How-to guides · 3 min read
Reverse Percentage: How to Find the Original Price
The common mistake
Adding 20% to 64 gives 76.8, which is wrong. The 20% was taken off the original, not off 64, so the base is different.
The correct method
Convert the situation to a multiplier. A 20% discount leaves 80% = 0.8 of the original. So original = sale price ÷ 0.8.
64 is 80% of what?
- 64 is 80% of 80
Step-by-step working 2 steps
- 1Turn the percent into a decimal
80% = 80 ÷ 100 = 0.8
- 2Divide the part by that decimal
64 ÷ 0.8 = 80
Working backwards from an increase
A price of 150 after a 25% rise means 150 is 125% of the original: original = 150 ÷ 1.25 = 120.
150 is 125% of what?
- 150 is 125% of 120
Step-by-step working 2 steps
- 1Turn the percent into a decimal
125% = 125 ÷ 100 = 1.25
- 2Divide the part by that decimal
150 ÷ 1.25 = 120
Removing sales tax
A total of 108 includes 8% tax: price before tax = 108 ÷ 1.08 = 100. See also how to calculate a discount and sale price.
Frequently asked questions
How do I find the original price before a discount?
Divide the sale price by (1 − discount as a decimal).
How do I find the price before tax?
Divide the total by (1 + tax rate as a decimal).
Keep reading
Percentage Increase and Decrease: Formulas and Examples
How to calculate percentage increase and decrease, find the new value, and why a 25% rise followed by a 25% fall does not return you to the start.
Money & everydayMarkup vs Margin: The Difference, Formulas and Examples
Markup is profit as a percent of cost; margin is profit as a percent of price. Formulas, conversions and a worked example with a comparison table.
Money & everydayHow to Calculate a Discount and Sale Price (Stacked Too)
Calculate the discount amount, the sale price, stacked discounts and tax with clear formulas and worked examples.
How-to guidesHow to Convert a Fraction to a Percent (With Examples)
Convert any fraction to a percent in two steps: divide, then multiply by 100. Worked examples for 3/8, 7/20 and 5/6, plus mixed numbers.