Math
Reverse percentages: how to find the original value
Recover an original value from a final amount after a discount, increase, tax or markup.
A reverse percentage starts with the final value and works backward to the original base.
After a discount
original = final value / (1 - discount / 100)If a price is 720 after a 20% discount:
720 / 0.80 = 900After an increase or tax
original = final value / (1 + increase / 100)If a total of 116 includes a 16% increase:
116 / 1.16 = 100Do not simply add 20% to a price after a 20% discount. The final value and original value are different bases: 80 x 1.20 = 96, not 100. Divide by the multiplier that produced the final value.
Verify by applying the original percentage again. The percentage calculator can help with both the forward check and the intermediate percentage amount.