Basic Math

Ratio Calculator

Enter a ratio using colons, such as 12:18:30. Simplify reduces it to its smallest whole-number form. Share divides a total amount into parts in that ratio.

Inputsa : b : c

What do you want to do?RatioTotal to share (only for sharing)

Step-by-step

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Fill in the fields and press Solve. The full method will appear here, one numbered step at a time.

6 tools in Basic Math.Back to the tool directory →

Worked example

Share 600 in the ratio 2 : 3 : 5.

1.
Find the highest common factor of all the parts.
```
HCF(2, 3, 5) = 1
```
2.
Divide every part by that factor. Dividing all parts by the same number keeps the ratio the same.
```
2 : 3 : 5 ÷ 1 = 2 : 3 : 5
```
3.
Add the ratio parts to find how many equal shares the total is split into.
```
2 + 3 + 5 = 10
```
4.
Divide the total by that number of shares to find the value of one share.
```
600 ÷ 10 = 60
```
5.
Multiply one share by part 1 of the ratio.
```
2 × 60 = 120
```
6.
Multiply one share by part 2 of the ratio.
```
3 × 60 = 180
```
7.
Multiply one share by part 3 of the ratio.
```
5 × 60 = 300
```
8.
Check: the parts add back up to the original total.
```
120 + 180 + 300 = 600
```

Answer: 120 : 180 : 300

Note: Ratio parts must be positive numbers.

Use “Load worked example” above to run this in the solver.

Related formulas

The formulas this tool uses, each explained with symbols, conditions and its own example in the Formula Library.

Sharing in a ratioshare of part a = a ÷ (a + b) × T