Discount % problems look simple until a second discount gets stacked on top, or tax gets added afterward — both change the math in ways that trip people up at checkout and in spreadsheets alike.
The Core Formula
Final Price = Original Price × (1 − Discount% ÷ 100)
Savings = Original Price − Final Price
Why Two Stacked Discounts Don't Add Up
A common mistake: assuming "20% off, then an extra 10% off" equals 30% off the original price. It doesn't, because the second discount applies to the already-discounted price, not the original.
Worked example on a $100 item with 20% off, then an extra 10% off:
- After first discount: $100 × 0.80 = $80
- After second discount: $80 × 0.90 = $72
- Total savings: $100 − $72 = $28, an effective 28% discount — not the naive 30% you get from adding 20% + 10%.
The gap between the "naive sum" and the real effective discount grows as the individual percentages get larger, because each successive discount is taken off a smaller base.
Adding Tax After the Discount
Most sales tax is calculated on the price you actually pay, so it should be applied to the final discounted price, not the original list price: Price with tax = Final Price × (1 + Tax% ÷ 100). On the $72 example above with 8% tax, the total comes to $72 × 1.08 = $77.76 — still well under the original $100, but worth checking your receipt against if a store applies tax differently.
Frequently Asked
Q: Is 20% off + 10% off ever the same as 30% off?
A: No — stacked percentage discounts are never additive. The only way to get exactly 30% off is a single 30% discount, or a combination whose compounded effect happens to land there by coincidence at very specific numbers.
Q: Does the order of the two discounts matter?
A: No — multiplying by (1 − d1/100) then (1 − d2/100) gives the same result regardless of order, since multiplication is commutative. Applying 10% then 20% produces the identical $72 final price as 20% then 10%.
Q: Why is my receipt's tax higher than I expected?
A: Check whether the retailer taxes the pre-discount or post-discount price — this varies by jurisdiction and by whether the "discount" is a manufacturer coupon versus a store markdown, which some tax rules treat differently.
Disclaimer: This calculator is for general educational purposes only and does not constitute tax or financial advice. Sales tax rules vary by location — confirm exact tax treatment with your local tax authority or a qualified professional.