Reverse Percentages: Find the Original Value

A reverse-percentage calculation starts with a final value and works backward to the original. It is useful for sale prices, markups, tax-inclusive amounts and values after growth.

Original value before a discount

After a discount of d percent, the final amount represents 100% minus d percent of the original.

original = final value ÷ (1 − discount percentage ÷ 100)

Example: A price is 80 after a 20% discount. The remaining share is 0.80, so the original price is 80 ÷ 0.80 = 100.

Original value before an increase

After an increase of r percent, the final amount represents 100% plus r percent of the original.

original = final value ÷ (1 + increase percentage ÷ 100)

Example: A value is 120 after a 20% increase. The growth factor is 1.20, so the original value is 120 ÷ 1.20 = 100.

Why simply adding or subtracting fails

If 80 is the price after a 20% discount, adding 20% of 80 produces 96, not the original 100. The discount was calculated from the unknown original base, not from the final price. Reverse calculation therefore uses division by the remaining or increased share.

Recover a pre-tax amount

If a final amount includes a percentage tax, treat the tax as an increase.

Example: A tax-inclusive total is 107 with a 7% tax rate. The pre-tax amount is 107 ÷ 1.07 = 100.

This is different from subtracting 7% of 107, which would give 99.51. That subtraction uses the wrong base.

Boundary cases

A 100% discount leaves zero, so a non-zero original value cannot be recovered from the final zero alone.
A discount above 100% is unusual and may not represent an ordinary price calculation.
Keep the final amount and percentage in matching units and apply rounding only at the end.
If several increases or discounts occurred, reverse them in the opposite order using each separate factor.

Common mistake: “20% off” means 80% remains. Divide by 0.80; do not divide by 0.20.

Use the reverse-percentage calculator