Ratio Calculator

Simplify a ratio to its lowest terms, or scale a ratio up or down to find a missing value — for recipes, mixing, map scales and screen sizes — with each step shown.

12 : 18 simplified
2 : 3
As 1 : n
1 : 1.5
As n : 1
≈ 0.666667 : 1
Share of the total
40% : 60%A is 2/5 of the whole
As a fraction (A ÷ B)
2/3
  • Step 1, find the greatest common divisor of 12 and 18: it's 6 (Euclid's method: 18 = 1 × 12 + 6; 12 = 2 × 6 + 0).
  • Step 2, divide both parts by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so the ratio is 2 : 3.

Simplifying a ratio

A ratio compares two quantities: 12 : 18 means "12 of the first for every 18 of the second". Like a fraction, it can be simplified by dividing both parts by their greatest common divisor. The GCD of 12 and 18 is 6, so 12 : 18 = 2 : 3. The simplified ratio describes exactly the same proportion with the smallest whole numbers.

If a ratio contains decimals, multiply both parts by the same power of ten first to make them whole numbers: 1.5 : 2.5 becomes 15 : 25, which simplifies to 3 : 5. Order matters: 2 : 3 and 3 : 2 are different ratios.

Solving for a missing value

Two equal ratios form a proportion, A : B = C : D. If you know three of the numbers, write them as fractions (A/B = C/D) and cross-multiply: A × D = B × C. Then divide to isolate the unknown. Equivalently, find the scale factor between the known pair (C ÷ A) and apply it to the other part.

This is how you scale a recipe (2 cups of flour for 3 eggs means 6 cups for 9 eggs), read a map scale, resize an image without stretching it, or mix concrete, paint or fuel in the right proportion.

Parts of a whole

A ratio is not the same as a fraction of the total. In a 2 : 3 mix there are 5 parts in all, so the first ingredient is 2/5 (40%) of the mixture, not 2/3. The "Share of the total" result shows this split. To divide an amount in a given ratio, divide it by the total number of parts and multiply by each part: $100 split 2 : 3 is $40 and $60.

Ratio formulas

Simplify: A : B = (A ÷ g) : (B ÷ g), where g = GCD(A, B)Proportion: A : B = C : D ⇔ A × D = B × CMissing D = B × C ÷ A; missing C = A × D ÷ B
  • A, B = the known ratio
  • C, D = the scaled ratio; one of them is unknown
  • GCD = greatest common divisor

Worked example

  1. Simplify 12 : 18. The GCD of 12 and 18 is 6 (18 = 1 × 12 + 6; 12 = 2 × 6 + 0).
  2. 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 12 : 18 = 2 : 3.
  3. Now solve 12 : 18 = 30 : D. Cross-multiply: 12 × D = 18 × 30 = 540.
  4. D = 540 ÷ 12 = 45. Check: the scale factor is 30 ÷ 12 = 2.5, and 18 × 2.5 = 45.

Frequently asked questions

How do you simplify a ratio with decimals?

Multiply both parts by 10, 100 or another power of ten until they're whole numbers, then divide by the GCD. 1.5 : 2.5 × 10 = 15 : 25, and dividing by 5 gives 3 : 5.

How do I scale a recipe with a ratio?

Find the scale factor and multiply every ingredient by it. If a recipe for 4 servings needs 3 cups of flour and you want 10 servings, the factor is 10 ÷ 4 = 2.5, so you need 3 × 2.5 = 7.5 cups.

How do I split an amount in a ratio?

Add the parts, divide the amount by that total, then multiply by each part. Splitting $100 in the ratio 2 : 3: there are 5 parts, each worth $20, so the shares are $40 and $60.

What is a 16:9 ratio in numbers?

It's the shape of most widescreen displays: 16 units wide for every 9 tall. A screen 1,920 pixels wide is 1,920 × 9 ÷ 16 = 1,080 pixels tall at 16:9.

Is a ratio the same as a fraction?

Closely related but not identical. The ratio 2 : 3 can be written 2/3 to compare the parts, but the first part is 2/5 of the whole, because the whole has 2 + 3 = 5 parts.

Sources

Last reviewed for 2026. How we calculate.