quantities compare. The decimal reading, 0.75, is the first term divided by the second, which is what you want when comparing.

Is 0:5 a valid ratio?

Yes, and it reduces to 0:1. A ratio with a zero term is meaningful as long as they are not all zero. An all-zero ratio has no defined reduction, since every number divides zero, and the tool says that rather than returning 0:0 or dividing by zero.

How do I simplify a ratio of fractions?

Use a colon between fractional terms. For 1/2:3/4, the least common denominator is 4. Multiplying each term by 4 gives 2:3, which has no common factor above 1. For 2/3:4/5, multiply by 15 to get 10:12, then divide by 2 to get 5:6. Fractions can also appear in a proportion, and zero denominators are rejected.

How do I convert a ratio to a fraction or decimal?

For a comparison ratio a:b, the fraction is a/b. The simplified 3:4 is 3/4, and its decimal is 0.75. A part-to-whole fraction uses a different denominator: the first share of 3:4 is 3/(3+4) = 3/7 and the second is 4/7. The percentage split reports those shares, not 75%. Choose the slash output separator to copy the simplified comparison as a fraction.

How do I convert a percentage to a ratio?

For a percentage of a whole, compare it with the remainder: 25%:75% reduces to 1:3. If you mean the part against the entire whole, enter 25%:100% for 1:4. Percent signs are read as division by 100, so both sides must use matching units: 25:75% is a different ratio.

How do I scale a ratio or check equivalent ratios?

Use Solve for x. Scaling 3:4 to a first term of 9 is 3:4 = 9:x, giving x = 12. Scaling to a total of 70 requires 3:7 = x:70 for the first share and 4:7 = y:70 for the second, giving 30 and 40. For a three-part ratio, 2:3:5 = 20:x:y gives 20:30:50. Enter all known terms, such as 3:4 = 9:12, to check equivalence instead of solving an unknown.

Can this calculate aspect ratios, coffee ratios or specialized models?

For screen, image and video dimensions, use Aspect Ratio Calculator; for coffee and water weighed in grams, use Coffee Ratio Calculator. This page reduces supplied numeric terms and solves proportional scaling. It does not determine medical ratios, engine compression, fuel mixtures, debt qualification, geometry-derived surface-to-volume ratios or units from raw measurements.

Ratio Calculator

Simplify ratios of whole numbers, decimals, percentages or fractions, then inspect the exact scale factor and working. Enter 18:24 for 3:4, 1/2:3/4 for 2:3, or 25%:75% for 1:3. Switch to Solve for x to scale 3:4 = 9:x and get x = 12, or check whether two known ratios are equivalent.

Simplified · divided by 63 : 40.75 as a decimal · 42.86% : 57.14% · scale factor 6

Ratio

Mode

Separator

Use a colon or the word “to” between fractional terms: 1/2:3/4 reduces to 2:3. A lone slash, 18/24, means the ratio 18:24. Whole numbers, decimals, scientific notation and percentages also work.

Simplifiedgreatest common divisor 6
3 : 4
As a decimalfirst term ÷ second, exact
0.75
As a percentage spliteach term's share of the total, adding to exactly 100%
42.86% : 57.14%
Scale factormultiply the simplified form by this to get back what you typed
6
Greatest common divisorthe number every term was divided by, once the denominators were cleared
6

The working

Clear the denominators, then divide through by what every term shares, on paper, and only the steps this ratio actually needed.

Divide every term by their greatest common divisor, 6: 3:4

Ratios worth a try

1.5 : 2 is 3 : 4, not 1.5 : 2. A ratio with decimals has to be scaled to whole numbers before a common divisor means anything. Calculators that run the GCD straight on the decimals hand back the input unchanged and look like they worked. The same goes at the other end of the scale: above about 9 × 10¹⁵ a computer can no longer tell two whole numbers apart as decimals, and 1000000000000000002 : 1000000000000000004 quietly “simplifies” to 1 : 1. Everything here is big-integer arithmetic, so both answers come out right, and where a decimal readout had to be cut short, the row it sits on says so.

