🏷️ Discount Calculator
A discount calculator for stacked "extra % off" deals that compound rather than add, sales tax, and both reverse questions: original price and % off.
What Discount Calculator Does
A single discount is easy. What trips people up is the second one — the "take an extra 20% off sale prices" sign — because those two percentages do not add together. The extra discount comes off the already-reduced price, so 30% and then 20% is 44% off, not 50%. On a $100 item that is $56, not the $50 most people expect.
The gap grows with the numbers. A 70% clearance with a further 20% coupon sounds like 90% off and is 76%. Two 10% discounts are 19%, not 20%. This is the same compounding that makes interest work, running in the other direction, and it is the single most useful thing to understand about a sale.
The reverse question comes up just as often and has the same trap. If you paid $90 after 25% off, the original was not $112.50. You have to divide rather than add back: 90 ÷ 0.75 = $120. Adding the percentage to the smaller number always undershoots, because the discount was taken from the larger one.
And tax is charged on what you actually pay, after the discount — so a markdown quietly saves you the tax on the discount too. All three of those are handled here, along with the plain question of what percentage off a given sale price actually represents.
How to Use Discount Calculator
- Choose what you are solving for — the sale price, the original price, or the percentage off
- Enter the price and discount, or tap one of the common discount presets
- Add a second "extra % off" discount if the offer stacks; the calculator shows the true combined percentage
- Add your sales tax rate to see the real out-of-pocket total
Formula Used by Discount Calculator
The sale price
final = original × (1 − discount ÷ 100)
- The multiplier
- 25% off means paying 75%, so the multiplier is 0.75
- Saving
- original − final, which is original × discount ÷ 100
Worked example
$120 with 25% off
- Multiplier: 1 − 0.25 = 0.75
- 120 × 0.75
Result: $90 — a saving of $30
Stacked discounts multiply
final = original × (1 − d₁) × (1 − d₂), so combined = 1 − (1 − d₁)(1 − d₂)
- Why not add
- The second discount applies to the reduced price, not the original
- Always less
- The combined figure is always smaller than the two added together
Worked example
30% off, then an extra 20% off, on $100
- 100 × 0.70 = 70
- 70 × 0.80 = 56
- Combined: 1 − (0.70 × 0.80) = 0.44
Result: 44% off, not 50% — a $6 difference on a $100 item
Reversing a discount
original = paid ÷ (1 − discount ÷ 100)
- Divide
- Multiplication built the sale price, so division undoes it
- The common error
- Adding the percentage back to the smaller number
Worked example
$90 paid after 25% off
- 90 ÷ 0.75
Result: $120. Adding 25% to $90 would give $112.50, which is wrong
What percentage off is it?
percent off = (original − sale) ÷ original × 100
- Denominator
- Always the original price — that is what the discount is measured against
Worked example
Marked down from $120 to $90
- 120 − 90 = 30
- 30 ÷ 120 = 0.25
Result: 25% off
Stacked discounts are worth less than they sound
The combined figure is always below the naive sum, and the gap is widest when both discounts are large. This is the arithmetic behind "extra % off sale prices".
| First | Then | Looks like | Actually | $100 becomes |
|---|---|---|---|---|
| 10% | 10% | 20% off | 19% off | $81.00 |
| 20% | 20% | 40% off | 36% off | $64.00 |
| 30% | 20% | 50% off | 44% off | $56.00 |
| 40% | 25% | 65% off | 55% off | $45.00 |
| 50% | 10% | 60% off | 55% off | $45.00 |
| 70% | 20% | 90% off | 76% off | $24.00 |
Common discounts at a glance
The sale price for each percentage off, before tax.
| Original | 10% off | 25% off | 40% off | 50% off | 70% off |
|---|---|---|---|---|---|
| $25 | $22.50 | $18.75 | $15.00 | $12.50 | $7.50 |
| $50 | $45.00 | $37.50 | $30.00 | $25.00 | $15.00 |
| $100 | $90.00 | $75.00 | $60.00 | $50.00 | $30.00 |
| $150 | $135.00 | $112.50 | $90.00 | $75.00 | $45.00 |
| $250 | $225.00 | $187.50 | $150.00 | $125.00 | $75.00 |
Where the discount and the tax interact
A $120 item at 8% sales tax. Tax is charged on the discounted price, so a markdown saves you the tax on the discount as well.
