Ratio Calculator
Simplify ratios to lowest terms or solve A:B = C:D for the missing value.
Written by Golam Rabbani, Founder & Lead Engineer
How to use this ratio calculator
- Choose Simplify to reduce a single ratio, or Solve A:B = C:D to find a missing value.
- In Simplify mode, enter integer values for A and B.
- In Solve mode, fill three of the four fields and leave the unknown blank or as "?".
- Press Calculate to see the simplified ratio or the missing term.
- Use Copy to put the result on your clipboard, or Reset to clear the inputs.
About this ratio calculator
The ratio calculator handles the two most common tasks involving ratios: reducing a ratio to its lowest terms and finding the missing value in an equivalent-ratio equation. Both rely on the same underlying number theory.
Simplifying uses the greatest common divisor: simplified = (A ÷ gcd(A, B)) : (B ÷ gcd(A, B)). For example, 18:24 has gcd(18, 24) = 6, so it simplifies to 3:4. Solving A:B = C:D uses cross-multiplication, since A × D = B × C. If three of the four values are known, the fourth can be rearranged as D = (B × C) ÷ A or C = (A × D) ÷ B. For instance, 2:5 = 6:? cross-multiplies to 2 × ? = 5 × 6, so ? = 30 ÷ 2 = 15, giving 2:5 = 6:15.
Use cases include scaling recipes, comparing aspect ratios, mixing solutions in chemistry, splitting bills proportionally, and reducing fractions.
FAQ
- What does the ratio calculator do?
- It reduces a ratio to its lowest terms in Simplify mode and finds the missing value in an equation of the form A:B = C:D in Solve mode.
- What formula is used to simplify a ratio?
- Both parts are divided by their greatest common divisor: simplified = (A ÷ gcd(A, B)) : (B ÷ gcd(A, B)). The GCD is found with the Euclidean algorithm.
- How is the missing value in A:B = C:D calculated?
- By cross-multiplication. Because A × D = B × C, the missing value is rearranged as D = (B × C) ÷ A or C = (A × D) ÷ B depending on which field is blank.
- What happens if I enter two zeros?
- In Simplify mode, 0:0 is undefined and the tool shows an error. In Solve mode, the divisor must be non-zero — A cannot be zero when solving for D, and B cannot be zero when solving for C.
- Does this tool store my numbers?
- No. The ratio calculator runs entirely in your browser and nothing you enter is sent to a server or saved between visits.
- Is the ratio calculator free?
- Yes. It is free to use with no signup, no account, and no usage limit.