Why should I not add the percent back after a discount?
Because the percent was based on the original value, not the discounted value. A 20% discount leaves 80%, so the reverse step is dividing by 0.80.
Reverse Percentage Calculator
Back out the original value when you know the final value and the percentage increase or decrease that produced it.
Work backward from the final value
Every percent increase or decrease creates a multiplier. Reverse percentage divides by that multiplier instead of adding or subtracting the percentage a second time.
Find the original value
- Choose increase or decrease.
- Convert the percent to a multiplier.
- Divide the final value by the multiplier.
- Sanity-check that the direction makes sense.
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Reverse percent change
Use the increase multiplier for values that grew and the decrease multiplier for values that shrank.
Increase multiplier
Decrease multiplier
Original from multiplier
Reverse increase
Reverse decrease
Mistakes this avoids
- Adding 20% after a 20% discount.
- Mixing up final value and original value.
- Using a zero multiplier after a 100% decrease.
- Treating a reverse problem like a forward percent-change problem.
FAQ
What happens with a 100% decrease?
The multiplier is zero. If the final value is zero, many originals could have led there; if the final value is not zero, the inputs contradict each other.
