Percent Off Calculator
Stack up to three successive discounts on a price and get the final amount, the total saved and the single discount the stack is really worth.
Percent Off Calculator: with the default inputs, final price is $72.00.
The sale or list discount.
“Extra 10% off sale prices” — applied to what's left after the first.
After every discount, before tax.
- Total saved
- $28.00
- Effective single discount
- 28%The one discount that would give the same price.
- What the percentages add up to
- 30%Shown only to make the gap obvious — stacked discounts never add.
- Gap between the two
- 2%
- Price with sales tax
- $72.00
- In words
- $100.00 with 20% off then 10% off comes to $72.00 — you save $28.00, an effective 28% off.
Assumptions
- Percentage discounts are applied successively, each to the balance left by the one before.
- A flat coupon is applied after all percentages and cannot take the price below zero.
- Sales tax is charged on the final discounted price, which is the rule in every US state for retailer discounts.
- You pay$7272%
- You save$2828%
| Discounts | They look like | Actually | On your price |
|---|---|---|---|
| 10% then 10% | 20% | 19% | $81.00 |
| 20% then 10% | 30% | 28% | $72.00 |
| 25% then 20% | 45% | 40% | $60.00 |
| 30% then 20% | 50% | 44% | $56.00 |
| 40% then 20% | 60% | 52% | $48.00 |
| 50% then 20% | 70% | 60% | $40.00 |
| 50% then 30% | 80% | 65% | $35.00 |
| 60% then 25% | 85% | 70% | $30.00 |
Two discounts never add. 50% then 20% is 60% off, not 70% — which is why "50% off, extra 20% off" beats a flat 60% by exactly nothing.
How this is worked out
The formula
Final price = P × (1 − d₁) × (1 − d₂) × (1 − d₃) − coupon Effective single discount = (1 − (1 − d₁)(1 − d₂)(1 − d₃)) × 100 P = original price, dᵢ = each discount as a decimal Total saved = P − final price With tax = final price × (1 + tax rate)
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Original price
- A number.in dollars · 0 or more · defaults to 100
- First discount
- The sale or list discount.a percentage · from 0 to 100 · defaults to 20
- Second discount
- “Extra 10% off sale prices” — applied to what's left after the first.a percentage · from 0 to 100 · defaults to 10
- Third discount(under More options)
- A loyalty or staff discount stacked on top. Leave at 0 if unused.a percentage · from 0 to 100 · defaults to 0
- Flat amount off(under More options)
- A dollars-off coupon applied after the percentages.in dollars · 0 or more · defaults to 0
- Sales tax(under More options)
- Charged on the discounted price, so a discount also shrinks the tax.a percentage · from 0 to 30 · defaults to 0
What you get back
- Final pricemain answer
- After every discount, before tax.
- Total saved
- Effective single discount
- The one discount that would give the same price.
- What the percentages add up to
- Shown only to make the gap obvious — stacked discounts never add.
- Gap between the two
- Price with sales tax
- In words
What this assumes
- Percentage discounts are applied successively, each to the balance left by the one before.
- A flat coupon is applied after all percentages and cannot take the price below zero.
- Sales tax is charged on the final discounted price, which is the rule in every US state for retailer discounts.
About this calculator
"40% off, plus an extra 20% off sale prices" is not 60% off. It is 52% off, and the difference on a $200 coat is $16 you never actually save. Stacked discounts multiply rather than add, because each one applies to whatever the previous one left behind. This calculator does the multiplication and, more usefully, tells you the single discount the whole stack is worth.
How to use it
Enter the original price and the discounts in the order the till applies them — the order does not change the answer, which is worth knowing when a cashier insists otherwise. Under More options there is a third percentage for a loyalty or staff discount, a flat dollars-off coupon (applied after the percentages, which is how nearly every retailer sequences it), and a sales-tax rate.
Why stacked discounts don't add
Take 20% off $100 and you have $80. The "extra 10%" is 10% of $80, not of $100, so it saves $8 rather than $10. The final price is $72 and the effective discount is 28%, not 30%. Formally, the discounts survive as a product of what remains: 0.8 × 0.9 = 0.72. The shortfall grows with the size of the discounts — 50% and 50% is 75% off, not 100%, and no chain of percentage discounts can ever reach free.
The same arithmetic runs through wholesale "discount chains" (list less 30/10/5), through a percentage rebate on a percentage-discounted invoice, and through the trap of thinking a 20% price cut undoes a 20% price rise. It does not: 100 → 120 → 96.
Percentages versus a flat coupon
Order matters here. A $20 coupon before a 25% discount is worth $20 to you; the same coupon after is still $20, but the 25% now applies to the full price, so you end up better off. Most retailers apply percentages first and coupons last, which favours them. If the terms let you choose, take the flat amount off last only when the percentage is applied to the larger number.
Reading the results
Effective single discount is the number to compare offers with, and it regularly overturns the obvious answer. "30% off everything" looks better than "20% off plus an extra 15%", but the stack is worth 32% and the flat offer only 30%. What the percentages add up to is shown purely so the gap between the two is visible; it is never the real discount.
Remember that the discount is measured against the retailer's own reference price. A 60% discount from a list price nobody has paid in two years is a marketing artefact, not a saving.
Frequently asked questions
▸How do I calculate a percent off?
Multiply the price by (1 − discount ÷ 100). For 25% off $80: 80 × 0.75 = $60. To find the saving, subtract that from the original.
▸Is 20% off then 10% off the same as 30% off?
No. It comes to 28% off, because the 10% applies to the already-reduced price. On $100 you pay $72, not $70.
▸Does the order of stacked discounts matter?
For percentages, no — multiplication commutes, so 20% then 10% equals 10% then 20%. For a flat dollars-off coupon mixed with percentages, order matters a lot.
▸Can stacked discounts ever reach 100% off?
Never, with percentages alone. 50% and 50% is 75% off; 90% and 90% is 99%. Only a single 100% discount or a coupon larger than the balance makes something free.
▸Is sales tax charged before or after the discount?
After, in every US state — tax applies to the price you actually pay, so a discount reduces the tax too. Manufacturer coupons are the exception in some states, where tax is charged on the pre-coupon price.
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