Formulas and sources
Each formula this calculator uses, where it comes from, and what it leaves out. "How it works" shows the same formula with your own numbers.
Final price, percentage off
Simple mode, with one percentage discount
- Final Price
- the price after the discount
- P
- the original price
- D
- the discount as a share of P (20% is 0.20)
A percentage above 100 is not accepted, and the price never goes below zero.
Source: Standard formula; no single publisher.
Final price, amount off
Simple mode, with one amount off
- Final Price
- the price after the discount
- P
- the original price
- D
- the amount off
An amount larger than the price takes it to zero, never below: a $120 coupon on $100 saves $100.
Source: Standard formula; no single publisher.
Two percentage discounts in a row
Simple mode, with a stacked percentage discount
- P
- the original price
- D
- the first discount
- Final Price
- the price after both
- S
- the second discount, taken from the price after the first
20% then 10% takes off 28% in total, not 30%. The effective discount is the total saved ÷ P × 100.
Source: Standard formula; no single publisher.
Two amounts off in a row
Simple mode, with a stacked amount off
- P
- the original price
- D
- the first amount off
- Final Price
- the price after both
- S
- the second amount off
A percentage and an amount can be mixed: each step then uses its own line. Each step takes off at most what is left.
Source: Standard formula; no single publisher.
Percent off from two prices
Find % Off mode
- % Off
- the discount, in percent
- P
- the original price
- S
- the sale price
It is the percentage change from the original price to the sale price, with the sign reversed. A sale price above the original is not a discount and shows an error.
Source: Standard formula; no single publisher.
Original price after a percentage off
Find Original mode, with one percentage discount
- P
- the original price
- S
- the sale price
- D
- the discount as a share of P (30% is 0.30)
A 100% discount cannot be undone: every original price ends at zero, so the calculator says so instead.
Source: Standard formula; no single publisher.
Original price after an amount off
Find Original mode, with one amount off
- P
- the original price
- S
- the sale price
- D
- the amount off
Source: Standard formula; no single publisher.
Sales tax and coupons
Every mode
The tool adds no tax. A store's own coupon generally lowers the price that sales tax is charged on; a manufacturer's coupon may not.
Source: New York taxes the price before a coupon marked as the manufacturer's [1]. California lets the store charge tax on the manufacturer's payment, by contract [2]. The Streamlined Sales and Use Tax Agreement keeps a repaid coupon in the taxed price by default, and lets each member state exclude manufacturers' coupons [3].
Sources
- New York State Department of Taxation and Finance. Tax Bulletin ST-140: Coupons and Food Stamps. Issued March 26, 2010.
- California Department of Tax and Fee Administration. Regulation 1671.1: Discounts, Coupons, Rebates, and Other Incentives, subdivision (b)(5). Business Taxes Law Guide, revision 2026.
- Streamlined Sales Tax Governing Board. Streamlined Sales and Use Tax Agreement, Appendix C, Part I, "Sales price", paragraphs C.1, D.4.a and E.3. As amended through December 19, 2025.
What this calculator does not cover
- It adds no sales tax, shipping or fees.
- It takes the original price as given and does not check how a seller set its "regular" price.
- Find Original works back through one discount, not a stack of two.
- Find Original and Find % Off take the sale price as entered. A total that includes sales tax, shipping or fees gives a wrong original price or percent off.
Sources checked on .