Define the Price Question Before Touching the Formula
Discount problems can ask for different unknowns. A forward checkout calculation starts with an original price and offers, a percent-off comparison starts with original and sale prices, and a reverse calculation starts with sale price and discount terms. Identify the unknown before mixing before-tax prices with checkout totals.
For a direct comparison, confirm that both prices describe the same product, variant, quantity, and included features. Tax, shipping, financing, memberships, add-ons, and different return conditions can change value without being a merchandise discount.
Build One Percentage Discount From a Remaining-Price Factor
A discount rate d removes original price x d. Sale price is original price x (1 - d). The expression in parentheses is the remaining-price factor: 25% off leaves 0.75, while 100% off leaves zero.
Multiply by the factor to move from original to sale price. Divide by a nonzero factor to move from sale price back to original. OpenStax presents these relationships with worked discount and reverse-price examples.
Formula notes
Discount amount = original price x discount rateSale price = original price x (1 - discount rate)Original price = sale price / (1 - discount rate)
Multiply Stacked Discount Factors Instead of Adding Rates
When 20% off is followed by 10% off, the second offer acts on the 80% remaining after the first. Multiplying 0.80 by 0.90 leaves 0.72, so total savings equal 28% of the original price. The common 30% shortcut removes too much because it treats both percentages as if they used the same original base.
Unrestricted percentage factors are commutative, so reversing 20% and 10% produces the same exact price. Real promotions can still make order relevant through eligibility, caps, exclusions, coupon limits, and line-item rounding.
Formula notes
Price after two discounts = original x (1 - d1) x (1 - d2)Effective stacked rate = 1 - ((1 - d1) x (1 - d2))
Keep Fixed Coupons Separate From Percentage Offers
A fixed coupon removes a currency amount, not a share of every possible order. Ten dollars off equals 10% only when the eligible base is $100. On a $40 base it equals 25%; on a $250 base it equals 4%. Converting it to a percentage too early hides that dependence.
The calculator applies two percentage discounts first and the fixed coupon afterward. That is a declared model, not a universal rule. Check minimum spend, eligible lines, caps, funding source, and stacking limits. A coupon cannot produce a negative sale price.
Construct the Taxable Base From the Applicable Receipt Rule
Sales tax is tax rate multiplied by the amount legally treated as taxable. The difficult part is often defining that amount. Retailer discounts, manufacturer-funded coupons, rebates, delivery, service charges, and mandatory fees can be treated differently across jurisdictions and transactions. The calculator therefore asks which entered components belong in the base.
California and New York guidance provides examples, but neither source applies everywhere. Select discounted merchandise, shipping, and fees only after checking a current official rule or the actual point-of-sale treatment.
Formula notes
Tax = selected taxable base x tax rateCheckout total = discounted merchandise + shipping + fees + tax
Reconcile the Checkout Ledger From Top to Bottom
Begin with unit price multiplied by quantity. Confirm the first discount amount and remaining merchandise, then confirm the second discount uses that remainder. Subtract the fixed coupon, add shipping and fees, inspect the selected tax base, calculate tax, and finally add the components that create the amount due.
The first row that differs from a receipt identifies the assumption to investigate. Offer-row mismatches suggest eligibility, order, or rounding. Tax-row mismatches suggest taxable-base or coupon treatment. Final-only differences can reveal an omitted fee, minimum, surcharge, or credit.
Audit Advertised Savings and Reference Prices Separately
Correct percentage arithmetic does not prove that a reference price is genuine. A claimed 50% reduction can be mathematically accurate relative to an entered number while the advertised former price, comparison period, or product equivalence is misleading. Preserve the listing and compare the final amount with other current offers when the claim matters.
FTC guidance covers deceptive former-price comparisons. UK CMA material emphasizes complete prices and mandatory charges, while EU guidance addresses prior-price announcements. These are jurisdiction-specific, but each shows why arithmetic cannot certify an advertisement.
Perform a Final Independent Discount Check
For percent off, subtract sale from original and divide by original. For a recovered original price, apply every entered offer forward and verify that the known sale price returns. For checkout mode, add discounted merchandise, shipping, fees, and tax independently from the ledger. These checks use the same source values through a different path.
Allow for documented point-of-sale rounding, but investigate larger differences. Confirm currency, quantity, offer order, coupon, taxable base, and mandatory charges before reconciling the estimate with the receipt.
Formula notes
Percent off = (original - sale) / original x 100Recovered original = (sale + coupon) / ((1 - d1) x (1 - d2))Forward check = recovered original x (1 - d1) x (1 - d2) - coupon
Frequently asked questions
How do I calculate 20% off a price?
Multiply the original price by 0.20 to find the savings, then subtract that amount. Equivalently, multiply the original price by 0.80. For $75, the savings are $15 and the sale price is $60 before tax or other charges.
Why are 20% off and then 10% off not 30% off?
The second 10% acts on the 80% that remains after the first offer. The remaining factor is 0.80 x 0.90 = 0.72, so the effective discount is 28%. Adding the rates would overstate the savings by 2% of the original price.
How do I calculate a sale price after two discounts and tax?
Multiply the original subtotal by each remaining-price factor in sequence, subtract any fixed coupon, build the taxable base, calculate tax on that base, then add tax, shipping, and fees. Checkout mode displays each stage separately.
Is sales tax calculated before or after a discount?
Often tax is based on a reduced selling price, but coupon funding, rebates, shipping, fees, and local law can change the taxable receipt. Select the base supported by the applicable rule or actual receipt rather than assuming one universal treatment.
How do I find percent off from the original and sale price?
Subtract sale price from original price, divide the difference by original price, and multiply by 100. Both values should describe the same item, quantity, variant, and included features before tax and checkout charges.
How do I find the original price before a discount?
Divide the known sale price by the remaining-price factor. With sequential discounts and a fixed coupon, first add the coupon back, then divide by (1 - d1) x (1 - d2). Original-price mode performs and verifies that calculation.
References
These sources support the method or guidance used for Discount Calculator. Verify time-sensitive rules at the source.
Try the calculator
Open Discount Calculator, enter your scenario, and compare its supporting rows with this guide's method and checks.