Calculator for Plus-Minus Percent

If to a value x percent is added and then x percent of the new value is subtracted, the result is lower than the initial value. Also if subtracted first and then added, the value will be lower, the result is identical in both cases.

± % is .

This is % of the initial value.

Example: if to 200 30 % is added, you get 260. If from 260 30 % is subtracted, the result is 182. This is 91 percent of the initial value.
If from 200 30 % is subtracted, you get 140. Add 30 % to 140 to get 182 again.

This effect stems from the mathematical properties of percentage change and the non-linear scaling of values in multiplicative operations. The cause of this phenomenon lies in the way percentage changes build upon one another. A percentage increase or decrease always refers to the current value, not the original starting value. If you increase a value by x percent, then the new value becomes the basis for the subsequent percentage decrease, and vice versa. Since the percentage change is not symmetrical about the starting value, this results in a net loss. Put simply: there is a starting value and a result value. Profit always works with the lower of the two, loss always with the higher of the two.

This principle is particularly relevant when calculating price changes, currency exchange rates, or compound interest. For example, if a currency depreciates by 10 % and then appreciates by 10 %, the final value will not return to its initial level, but will be lower. The same applies to securities such as stocks and bonds. A 20 % price increase followed by a 20 % decrease does not lead back to the original price, but rather to a net loss of 4% of the initial value. This effect demonstrates that percentage changes cannot simply be reversed by applying the inverse operation.