Ratio Calculator

Simplifying and scaling

A ratio compares two quantities. 16:9 and 1920:1080 describe exactly the same proportion — the second is just the first multiplied by 120. Simplifying divides both sides by their greatest common divisor to give the smallest whole-number form.

Scaling works the other way. Fix one side to the value you need, and the other follows by the same multiplier. That's the operation behind resizing an image without distortion, adjusting a recipe, or converting a scale drawing.

Ratios, fractions and percentages

The same relationship, three notations:

• Ratio — 3:1, comparing parts to each other.
• Fraction — 3/4 of the total is the first part.
• Percentage — 75% of the total is the first part.

The trap is mixing part-to-part with part-to-whole. In a 3:1 ratio there are four parts in total, so the first part is three quarters — not three thirds.

Common uses

• Screen and image sizing — 16:9, 4:3, 3:2 aspect ratios.
• Recipes — scaling a 2:1 rice-to-water ratio to any quantity.
• Mixing — paint, fuel, concrete and cleaning solutions.
• Finance — debt-to-income, current ratio, price-to-earnings.

Scaling a recipe

To triple a recipe that uses 2 cups of rice to 1 cup of water, enter 2:1, then put 6 in the first scaled field. The second solves to 3. Every other ingredient scales by the same factor of three — the ratio is what stays fixed.