Common questions

How do I simplify a ratio?: Divide every term by the greatest common divisor of all of them. For 18:24 the GCD is 6, giving 3:4. The tool shows the divisor it used and the scale factor to get back, so you can check the reduction rather than trust it. Ratios of three or more terms reduce the same way, so 12:18:30 becomes 2:3:5.
What about ratios with decimals?: They are scaled to integers first. 1.5:2 is multiplied by 10 to give 15:20, which reduces to 3:4. This matters because a greatest common divisor is only defined for integers: a calculator that runs GCD directly on 1.5 and 2 returns the input unchanged and looks like it worked, which is the most common wrong answer in this category.
How do I solve a proportion?: Choose Solve for x and enter 3:4 in the first box and 9:x in the second. Cross-multiplication gives x = (4 × 9) ÷ 3 = 12. Fractional terms work too: 1/2:3/4 = 2:x gives x = 3. You may put the whole proportion in the first box if the second is empty. Multiple distinct unknowns can be solved when a known matching pair fixes the scale: 3:4:5 = 9:x:y gives x = 12 and y = 15. A repeated unknown or an unknown on both sides of the same position needs algebra this page does not solve.
Can I use / or the word 'to' instead of a colon?: A lone slash separates a ratio: 16/9, 16:9 and 16 to 9 mean the same thing. When a colon or the word to separates the ratio terms, a slash within a term is a fraction bar: 1/2:3/4 or 1/2 to 3/4 means two fractional terms and reduces to 2:3. Use this explicit form for fractions; mixed numbers such as 1 1/2 must first be written as 3/2 or 1.5.
What does the percentage split mean?: Each term expressed as a share of the whole. For 3:4 that is 42.86% and 57.14%, which is the form you want when the ratio describes how something is divided rather than how two quantities compare. The decimal reading, 0.75, is the first term divided by the second, which is what you want when comparing.
Is 0:5 a valid ratio?: Yes, and it reduces to 0:1. A ratio with a zero term is meaningful as long as they are not all zero. An all-zero ratio has no defined reduction, since every number divides zero, and the tool says that rather than returning 0:0 or dividing by zero.
How do I simplify a ratio of fractions?: Use a colon between fractional terms. For 1/2:3/4, the least common denominator is 4. Multiplying each term by 4 gives 2:3, which has no common factor above 1. For 2/3:4/5, multiply by 15 to get 10:12, then divide by 2 to get 5:6. Fractions can also appear in a proportion, and zero denominators are rejected.
How do I convert a ratio to a fraction or decimal?: For a comparison ratio a:b, the fraction is a/b. The simplified 3:4 is 3/4, and its decimal is 0.75. A part-to-whole fraction uses a different denominator: the first share of 3:4 is 3/(3+4) = 3/7 and the second is 4/7. The percentage split reports those shares, not 75%. Choose the slash output separator to copy the simplified comparison as a fraction.
How do I convert a percentage to a ratio?: For a percentage of a whole, compare it with the remainder: 25%:75% reduces to 1:3. If you mean the part against the entire whole, enter 25%:100% for 1:4. Percent signs are read as division by 100, so both sides must use matching units: 25:75% is a different ratio.
How do I scale a ratio or check equivalent ratios?: Use Solve for x. Scaling 3:4 to a first term of 9 is 3:4 = 9:x, giving x = 12. Scaling to a total of 70 requires 3:7 = x:70 for the first share and 4:7 = y:70 for the second, giving 30 and 40. For a three-part ratio, 2:3:5 = 20:x:y gives 20:30:50. Enter all known terms, such as 3:4 = 9:12, to check equivalence instead of solving an unknown.
Can this calculate aspect ratios, coffee ratios or specialized models?: For screen, image and video dimensions, use Aspect Ratio Calculator; for coffee and water weighed in grams, use Coffee Ratio Calculator. This page reduces supplied numeric terms and solves proportional scaling. It does not determine medical ratios, engine compression, fuel mixtures, debt qualification, geometry-derived surface-to-volume ratios or units from raw measurements.

Simplified ratios, scale factors and solved proportions use exact integer fractions. Decimal previews are truncated and marked with an ellipsis; percentage shares are rounded to two places using largest remainders so they sum to 100%. Inputs that exceed the computational work budget are refused with guidance to reduce the work.