How to Calculate Discounts
Sale price, amount saved, and successive percent-off deals, including why 20% then 10% is not 30% off and how coupons change the order.
By Ricardo Rodrigues · 6 min read · Updated
A discount is a decrease with a shop attached. You usually want two outputs, not one: the sale price you will pay, and the savings the sign is boasting about. They are complements. If you know one and the original price, you know the other, and if they do not add up, the sign or the arithmetic is off.
The discount calculator is the one-step version. This page is the version that still works when there are two signs, a coupon, and a tax line.
One discount
Savings = price × (discount / 100)
Sale price = price − savings = price × (1 − discount / 100)
30% off €99.99. Savings = 99.99 × 0.30 = €29.997, which a shop will round to €30.00 or €29.99 depending on its rule. Sale price ≈ €69.99. Paying 70% gives the same shelf number: 99.99 × 0.70.
25% off €80. Savings = €20. Sale = €60. This is the friendly one: a quarter off is a quarter of the price, and the rest is three quarters.
50% off €49.99. Sale = €24.995, which becomes €25.00 or €24.99. “Half price” is the discount people estimate best and the one cashiers still mistype, because half of 49.99 is not 25.00 exactly. A one-cent policy is a business rule sitting on top of the percent.
| Original | Off | You pay | You save | Check (pay + save) |
|---|---|---|---|---|
| €80 | 25% | €60 | €20 | €80 |
| €99.99 | 30% | €69.99 | €30.00 | €99.99 |
| €120 | 15% | €102 | €18 | €120 |
| €45 | 10% | €40.50 | €4.50 | €45 |
The check column is worth doing with a pen. Sale plus savings must return the original, before tax. If a receipt’s discount line fails that, you are looking at tax, a second promotion, or a rounding policy, not at a mysterious percent.
“You save” versus “you pay”
Shops advertise the savings because €30 off sounds larger than “pay €70.” Your budget cares about the pay line. Translate every sign into the pay factor:
- 10% off → pay 90% → × 0.90
- 20% off → × 0.80
- 30% off → × 0.70
- 70% off → × 0.30 (you are paying less than a third; the savings are the big number)
A sign that says “70% off” and a sign that says “pay 70%” are opposites. Read the word off. The percentage decrease calculator is the same math with less retail language, useful when the “discount” is actually a budget cut or a markdown in a spreadsheet.
Two discounts in a row
20% off, then an extra 10% off, original €100.
- After 20%: €80.
- After 10% of what remains: €80 × 0.90 = €72.
- Total saved = €28, which is 28% off, not 30%.
The combined pay factor is 0.80 × 0.90 = 0.72. Order does not matter for two pure percents: 0.90 × 0.80 is also 0.72. What matters is that you multiply, and that the second percent applies to the reduced price. Adding 20 + 10 and taking 30% off would give €70, which is €2 too optimistic on a €100 item and €20 too optimistic on a €1,000 one.
| First off | Second off | Pay factor | True total off | Naive sum |
|---|---|---|---|---|
| 10% | 10% | 0.81 | 19% | 20% |
| 20% | 10% | 0.72 | 28% | 30% |
| 25% | 25% | 0.5625 | 43.75% | 50% |
| 50% | 50% | 0.25 | 75% | 100% |
The last row is the cartoon version: half off, then half off again, is not free. It is 75% off. You still pay a quarter. I keep this row because it is the fastest way to see why percents do not add. A longer treatment with coupons that are fixed amounts — where order suddenly matters — is stacked discounts.
Coupons that are euros, not percents
A €100 jacket, 20% off, plus a €10 voucher.
- Percent first: 100 × 0.80 = €80, then €10 → €70.
- Voucher first: 100 − 10 = €90, then 20% → €72.
Now order matters, and the shop’s terms decide it. “Voucher applies to full-price items only” and “voucher applies after promotions” are different prices. A percentage calculator cannot read the terms. It can show you both orders so you know how much the ambiguity is worth before you argue at the till. On this jacket the ambiguity is €2. On a €1,500 sofa with 15% off and a €100 voucher, compare both sequences before you assume the larger saving.
Also notice the voucher is a worse or better *percent* depending on the base. €10 off €100 is 10%. €10 off the already reduced €80 is 12.5%. Quoting the voucher as “an extra 10%” is only true against the original price.
Tax after the discount
Most VAT and sales-tax systems want the tax on the amount you actually pay for the goods, so the discount comes first.
€100 net, 20% off, then 23% VAT.
- Net after discount = €80
- VAT = 80 × 0.23 = €18.40
- Gross = €98.40
If someone charges VAT on €100 (€23) and only then takes 20% off the gross (123 × 0.80 = €98.40), you land on the same gross because the discount was a percent of everything including tax. A fixed voucher breaks the coincidence: 20% off then VAT, versus VAT then a €10 voucher, will not match. When the receipt looks “a bit high,” recompute discount-then-tax as two steps instead of blending the rates. 20% off and 23% VAT is not a single 3% anything.
From the sale price back to the original
The rack says €70 and the sticker says 30% off. What was it?
You are paying 70% of the original, so original = 70 / 0.70 = €100. Check: 30% of 100 is 30, and 100 − 30 = 70.
Subtracting 30% of 70 (which is 21) yields 49, and that number times 0.70 is 34.3, not 70. The subtraction felt like “undo” and was not. This is the reverse-percent problem, with the pay factor as the divisor. Reverse percentages collects several of these, including “what was the price before the increase?”
Comparing two offers
Offer A: €120 with 25% off → pay €90.
Offer B: €100 with 10% off → pay €90.
The sale prices match. The “you save” banners do not (€30 versus €10), because the shops started from different fantasies of the original price. A discount percent is not a measure of value unless you believe the original. Compare sale prices (and what is included) when the originals are set by the seller. Compare percents when the original is a real previous price you actually saw.
When to use the discount calculator
Use it on a single percent-off when the price is awkward (€47.90, 35% off) and you want both pay and save. Use it as a check on a mental estimate: 10% of €47.90 is €4.79, so 35% is about €16.77, sale about €31. If the tool says €40, you applied the percent to the wrong idea of “pay.”
For two promotions, do not type the sum of the percents. Run the first sale price, then the second percent on that result, or multiply the pay factors yourself. Use the calculator once per step so each base is visible.
Do not use a discount percent to compare quality, and do not treat a crossed-out price as historical fact. The math of the markdown can be perfect while the “was” price was never charged. The formula’s job is the gap between the two numbers printed in front of you, not the honesty of the higher one.
FAQ
- How do I find the sale price in one step?
- Pay (100 − discount) percent of the original. Thirty percent off means you pay 70%: price × 0.70. The amount saved is price × 0.30. Those two pieces add back to the original price.
- Does the order of two percent-off discounts matter?
- No. 20% off then 10% off is the same factor as 10% then 20%, because 0.80 × 0.90 = 0.90 × 0.80. A fixed-amount coupon does care about order, because €10 off a smaller number is a different percent.
- How do I recover the original price from a sale price?
- Divide by the fraction you paid. If you paid 70% of the original, original = sale / 0.70. Subtracting 30% of the sale price gives the wrong original.