| Discount | Price | Tax at 8% | Total | True saving |
|---|---|---|---|---|
| None | $120.00 | $9.60 | $129.60 | — |
| 10% | $108.00 | $8.64 | $116.64 | $12.96 |
| 25% | $90.00 | $7.20 | $97.20 | $32.40 |
| 40% | $72.00 | $5.76 | $77.76 | $51.84 |
| 50% | $60.00 | $4.80 | $64.80 | $64.80 |
How to Read Your Result
Percentages only compare at the same price
A bigger percentage is not automatically a better deal. 40% off a $100 item leaves $60; 25% off a $75 item leaves $56.25. The smaller discount wins because it starts lower. This sounds obvious and is routinely missed, because retail signage puts the percentage in large type and the price in small type. Compare the number you would actually hand over.
Why "extra % off" is such a common offer
Because it sounds additive and is not. A retailer advertising "50% off, plus an extra 20% off" is offering 60% off, and most shoppers read 70%. The structure is entirely legitimate — the maths is stated correctly if you work it out — but the perception gap is the point of the format. Working out the true combined figure before you decide is the whole value of a discount calculator.
Order does not matter, which is a useful check
Applying 30% then 20% gives exactly the same result as 20% then 30%, because multiplication commutes: 0.7 × 0.8 and 0.8 × 0.7 are both 0.56. So if a cashier applies your coupon in a different order than you expected, the total is unaffected. If it does change, something other than a straight percentage is going on — a minimum spend, an exclusion, or a fixed-amount coupon, which does not commute with a percentage.
A fixed-amount coupon behaves differently
Ten dollars off is not a percentage, and the order genuinely matters when it is combined with one. Taking $10 off $100 and then 20% off gives $72; taking 20% first and then $10 gives $70. Retailers specify the order in their terms, and it is usually the one that favors them. If an offer mixes a percentage with a fixed amount, work out both orders and check which one the till used.
The reverse calculation is the one that costs money
Recovering an original price matters for expense claims, insurance valuations, price-match policies and checking that a "was $200, now $99" claim is honest. The rule is always to divide by the multiplier, never to add the percentage back. The error is asymmetric and always in the same direction: adding back understates the original, and the bigger the discount the worse it gets. At 50% off, adding back gives you three quarters of the right answer.
Tax comes last, and that helps
Sales tax is charged on the amount actually paid, so it falls with the discount. On a $120 item at 8% tax, a 25% discount saves $30 on the price and a further $2.40 in tax — $32.40 in total. Because the tax scales with the price, the saving stays exactly 25% of the bill either way — which is the neat part: a percentage discount is worth the same percentage of your total whether or not tax is charged. Worth knowing when weighing a discount against a "no sales tax" promotion, which is not the same thing at all.
Limitations & Accuracy Notes
- Discounts are treated as straight percentages applied in sequence. Buy-one-get-one, tiered thresholds, bundle pricing and loyalty points do not reduce to a single percentage.
- A fixed-amount coupon combined with a percentage is order-dependent and is not modeled here. Work out both orders and check which one the retailer applies.
- Sales tax is applied to the discounted price at a single rate. US rates vary by state, county and city, and some jurisdictions tax certain goods differently or not at all.
- Shipping, handling and any non-discountable fees are excluded, and are often charged on the pre-discount amount.
- Nothing here judges whether the original price was genuine. A discount from an inflated reference price is arithmetically correct and commercially meaningless.
Frequently Asked Questions
Do stacked discounts add together?
How do I find the original price from what I paid?
What percentage off is a sale price?
Is sales tax charged before or after the discount?
How do I calculate 10% off in my head?
Is a bigger discount on a higher price always better?
References & Further Reading
- Federal Trade Commission — Advertising and Marketing: pricing — US guidance on deceptive pricing, including former-price and comparison-price claims — the reason a stated percentage off is only meaningful if the reference price was real
- Calculator.net — Discount Calculator — The #1 result for this term, covering final price, amount saved and original price before discount
- Omni Calculator — Discount Calculator — The clearest competing explanation of the discount formula and the amount-saved calculation