Ratio Calculator
Simplify any ratio to its lowest whole-number terms, or solve a proportion (a:b = c:x) for the missing value — with decimal and percentage equivalents.
Ratio Calculator
Simplified Ratio
16 : 9
Decimal: 1.7778
How It Works
A ratio compares two (or more) quantities. This calculator does the two most common ratio tasks. First, simplifying: a ratio like 16:9 or 40:60 is reduced to lowest terms by dividing both numbers by their greatest common divisor (GCD) — so 40:60 becomes 2:3. It also shows the ratio as a decimal and as percentages, which is handy for splits and mixes. Second, solving a proportion: when two ratios are equal (a:b = c:x) and one value is unknown, you find it by cross-multiplication — x = (b × c) ÷ a. Proportions appear constantly in real life: scaling recipes, converting map distances, mixing paint or fuel, adjusting screen aspect ratios, and splitting profits or bills. Because ratios are unit-free, the same simplified ratio applies whether you are dealing with rupees, litres, or pixels.
Formula
Simplify: divide both terms by their GCD. Proportion a:b = c:x → x = (b × c) ÷ a (cross-multiplication).
Frequently Asked Questions
How do I simplify a ratio?
Divide both numbers by their greatest common divisor (GCD). For 40:60, the GCD is 20, so the simplified ratio is 2:3. This calculator does it automatically, even for decimals.
How do I solve a proportion?
For a:b = c:x, cross-multiply: x = (b × c) ÷ a. Example: 2:3 = 8:x → x = (3 × 8) ÷ 2 = 12. Use the "Solve Proportion" tab to find the missing value.
Can I use decimals in a ratio?
Yes — the calculator scales decimal inputs to whole numbers before simplifying, so 1.5:2.5 correctly reduces to 3:5.
What is the difference between a ratio and a fraction?
A ratio compares two quantities (a:b), while a fraction expresses a part of a whole (a/b). They are closely related — a:b can be written as the fraction a/b — but ratios can also compare more than two parts (a:b:c).
Where are ratios used in real life?
Everywhere: recipe scaling, map scales, aspect ratios (16:9), fuel/oil mixes, financial ratios, splitting bills or profits, and mixing solutions. Simplifying and solving proportions makes these calculations quick.