Reverse Percentage: Find the Original Value
After increase: original = final ÷ (1 + p/100). After decrease: original = final ÷ (1 − p/100)..
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Formula and worked example
$120 after a 20% increase came from $100. $80 after a 20% decrease came from $100. Adding the same percentage back is wrong because the base has changed.
Why reverse percentages use division
The percentage was applied to the unknown original value. Reversing the operation therefore means dividing the final value by the multiplier, not applying the percentage in the opposite direction.
Common mistake
Use the original value as the baseline for relative change. A percentage calculation can give a different answer when the denominator changes.
Related percentage guides
Sources & methodology
The formulas are displayed so the result can be checked manually. NIST defines the percent symbol as representing 0.01. The UK Office for National Statistics defines a percentage point as the difference between percentages.