Ratio Calculator
Simplify any ratio to its lowest terms and solve proportions. Enter two numbers to reduce A:B, and a third to solve A:B = C:?
16 : 9 = 32 : 18
How to use this calculator
Enter the two numbers of your ratio (A and B) to see it simplified and as a decimal. To solve a proportion, also enter C and the calculator finds the missing value so that A:B = C:?.
How ratios work
A ratio compares two quantities. Simplifying means dividing both sides by their greatest common divisor so the ratio is in its smallest whole‑number form. A proportion states that two ratios are equal, and you can solve for any missing term by cross‑multiplying.
Worked example
To scale a recipe: if 2 cups flour : 3 cups water and you use 6 cups flour, solve 2:3 = 6:? → ? = (3 × 6) ÷ 2 = 9 cups water.
The formula
Simplify: divide A and B by GCD(A, B) · Solve: ? = (B × C) ÷ A
Frequently asked questions
How do you simplify a ratio?
Divide both numbers by their greatest common divisor (GCD). For example, 16:9 is already in lowest terms, while 20:30 simplifies to 2:3 because both divide by 10.
How do you solve a proportion?
A proportion sets two ratios equal: A:B = C:D. To find a missing value, cross‑multiply. Given A, B, and C, the missing D = (B × C) ÷ A.
What is a ratio as a decimal?
Divide the first number by the second. The ratio 16:9 equals 16 ÷ 9 ≈ 1.78, which is how aspect ratios are often compared.
Can I use decimals in a ratio?
Yes. The calculator accepts decimal inputs and still simplifies and solves correctly by scaling the values to whole numbers internally.