Work backwards from a value that has already changed. Enter the final amount and the percentage to find the original price before a raise, a discount or sales tax, the whole when you know a part, or the starting value before several changes in a row.
Last updated:
What happened to the original value?
In “part” mode: the known part
%
Use + for increases and - for decreases, e.g. +10, -20, +5
Enter your values to see the result.
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How to use the Reverse Percentage Calculator
Choose what happened: an increase, a decrease, added tax, a part of a whole or several changes.
Enter the final value, the amount you can see now.
Enter the percentage, or list each change in order for several changes.
Press Calculate to get the original value, the size of the change and the working.
Reverse percentage formulas
Situation
Formula
Example
Value after a p% increase
original = final ÷ (1 + p/100)
138 ÷ 1.15 = 120
Value after a p% decrease or discount
original = final ÷ (1 − p/100)
68 ÷ 0.80 = 85
Price including tax at p%
pre-tax = total ÷ (1 + p/100)
54 ÷ 1.08 = 50
Part is p% of the whole
whole = part ÷ (p/100)
45 ÷ 0.30 = 150
Several changes p₁, p₂, …
original = final ÷ [(1 + p₁/100)(1 + p₂/100)…]
92.4 ÷ 0.924 = 100
The key idea is that a percentage change multiplies the original. To reverse it, divide by the same multiplier. This is why a 20% discount followed by a 20% increase does not bring you back to the starting price: 100 × 0.8 × 1.2 = 96.
Quick multiplier table
Percent
Increase: divide by
Decrease: divide by
5%
1.05
0.95
10%
1.10
0.90
15%
1.15
0.85
20%
1.20
0.80
25%
1.25
0.75
30%
1.30
0.70
50%
1.50
0.50
Tips
Ask yourself what the percentage was taken of. That amount is the 100% you are looking for.
For receipts, check whether the total includes tax before working backwards, and remember that tax may be rounded to the cent.
A quick check: apply the percentage to your answer and you should get the final value again.
Frequently asked questions
How do you calculate a reverse percentage?
Divide the final value by the multiplier. After a p% increase the multiplier is 1 + p/100; after a p% decrease it is 1 − p/100. If a price is $138 after a 15% rise, the original is 138 ÷ 1.15 = $120.
How do I find the original price before a discount?
Divide the sale price by (1 − discount). A $68 item at 20% off was originally 68 ÷ 0.80 = $85. Adding 20% to $68 gives $81.60, which is wrong because the discount was taken from $85, not $68.
How do I remove sales tax or VAT from a price?
Divide the tax-inclusive price by 1 + the tax rate. With 8% sales tax, $54.00 ÷ 1.08 = $50.00 before tax, so the tax was $4.00. For 20% VAT, 240 ÷ 1.2 = 200.
Why can't I just subtract the percentage?
The percentage was applied to the original value, not to the final one. 15% of $138 is more than 15% of $120, so subtracting 15% of the final price takes off too much. Dividing by the multiplier always gives the exact original.
How do I find the whole when I know a part and its percent?
Divide the part by the percent as a decimal. If 45 is 30% of a number, the number is 45 ÷ 0.30 = 150.
How do I reverse several percentage changes?
Multiply the multipliers together and divide by the result. A value that rose 10%, fell 20% and rose 5% was multiplied by 1.10 × 0.80 × 1.05 = 0.924, so a final value of 92.4 started at 92.4 ÷ 0.924 = 100.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.