Reverse percentage calculator
To work backwards from a figure that has already been increased or discounted, divide rather than subtract. The boxes above do the division; below is which number to divide by.
12 × 12 = 144
Adding 12 to itself 12 times gives the same answer.
The one rule
A percentage change is a multiplication, so undoing it is a division. Find the multiplier first, then divide the figure you have by it.
- After an increase of r%: divide by 1 + r/100. A price of 120 after a 20% rise was 120 ÷ 1.2 = 100.
- After a discount of r%: divide by 1 − r/100. A sale price of 63 after 30% off was 63 ÷ 0.7 = 90.
Why subtracting fails
Taking 20% off 120 gives 96, not 100 — because that 20% is calculated on the larger figure rather than on the original. The bigger the percentage, the wider the gap: 50% off 100 leaves 50, but adding 50% back to 50 only reaches 75. Division is the only move that returns you to where you started.
Removing a tax already included
Prices quoted with a sales tax or VAT already inside them are handled the same way. At a 20% rate, divide the gross figure by 1.2 to get the net; the difference between the two is the tax. Dividing by 1.2 and multiplying by 0.2 answer two different questions, so decide which you want before you press anything.
When the answer looks wrong
- An original smaller than a discounted price means you divided by 1.3 where you needed 0.7.
- An original barely different from the figure you started with means the rate went in as 0.3% instead of 30%.
- Check by going forwards: multiply your answer by the multiplier and you should land exactly on the figure you began with.
For the forward direction, use the discount percentage calculator, and for turning rates into multipliers see the decimal to percentage calculator. The full list is under calculators.