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 |