Normally, percentages and ratios are related by the following formula.

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

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