Recovering the original amount before a change
The original amount is the base on which the percentage was applied. The change amount is the difference between that base and the final value. The forward check multiplies the recovered original by the same factor to confirm the entered final amount. With two changes, the intermediate amount is after the first, and the net percentage uses the original amount as its base. A negative net percentage means the final amount is lower.
If you know both the original and final amounts and want the change rate instead, use the Percentage Calculator in its percentage-change mode.
The formula
p is the nonnegative percentage of the original amount. A decrease must be below 100% to have a unique reversible nonnegative base. A 100% reduction makes every original amount become zero, so the original cannot be recovered from the final value alone. Each stage has its own base. Multiply stage multipliers rather than adding percentages; then divide the known final amount by their product.
Recovering a price before a discount
An item costs 80 after a 20% discount. The final price is 80% of the original, so divide 80 by 0.8 to get 100. Adding 20% to 80 gives 96 and does not undo the discount, because that percentage uses a different base.
How to use this calculator
- Enter the final amount and first change percentage and direction.
- If a second change followed, enable it and enter its percentage and direction. Each decrease must be below 100%.
- Read the live original amount, intermediate amount and combined percentage. Expand the chronological amount table to verify the final amount.
Undo multiple changes in the right order
Successive changes multiply. An increase followed by a discount is not generally equivalent to adding their percentages. To undo several known changes, divide by each corresponding multiplier, keeping the interpretation of the original bases clear.
A percentage increase can exceed 100%: an increase of 200% triples an amount. A decrease of more than 100% would move a positive amount below zero and is outside this nonnegative price-and-quantity model. Negative changes should instead be represented by choosing the other direction.
Reverse two successive changes
An amount increased by 20% and then decreased by 10% has multiplier 1.2 × 0.9 = 1.08. If the final amount is 108, the original is 108 ÷ 1.08 = 100 and the intermediate amount is 120. The net increase is 8%, not 10%.
Enter the changes in the order they originally happened. Turning off the second change retains its fields for later use, but excludes it from the calculation. The optional stage supports two known adjustments; it cannot infer a missing rate or recover an original destroyed by a 100% decrease.
Assumptions & limitations
What this calculation assumes
- One or two known successive percentage changes relate the original and final amounts.
- Both amounts are nonnegative.
- Each percentage uses the amount immediately before its change as the base.
What to keep in mind
- A rounded final amount can imply a range of possible original amounts.
- The tool does not infer unknown taxes, discount rates or other missing adjustments; it reverses at most two entered changes.
Common questions
Can I reverse a zero percent change?
Yes. The multiplier is one, so the original and final amounts are identical.
Why not subtract the percentage from the final value?
The final value is a different base. Dividing by the original growth factor restores the correct original amount.
Can I undo two consecutive discounts?
Yes. Enable the second change and choose Decrease for both. For 20% then 10%, the combined multiplier is 0.8 × 0.9 = 0.72, so a final 72 comes from an original 100.
Sources & further reading
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