How to use this ratio calculator
- Enter three values across the boxes A, B, C and D.
- Leave one box blank, that is the term you want to find.
- Read the missing value and the simplified ratio, they update as you type.
How to solve a ratio
Two equal ratios form a proportion, written A : B = C : D. Because the two sides are equal, the cross-products match: A × D = B × C. That single rule lets you find any missing term. If D is unknown, rearrange to D = B × C ÷ A. The same idea works for any position: C = A × D ÷ B, B = A × D ÷ C, or A = B × C ÷ D.
To simplify a ratio, divide both sides by their greatest common divisor (GCD), the largest number that divides both terms exactly. Reducing a ratio does not change its meaning, it just states it in the smallest whole numbers, which makes proportions far easier to read and compare.
A worked example
Suppose a recipe uses flour and sugar in the ratio 2 : 5, and you have 8 cups of flour. How much sugar keeps the same proportion? Set it up as 2 : 5 = 8 : D and cross-multiply: D = 5 × 8 ÷ 2 = 20 cups. To simplify a ratio such as 18 : 24, the GCD of 18 and 24 is 6, so dividing both by 6 gives 3 : 4.
Frequently asked questions
How do I solve a ratio with a missing value?
Write the two ratios as a proportion, A:B = C:D, then cross-multiply. If D is the unknown, D = B × C ÷ A. For example, 2:5 = 8:? gives ? = 5 × 8 ÷ 2 = 20.
How do I simplify a ratio?
Divide both numbers by their greatest common divisor. For 18:24 the GCD is 6, so the simplified ratio is 3:4. The calculator does this automatically for whole numbers.
What is a proportion?
A proportion is a statement that two ratios are equal, written A:B = C:D. If three of the four terms are known you can always solve for the fourth.
Can I use decimals?
Yes. Enter decimal values in any box and the missing value is solved the same way, shown rounded to four significant figures.