Percentages
Recovering the original from the new value
Divide rather than subtract. Removing 25.00% from 100 is not the same as undoing a 25.00% rise, which is why this form is worth memorising.
The Formula
Original = New / (1 + p)
Divide rather than subtract. Removing 25.00% from 100 is not the same as undoing a 25.00% rise, which is why this form is worth memorising.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| p | Known increase as a decimal | decimal | The rate that was applied, so 25.00% is entered as 0.25. |
| Vn | Value you already have | number | 100 divided by 1.25 returns the original 80. |
| V0 | Value you are solving for | number | Always smaller than the new value when the increase was positive. |
What Each Symbol Means
pdecimal
Known increase as a decimal
The rate that was applied, so 25.00% is entered as 0.25.
Vnnumber
Value you already have
100 divided by 1.25 returns the original 80.
V0number
Value you are solving for
Always smaller than the new value when the increase was positive.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate percent increase page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Percent Increase, filed under Math. Every number the guide produces comes from substituting into this one line.