How this is calculated

The final amount is the original multiplied by a factor. Divide by that factor to recover the original.

original = final / (1 ± percent / 100)

  1. After an increase, divide by 1 plus the rate. 110 / 1.10 = 100.
  2. After a decrease, divide by 1 minus the rate. 90 / 0.90 = 100.
  3. A 100% decrease is not reversible, because the factor would be zero.

110 decreased by 10% is 99, not 100. That is why reverse percentage is a division, not a second application of the same percent.

Not the same as

Reverse percentage looks backward. The nearby tool looks forward.

Reverse-percentage questions

100. Divide 110 by 1.10.

100. Divide 90 by 0.90.

10% of 110 is 11, so 110 − 11 = 99. The 10% was taken on the original amount, not on the final amount.

Change needs both original and new values. Reverse percentage needs the final amount and the percent that was applied.

Open percentage change

No. The factor would be zero. The calculator reports that the percentage must be less than 100 in that mode.

200. That is the same reverse-decrease math with shopping labels, also available on the discount calculator.

Open the discount calculator