Normally, percentages and ratios are related by the following formula.
| percent | = | 100 | × | ratio |
However, when you are comparing the value of something before and after a change the above formula is not used. The ratio is computed as usual:
| improvement ratio | = | value after change | |||
| value before change |
But the improvement percentage is given by:
| improvement percent | = | 100 | × | (improvement ratio | - | 1) |
This formula should also be used when you are looking for a percent change or a percent increase.
The above formula can also be solved to compute an improvement ratio given an improvement percent.
| improvement ratio | = | improvement percent/100 | + | 1 |