How do I work back to the original price from a discounted price?
To find the original price, divide the discounted price by one minus the discount rate, and do not simply add the percentage back, which gives a wrong answer.
It happens to every seller. You sold an item at a discount, the price on the invoice is final, and now you need the original price. Maybe you are checking your margin, fixing a listing, or answering a customer. The method is short, but one common shortcut gives the wrong answer.
The correct method
If the discount is a percentage, the customer paid a fraction of the original price. Divide the discounted price by that fraction.
Original price = discounted price divided by (1 minus discount rate).
For 20 percent off, the fraction paid is 1 - 0.20 = 0.8.
A worked example
An item sells at Rs 720 after 20 percent off.
720 divided by 0.8 = Rs 900.
Check it by going forward. 20 percent of Rs 900 is Rs 180. Rs 900 - Rs 180 = Rs 720. It matches.
The common mistake
Many people take Rs 720 and add 20 percent on top. 20 percent of 720 is Rs 144, so they get Rs 864.
This is wrong, because the 20 percent was taken from the original price, not from Rs 720. Test it. 20 percent off Rs 864 is Rs 172.80, which leaves Rs 691.20, not Rs 720. So Rs 864 is too low by Rs 36.
The error grows as the discount grows. At 50 percent off, adding 50 percent to the sale price gives you only 1.5 times it, when the right answer is double.
Other discount rates
You can apply the same method to any discount.
- 10 percent off, divide by 0.9. A price of Rs 450 came from Rs 500.
- 25 percent off, divide by 0.75. A price of Rs 600 came from Rs 800.
- 40 percent off, divide by 0.6. A price of Rs 480 came from Rs 800.
If two discounts were stacked, multiply the fractions first. For 20 percent then 10 percent, the fraction is 0.8 x 0.9 = 0.72. That is why successive discounts do not add up. Then divide the final price by 0.72.
When this helps you
- Auditing an old sale. You can see if a product that sold at Rs 720 had enough margin by comparing it with your cost.
- Checking a coupon. A customer reports the final amount she paid, and you want to confirm the right discount was applied.
- Setting the listed price for a planned sale. If you want the customer to see a final price of Rs 720 after 20 percent off, you should list the product at Rs 900.
- Reading your own order exports, where you may only have the final amount.
One thing to be careful about
If you show a "was" price next to the sale price, that original price should be one that you genuinely charged before. Inflating a list price only to show a larger discount may mislead buyers and can run into consumer protection rules. Confirm the details with a legal advisor if you are unsure. Avoiding exaggerated claims in product descriptions is a useful read on the same attitude.
Last tip. Whenever you work backwards, run the forward calculation to double-check. It takes ten seconds, and prevents wrongly priced listings. Also see profit when selling below list price to turn the answer into margin.