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Ratio Calculator

This ratio calculator simplifies a ratio such as 24 : 36 to its lowest terms, and solves proportions of the form A : B = C : D when one value is missing. It also shows the ratio as a fraction, a decimal and in 1 : x form.

What do you want to do?

Result

24 : 36 = 2 : 3

As a fraction2/3
As a decimal (A ÷ B)0.666667
As 1 : x1 : 1.5

Results update as you type.

How to Simplify a Ratio

  1. If either part is a decimal, multiply both parts by the same power of 10 to make them whole numbers. 1.5 : 2.25 becomes 150 : 225.
  2. Find the greatest common factor of the two parts.
  3. Divide both parts by it.

Example: 24 : 36. The GCF of 24 and 36 is 12, so 24 ÷ 12 : 36 ÷ 12 = 2 : 3.

How to Solve a Proportion

A proportion says two ratios are equal: A : B = C : D. Cross-multiplying gives:

A × D = B × C

Rearrange for the missing value:

  • D = B × C ÷ A
  • C = A × D ÷ B
  • B = A × D ÷ C
  • A = B × C ÷ D

Worked Example

Solve 2 : 3 = 10 : D:

  1. Cross-multiply: 2 × D = 3 × 10
  2. 2D = 30
  3. D = 30 ÷ 2 = 15

Check: 10 : 15 simplifies to 2 : 3. ✓

Tips and Common Mistakes

Keep the order consistent

In a proportion, both ratios must compare things in the same order. If the first ratio is cups of flour : servings, the second must be too.

Parts versus totals

A 1 : 4 mix has 5 parts in total, so the first ingredient is 1/5 of the mix, not 1/4.

Use the same units

Convert both parts to the same unit before simplifying: 30 minutes : 2 hours is 30 : 120, which is 1 : 4, not 15 : 1.

To find the greatest common factor directly, use the GCF and LCM calculator. For ratios written as fractions, the fraction calculator simplifies and combines them.

Frequently Asked Questions

How do you simplify a ratio?

Divide both parts by their greatest common factor. For 24 : 36 the GCF is 12, so the ratio simplifies to 2 : 3. If the ratio has decimals, multiply both parts by 10, 100 or more first to make them whole numbers.

How do you solve a proportion?

Cross-multiply. In A : B = C : D, A × D = B × C. For 2 : 3 = 10 : x, 2x = 30, so x = 15. Then check that both ratios simplify to the same thing.

How do I scale a recipe or mix with a ratio?

Set up a proportion. If a recipe uses 2 cups of flour for 3 servings and you want 10 servings, solve 2 : 3 = x : 10, giving x = 6.67 cups. The same works for mixing ratios, such as fuel and oil or concrete.

What is a 16 : 9 ratio?

It's the standard widescreen aspect ratio. Screens of 1920 × 1080 and 3840 × 2160 pixels both simplify to 16 : 9. To find a matching height for a given width, solve 16 : 9 = width : height.

Is a ratio the same as a fraction?

Closely related. The ratio 2 : 3 compares two parts, and can be written as the fraction 2/3 when comparing the first part to the second. But in a 2 : 3 mix, the first part is 2/5 of the total, not 2/3, because there are 5 parts in all.

How do I split an amount in a given ratio?

Add the parts of the ratio, divide the amount by that total, then multiply by each part. To split $500 in the ratio 2 : 3, there are 5 parts of $100 each, so the shares are $200 and $300.

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