Ratio Calculator
Solve a proportion A : B = C : D for the missing value, and see A : B reduced to its simplest whole-number form.
Solve and simplify
Enter three terms to find the fourth, and read off the simplified version of your ratio at the same time.
A cannot be zero
Solving for D divides by A, so the first term must not be zero — division by zero is undefined.
What is a ratio?
Comparing two quantities in proportion
A ratio compares two quantities, written A : B — for example 1 : 2 means the second quantity is twice the first. A proportion states that two ratios are equal, A : B = C : D, so the same relationship holds at a different scale. This calculator answers two everyday questions at once: given three of the four terms, what is the missing one, and what does the reference ratio A : B look like once reduced to its smallest whole numbers?
Enter A, B, and C, and the calculator solves for D while simplifying A : B automatically.
To find the missing fourth term, cross-multiply the diagonal pair and divide by the term opposite the unknown.
D = (B × C) ÷ ASimplifying is separate from solving: divide both terms of A : B by their greatest common divisor (GCD). A ratio of 4 : 6 shares a GCD of 2, so it reduces to 2 : 3 — the same relationship expressed in the smallest possible whole numbers. Simplification only applies when both terms are whole numbers; decimal ratios are left as you entered them.
Suppose a recipe uses 1 cup of rice to 2 cups of water, and you want the water for 5 cups of rice.
Set up the proportion
Write it as 1 : 2 = 5 : D, where D is the unknown amount of water.
Cross-multiply
Multiply the known diagonal: 2 × 5 = 10.
Divide by the opposite term
10 ÷ 1 = 10, so 5 cups of rice need 10 cups of water.
Read the simplified ratio
1 : 2 is already in lowest terms, so the reference ratio stays 1 : 2.
The missing value D only makes sense when the relationship is genuinely proportional — twice the rice means twice the water, every time. Two ratios are equivalent when one is a clean multiple of the other, so 1 : 2, 5 : 10, and 50 : 100 all describe the same mix. The simplified ratio strips a comparison down to its essentials, which makes two ratios easy to compare at a glance: 4 : 6 and 6 : 9 both reduce to 2 : 3, so they are equivalent even though no original term matches.
If you only want to reduce a ratio to lowest terms, the GCF / LCM calculator gives the greatest common divisor directly. For proportion problems that can also run in reverse, or that distinguish direct from inverse relationships, the rule of three calculator covers the same cross-multiplication with both directions.
The arithmetic is exact, but a ratio only models a fixed, proportional relationship.
A constant ratio is an assumption
Solving for D assumes A : B holds at every scale, which real-world quantities often break — bulk discounts, fixed costs, or diminishing returns mean doubling one term need not double the other. Two hard limits also apply: A cannot be zero, because the formula divides by it, and simplification only works on whole numbers, so decimal terms are returned unchanged rather than reduced.