Ratio Calculator
Simplify and compare ratios.
Inputs
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Formula
Simplified ratio a:b = (a ÷ GCD) : (b ÷ GCD)
Both parts of the ratio are divided by their greatest common divisor to express the same relationship in the smallest whole numbers. The decimal form is a ÷ b.
Worked example
16:9 is already in simplest form (GCD is 1) — it's the classic widescreen aspect ratio, and as a decimal 16 ÷ 9 ≈ 1.778.
Where this can give the wrong answer
- The second value (b) cannot be zero — a ratio with a zero second part is undefined, just like division by zero.
- The first value (a) can be zero (0:5 simplifies to 0:1), which means 'none of the first quantity per unit of the second'.
- Non-integer inputs are rounded when computing the GCD internally, so ratios like 16.5:9 may not simplify exactly the way you'd expect from pencil-and-paper integer arithmetic.
FAQ
- A fraction compares one part to a whole (3/12 of a pizza). A ratio compares two quantities to each other (3:12 cups of flour to sugar). This calculator treats the inputs as a ratio a:b, not as 'a out of a+b'.