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CalcMyWay

Ratio Calculator

Your details

Result

Answer

16 : 9
Working
Divide both terms by their greatest common divisor, 1: 16 ÷ 1 = 16 and 9 ÷ 1 = 9.
As a decimal
1.7778 : 1
As percentages
64% : 36%
  • This ratio is already in its lowest terms.

How do you calculate a ratio?

To simplify a ratio, divide both terms by their greatest common divisor — 16 : 9 is already lowest, while 16 : 8 reduces to 2 : 1. To solve a proportion written A : B = C : D, cross-multiply so that D equals B times C divided by A.

A : B → A/g : B/g where g = gcd(A, B) A : B = C : D → D = BC / A
A, B
The two terms of the original ratio
g
Greatest common divisor of A and B
C, D
The two terms of the equivalent ratio

A ratio expresses relative size, so multiplying or dividing both terms by the same number leaves it unchanged — 2 : 3, 4 : 6 and 20 : 30 are the same ratio. Simplifying means finding the largest number that divides both terms exactly, the greatest common divisor, and dividing through by it. Decimal terms are scaled up to whole numbers first, so 1.5 : 2 is handled as 15 : 20 and reduces to 3 : 4. A proportion is the statement that two ratios are equal. Cross-multiplication works because multiplying both sides of A/B = C/D by BD clears the denominators and leaves AD = BC, which rearranges for whichever term is unknown. Scaling is a third, distinct operation: it distributes a known total across the parts in the ratio's proportions, which is what you want for splitting a bill, mixing concrete, or sizing a recipe.

  1. Write the two quantities in order as A : B.
  2. Find the greatest common divisor of both terms.
  3. Divide each term by that divisor.
  4. For decimals, multiply both terms by ten until they are whole first.
  5. To solve a proportion, cross-multiply and divide by the known term.

Worked example: Simplifying 16 : 9, then scaling it to a total of 100

Simplifying 16 : 9, then scaling it to a total of 100

The factors of 16 are 1, 2, 4, 8 and 16; the factors of 9 are 1, 3 and 9. The only common factor is 1, so the greatest common divisor is 1 and 16 : 9 is already in its lowest terms — which is why it is the standard widescreen aspect ratio rather than something larger. As a decimal, 16 ÷ 9 = 1.7778, so the ratio is 1.7778 : 1. Scaling it to a total of 100 is a different operation: the parts sum to 25, so one part is 100 ÷ 25 = 4, giving 64 : 36. That also tells you the percentage split directly — 64% and 36%. Compare 16 : 8, where the greatest common divisor is 8: dividing through gives 2 : 1, which is the same relationship written in the smallest possible whole numbers.

What each ratio input means

What do you want to do?
Pick the question you are answering. The inputs below change to match.
A
The first term of the ratio.
B
The second term of the ratio.
C
Used when solving a proportion: the first term of the second ratio. Leave the unknown term blank.
New total
Used when scaling: the total the parts should add up to.

What this ratio does not account for

  • A ratio containing zero cannot be simplified, because dividing by the greatest common divisor would leave the relationship undefined.
  • Negative terms are reduced by magnitude and keep their signs. A ratio with one negative term is mathematically valid but rarely meaningful in practice.
  • Decimal terms are scaled to integers before reducing, so results are always whole numbers where one exists. Irrational ratios such as 1 : √2 cannot be expressed in whole terms at all.
  • A ratio is not a fraction, although they share notation. 2 : 3 means two parts to three parts, five parts in total — the fraction 2/3 means two of three parts. Mixing them up is the most common error on this topic.
  • When solving a proportion, A is the divisor and cannot be zero.

Frequently asked questions

How do you simplify a ratio?

Divide both terms by their greatest common divisor. For 18 : 24 the greatest common divisor is 6, so dividing gives 3 : 4. If the only common factor is 1, the ratio is already in its lowest terms.

What is the difference between a ratio and a fraction?

A ratio compares two parts to each other; a fraction compares one part to the whole. A ratio of 2 : 3 means five parts in total, with the first quantity being 2/5 of that whole, not 2/3.

How do you solve a proportion?

Cross-multiply. For A : B = C : D, multiply A by D and B by C and set them equal, then divide to isolate the unknown. With 3 : 4 = 9 : D, that gives D = (4 × 9) ÷ 3 = 12.

How do you convert a ratio to a percentage?

Add the terms to get the total, then divide each term by that total and multiply by 100. For 16 : 9 the total is 25, so the split is 64% and 36%. The percentages always sum to 100.

What is a 1 : 1 ratio?

Equal parts. A 1 : 1 ratio means both quantities are the same size, so a total split 1 : 1 is divided in half. It is the simplest form of any ratio where the two terms are equal.

How do you scale a recipe using a ratio?

Keep the ratio fixed and change the total. If a recipe is 2 : 1 flour to water and you want 600g of dough, the parts sum to 3, so one part is 200g — 400g flour and 200g water.

Sources and review

Last reviewed .