Understanding your result
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.
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.
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 amount after the change, not the original amount you want to find.
- Enter the percentage that was applied and whether it was an increase or decrease.
- Read the recovered original and use the forward check to verify the interpretation.
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.
Assumptions & limitations
What this calculation assumes
- One known percentage change relates the original and final amounts.
- Both amounts are nonnegative.
- The percentage uses the original amount as its base.
What to keep in mind
- A rounded final amount can imply a range of possible original amounts.
- The tool does not infer missing taxes, successive discounts, or other adjustments.
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.