How to use the Ratio Calculator
- Enter the first number, A.
- Enter the second number, B. Decimals are allowed up to four places.
- Read the simplified ratio, for example 3 : 4.
- Use the decimal value and the percentage shares to describe the ratio in other ways.
Formula used
Divide both numbers by their highest common factor. For decimals, multiply both by a power of 10 to make them whole numbers first.
Worked example
Here is the Ratio Calculator worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| First number (A) | 45 |
| Second number (B) | 60 |
| Result | |
| Simplified ratio A : B | 3 : 4 |
| A ÷ B | 0.75 |
| Share of A in the total | 42.86% |
| Share of B in the total | 57.14% |
How a ratio is simplified
To simplify a ratio, divide both numbers by their highest common factor. For 45 : 60 the HCF is 15, and 45 ÷ 15 = 3 and 60 ÷ 15 = 4, so the ratio is 3 : 4. As a decimal, A ÷ B is 0.75, and as shares of the total, A is 42.86% and B is 57.14%.
For decimals, the calculator first scales both numbers up to whole numbers. The ratio 1.5 : 2.5 becomes 15 : 25 and simplifies to 3 : 5.
Ratios in daily life
Screens and photos use ratios such as 16 : 9, which is 1920 : 1080 simplified. Recipes use ratios of ingredients, for example 1 part rice to 2 parts water. Investors compare debt to equity, and teachers talk about student to teacher ratios.
Mixing is a common use: if paint needs 3 parts base to 1 part colour and you want 20 litres in total, you need 15 litres of base and 5 litres of colour. Splitting profit between partners who invested 60,000 and 40,000 is the ratio 3 : 2, so they get 60% and 40% of the profit.
Ratio, fraction and percentage
A ratio compares parts to each other, while a fraction or percentage compares a part to the whole. A ratio of 3 : 4 means the whole has 7 parts, so A is 3/7 and B is 4/7, which is the 42.86% and 57.14% the calculator shows.
This is the most common source of mistakes. A ratio of 3 : 4 does not mean 3 out of 4, it means 3 out of 7 in total.
Edge cases
If one number is zero, the ratio is 0 : 1, which means that part is absent. If both are zero, there is no ratio. A ratio does not need to have whole numbers, but the simplified form always does.
When the numbers are very large or have many decimals, rounding to four decimal places keeps the answer readable.
Frequently asked questions
How do I simplify a ratio?
Divide both numbers by their HCF until no common factor is left.
What does the ratio 3 : 4 mean?
For every 3 units of the first, there are 4 units of the second. Together there are 7 parts.
Can ratios have decimals?
Yes. Multiply both by a power of 10 to make them whole numbers, then simplify.
How do I find a share from a ratio?
Divide the part by the sum of the parts. In 3 : 4, A is 3 ÷ 7.
Is a ratio the same as a fraction?
No. A ratio compares two parts to each other, while a fraction compares a part to the whole.
Can I use three numbers?
This calculator is for two numbers. For three, divide all by their common HCF.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.