The Complete Guide to Discount & Sale Price Math
By Arshi Khan, Founder of Just4Marketing · Last reviewed October 2026
A single discount is simple math, but 'extra 20% off already-reduced items' trips people up constantly because the order of operations changes the answer. This guide walks through exactly how stacked discounts and tax are applied, and why two 20% discounts don't add up to 40% off.
How stacked discounts and tax are calculated
Each discount is applied sequentially to the running price, not to the original price. The first discount multiplies the original price by (1 − discount₁ ÷ 100). The second, additional discount then multiplies that already-reduced result by (1 − discount₂ ÷ 100) — meaning it's a smaller dollar amount than the same percentage would remove from the original price. Finally, sales tax is applied by multiplying the fully-discounted price by (1 + tax rate ÷ 100), and total savings is simply the original price minus the discounted price before tax.
Worked example: stacking two discounts
Here's a $100 item with a 20% discount, an additional 10% off, and 8% sales tax, calculated step by step:
| Step | Calculation | Result |
|---|---|---|
| Original price | — | $100.00 |
| After 20% discount | $100 × (1 − 0.20) | $80.00 |
| After additional 10% off | $80 × (1 − 0.10) | $72.00 |
| Total savings | $100 − $72 | $28.00 (28%, not 30%) |
| Final price after 8% tax | $72 × (1 + 0.08) | $77.76 |
Working backwards: original price and percent off
If you only know the sale price, divide it by what's left after the discount to recover the original price: original = sale ÷ (1 − discount). A jacket on sale for $75 at 25% off was originally $75 ÷ 0.75 = $100. A common mistake is adding 25% back on to $75, which gives $93.75 — wrong, because the 25% was taken from the higher original price.
To find how big a discount really was, compare the two prices: percent off = (original − sale) ÷ original × 100. A $120 item selling for $90 is ($120 − $90) ÷ $120 = 25% off. Use the "Find original price" and "Find % off" modes above to do either in one step.
Things to double-check when comparing deals
"Extra X% off" always means less than it sounds
An additional discount on top of an existing one is always worth less in dollar terms than the same percentage taken off the original price — do the math before assuming two discounts add up.
Check whether tax applies before or after a coupon
Most retailers tax the discounted price, but store policies can vary — if a receipt looks off, this is the first thing to check.
Percentage-off and dollar-off aren't directly comparable
A "$20 off" coupon and a "20% off" coupon only save the same amount at exactly $100 — below that price the percentage saves less, above it the percentage saves more.
Rounding can shift the final cents
Retailers may round at each step differently than a single end-to-end calculation, so your receipt might differ from this calculator by a cent or two.
Frequently asked questions
Why don't two 20% discounts equal 40% off?
Because the second discount applies to the already-discounted price, not the original price. $100 with 20% off becomes $80; a second 20% off that $80 removes $16, not $20 — leaving $64, which is 36% total savings, not 40%.
Is tax applied before or after the discount?
After. The calculator applies both discounts first to get the discounted price, then applies sales tax on top of that already-reduced amount, which matches how most retailers calculate tax at checkout.
What's the difference between two 10% discounts and one 20% discount?
One flat 20% discount saves more. Two stacked 10% discounts leave you paying 0.9 × 0.9 = 81% of the original price (19% off), while a single 20% discount leaves you paying 80% (20% off) — stacking smaller percentages is always slightly less generous than one discount of their sum.
How do I calculate the original price from a sale price?
Divide the sale price by (1 − discount ÷ 100). For example, a $64 sale price after a 20% discount means the original price was $64 ÷ 0.8 = $80.