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Calculators

Ratio Calculator & Simplifier

Simplify ratios to lowest terms, scale one side of a ratio to a new value, and solve proportions for the missing number.

Simplify a ratio

:
16 : 9
Decimal: 1.777778

Scale proportionally

Matching other side
720

Solve proportion A : B = C : D (find D)

D = 8.4375

Simplification divides by the greatest common divisor. All math runs locally.

Interpreting the Result

A ratio of 3:1 is the same relationship whether the units are cups, pixels or dollars — but the direction matters: 3:1 water to concentrate is not 1:3. When a recipe or spec says "dilute 1:4", confirm whether it means one part in four total (20%) or one part added to four parts (25%); both conventions exist and the difference shows up in the result.

The Formula Behind the Result

  1. Enter two values to simplify their ratio using the greatest common divisor.
  2. Scale mode: change one side of the ratio and the other side scales proportionally.
  3. Proportion mode: enter three values of A:B = C:D and the fourth is solved for you.
  4. Decimal equivalents are shown alongside exact fraction results.
Formula & Technical Standard
Simplification divides both sides by GCD(a,b). Proportions solve via cross-multiplication: D = (B × C)/A.

Worked Example

Simplify a ratio
Input: 1920 : 1080
Output: 16 : 9
GCD(1920,1080) = 120; dividing both sides gives the familiar 16:9 display ratio.
Solve a proportion
Input: 3 : 4 = 15 : ?
Output: 20
Cross-multiplication recovers the missing value — the core of recipe scaling and map scales.

Common Questions

Can ratios include decimals?

Yes. Decimal inputs are converted to integer ratios by scaling before simplification, and the decimal equivalent of the result is shown.

How is this different from the aspect ratio calculator?

That tool is specialized for screen resolutions with pixel context. This one is a general-purpose ratio and proportion solver.