Ratio Calculator

Many everyday problems are proportions in disguise: if 3 parts concentrate make 4 litres, how much for 9 parts? Fill in any three of the four boxes (A is to B as C is to D) and leave one empty; this calculator finds the missing value. Fill in all four to test whether two ratios match.

How to use it

1. Enter three of the four values.
2. Leave the one you want to find empty.
3. Read the solved value and the completed proportion.
4. Fill in all four boxes to test whether two ratios are equal.

When it helps

• Scaling a recipe up or down.
• Working with map and model scales.
• Solving proportion problems in maths.
• Mixing paint, concrete or chemicals in the right proportions.

Good to know

• Keep units consistent on both sides of the proportion.
• A zero in the wrong spot makes some proportions unsolvable, and the tool tells you which.
• When the numbers allow it, the simplest whole-number form of the ratio is shown.

How a proportion is solved

A proportion says two ratios are equal: A divided by B equals C divided by D. To find a missing value, cross-multiply. If A, B and C are known, D equals B times C divided by A. The tool picks the right formula for whichever box you leave empty.

If all four are filled, it compares A times D with B times C. If they match, the ratios are equal.

Worked example: scaling a recipe

A recipe uses 3 cups of flour for 4 servings. How much for 9 servings? Put 3 as A, 4 as B, leave C empty, and enter 9 as D. The tool gives C equals 6.75 cups. Another example: a map scale of 1 to 50,000 means 3 cm on the map is 150,000 cm, or 1.5 km, on the ground.

The same approach works for mixing concrete, diluting cleaning products and converting currencies.

Simplifying ratios

To simplify a ratio such as 12:18, divide both numbers by their greatest common divisor, 6, giving 2:3. The tool shows this when the numbers are whole. For decimals, multiply both by a power of ten first.

Ratios can also be written as fractions, and a ratio of 2:3 means the first part is two fifths of the total.

Common ratio mistakes

The most common mistakes are mixing units, such as minutes with hours, and putting numbers in the wrong order. A:B is not the same as B:A. Keep the same quantity in the same position on both sides.

Also be careful when a ratio refers to parts of a whole. A 1:3 mix of paint and water is 1 part paint to 3 parts water, which makes 4 parts in total, so the paint is a quarter.

Questions