Everyday math
Find the original amount when you know a percentage and the resulting part.
Enter your numbers to see the answer.
Reverse Percentage Calculator guide
A reverse percentage problem starts at the end: you know a resulting amount and the percentage it represents, and you want the original figure it came from. Enter the known result and the percentage, and the calculator divides the result by the percentage expressed as a decimal. Typical questions are “the sale price is $60 after 25% off, what was the full price” (the sale price is 75% of the original), “I received $80, which is 80% of the invoice after a fee, what was the full invoice”, or “this tax-inclusive total includes 20% VAT, what was the net amount” (the total is 120% of the net). The key is to enter the percentage that the known amount represents of the original, not the percentage that was added or removed. This distinguishes the tool from the percentage-reverse calculator, which takes two amounts and returns a percent.
Original value = known result ÷ (percentage ÷ 100).
Worked example with the defaults: known result 80, percentage 80%. Convert the percentage to a decimal: 80 ÷ 100 = 0.8, which the calculator lists as “Percentage as decimal 0.8”. Divide the known result by it: 80 ÷ 0.8 = 100. The original value was 100, shown with the caption “80 is 80% of the original”. A sale example follows the same pattern: a $60 price after a 25% discount is 75% of the original, so 60 ÷ 0.75 = $80.
The known result carries whatever unit the original has (dollars, kilograms, points) and the answer comes back in the same unit. The percentage field is entered as a plain number, 80 for 80%, and the calculator divides it by 100 internally. A percentage above 100 is valid and means the known result is larger than the original, as with a tax-inclusive total.
The result follows directly from the numbers you entered, so its accuracy is the accuracy of those inputs. The most common source of a surprising answer is a mismatch between the question you meant to ask and the one the calculator answered, so re-read the field labels if the figure looks wrong. The formula is shown above so you can check the arithmetic yourself. On this page the figure rests entirely on known result and percentage, so start there if the reverse percentage calculator returns something you did not expect.
Good to know: after a discount, enter 100 minus the discount, not the discount itself; a 25% markdown means the price is 75% of the original. After a surcharge or tax, enter 100 plus the rate: a total including 20% tax is 120% of the net. Entering the discount rate directly (60 ÷ 0.25 = 240) gives an absurd answer. A percentage of zero returns no meaningful value because nothing can be recovered from 0%.
Results are planning estimates. Check the units, product coverage, carrier rules, or local rates before making a purchase or financial decision.
How it works
Find the original amount when you know a percentage and the resulting part. This tool explains the calculation so you can adjust the assumptions to match your situation.
Worked example
With Known result = 80 · Percentage = 80 % → 100 (80 is 80% of the original). Change an input above and this example updates with your numbers.
Common questions
100. Convert 80% to the decimal 0.8 and divide: 80 ÷ 0.8 = 100. Check by going forward: 80% of 100 is 0.8 × 100 = 80, which matches the known result.
Subtract the discount from 100 to get the percentage the sale price represents, then divide the sale price by that percentage as a decimal. A $60 price after 25% off is 60 ÷ 0.75 = $80 originally.
The gross total is (100 + rate)% of the net. For 20% tax, divide the total by 1.2: $120 ÷ 1.2 = $100 net, with $20 tax. Enter 120 as the percentage and the total as the known result.
Reverse percentage knows the percent and the part and finds the whole: 80 is 80% of 100. The “what percent is A of B” calculator knows both amounts and finds the percent: 36 of 240 is 15%.
Because the known result was produced by multiplying the original by the percentage. Dividing undoes that multiplication. If original × 0.8 = 80, then original = 80 ÷ 0.8 = 100.