Ratio Calculator: Simplify and Scale a Ratio
Enter the two parts of a ratio as whole numbers and a scale factor to see the simplest form and the scaled ratio.
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Formula
- Simplify:
a ÷ g : b ÷ g, where g is the greatest common divisor of a and b - Scale:
a × k : b × k - Decimal:
a ÷ b
Worked example
12:8: the greatest common divisor is 4, so the simplified ratio is 3:2. Scaled by 2.5 it is 12 × 2.5 : 8 × 2.5 = 30:20. As a decimal, 12 ÷ 8 = 1.5.
Frequently asked questions
How do you simplify a ratio?
Divide both parts by their greatest common divisor. For 12:8 the divisor is 4, so the ratio simplifies to 3:2.
How do you scale a ratio up or down?
Multiply both parts by the same number. Scaling 12:8 by 2.5 gives 30:20, which is still 3:2 in simplest form.
What does a ratio as a decimal mean?
It is the first part divided by the second. For 12:8 that is 12 ÷ 8 = 1.5, meaning the first part is one and a half times the second.
Why must the parts be whole numbers?
Simplifying needs a common whole-number divisor. To simplify a ratio with decimals, multiply both parts by 10 or 100 first, so 1.5:2.5 becomes 15:25, which simplifies to 3:5.