Discount Calculator

How discounts really work: a plain-English guide with worked examples

Almost everybody has stood in a shop with a tag in one hand and a half-working calculator in the other, trying to work out whether “25% off” is actually a good deal. This page is for that moment. The calculator above does the sums. The article below explains what they mean.

1. What a discount really is (and how to calculate it in your head)

A discount is a price cut, and it can be shown in two ways: as a percentage of the original price, or as a fixed amount of money. “20% off” and “1,000 off” are both discounts, but they behave very differently as prices change, and we’ll get to that.

The thing to remember is that a percentage discount is always a share of the price you started with. Take 20% off 5,000 and you are removing one fifth of it, which is 1,000. You then pay the other four fifths, 4,000.

2. The discount formula, piece by piece

There is really only one formula, and the rest of this guide is just that formula turned around in different directions.

Here’s what each piece does. The original price is what the shop shows before the offer. The discount rate is the percentage off. Dividing it by 100 turns 24% into 0.24. Subtracting that from 1 gives the share of the price you still pay, which is 0.76 in this case. Multiply the original price by 0.76 and you have the final price. Subtract the final price from the original and you have the amount you saved.

3. A worked example

Let’s say a clothing shop has a seasonal sale and a shirt is tagged 4,800 with 25% off.

1. Turn the percentage into a decimal: 25 ÷ 100 = 0.25.
2. Work out the amount saved: 4,800 × 0.25 = 1,200.
3. Subtract it from the original price: 4,800 − 1,200 = 3,600.

You could also go straight to the answer: 4,800 × (1 − 0.25) = 4,800 × 0.75 = 3,600. Same result, one step. And since you pay 75% of the original, the shirt costs three quarters of the tag.

4. How to find the discount percentage when you only see two prices

Sometimes a shop shows only a “was” price and a “now” price, and you want to know how big the cut really is. Subtract, then divide by the original:

Discount % = (original − sale price) ÷ original × 100

Say a phone was 85,000 and is now 68,000. The drop is 17,000. Divide 17,000 by 85,000 and you get 0.2, so that’s 20% off. The key is to divide by the original price, not the new one. If you divide 17,000 by 68,000 you’ll get 25%, which sounds better but is wrong, because the saving was measured against a price of 85,000.

The “Find the %” tab does this for you, and for any other percentage sum the Percentage Calculator is handy.

5. How to find the original price from a sale price (the reverse trap)

This is the one that catches people out. You see a shirt at 3,600 with “25% off” and wonder what it cost before. The tempting move is to add 25% back: 3,600 × 1.25 = 4,500. It feels right, but it’s wrong.

Here’s why. The 25% was taken from the original price, which was bigger than 3,600. So 25% of the original is a bigger number than 25% of 3,600. If you take 25% off 4,500 you get 3,375, not 3,600. The right way is to remember that 3,600 is the 75% you still pay:

Original = sale price ÷ (1 − discount), so 3,600 ÷ 0.75 = 4,800.

Check it: 25% of 4,800 is 1,200, and 4,800 − 1,200 = 3,600. The “Original price” tab shows this check for you, with the mistaken answer next to the correct one so the difference is easy to see.

6. Stacked discounts: why 20% + 10% isn’t 30%

Someone sees a banner that says “20% off, plus an extra 10% off at the till” and quietly adds them up to 30%. It’s a very natural thing to do. But the second discount is taken from the already reduced price, so it is worth less than the first.

Add a coupon and the order starts to matter. Take 10,000 again, with 20% off, then 10% off, then a 500 coupon: 10,000 becomes 8,000, then 7,200, then 6,700, a combined saving of 33%. But if the coupon were applied first, you’d have 9,500, then 7,600 after the 20%, then 6,840 after the 10%. Percentages work best on a large price, so a fixed coupon taken last usually leaves you better off. Try both orders in the “Stacked” tab and watch the waterfall chart step down.

7. Discount before tax or after tax? How it changes what you pay

Many bills add tax or VAT on top. Rates differ between countries and change over time, so the calculator doesn’t assume one. You type the rate that applies to you. For the examples here, let’s use an imaginary 10% just to keep the sums tidy.

With a percentage discount, the order doesn’t matter. 5,000 less 20% is 4,000, and 10% tax on that gives 4,400. Add the 10% tax first and you’d have 5,500, then 20% off gives 4,400 again. Multiplication doesn’t care about order.

With a fixed-amount coupon, it does. Take 5,000 with a 500 coupon. If the coupon comes off first, you pay tax on 4,500, which is 4,950 in total. If tax is added first (5,500) and the coupon comes off the total, you pay 5,000. Same coupon, same tax rate, 50 apart, because in the second case the coupon didn’t reduce the tax. Which method a shop uses depends on the shop and local rules, so check your receipt. Delivery is added at the end here and isn’t taxed; if yours is, add it to the price instead.

8. Percentage off vs fixed amount off vs “buy 2 get 1”: which is better?

Picture a family choosing a new phone. One shop says “30% off” and another says “2,000 off”. The better deal depends entirely on the price. A fixed amount wins on cheap things, and a percentage wins on expensive ones. The tipping point is the fixed amount divided by the percentage: 2,000 ÷ 0.30 = about 6,667.

“Buy 2 get 1 free” is its own animal. If you take all three items, you pay for two, which is the same as 33.3% off. Three shirts at 1,500 cost 3,000 instead of 4,500. A flat 30% off would leave you paying 3,150. But if you only need two shirts, buy-2-get-1 gives you nothing at all, and 30% off wins. So the honest answer is: it depends on how many you really want. The “Compare deals” tab lets you plug in the price and quantity and shows the winner. If you plan to pay for a big purchase in instalments, the Loan EMI Calculator shows what the financing really costs.

9. How to spot a fake or inflated “original” price

Most shops price honestly, and many sales are real. Still, a big percentage on a tag means little if the “was” price was never what people actually paid. A few neutral habits help:

First, keep a rough idea of the usual price. If a pair of headphones normally sells around 8,000 and a tag says “was 12,000, now 7,200, 40% off”, the real saving against the usual price is (8,000 − 7,200) ÷ 8,000 = 10%. You still got a slightly lower price, just not a 40% one. The “Is it a real deal?” box in the calculator does exactly this comparison.

Second, look at a couple of other shops or an old receipt before a big purchase. Third, be wary of words like “up to”, because “up to 70% off” may apply to one item. And fourth, compare the final price you’d pay, not the size of the percentage. A smaller discount on a lower starting price can beat a huge discount on a high one.

10. For shop owners: choosing a discount that doesn’t wipe out your margin

If you run a shop, a discount feels like an easy way to move stock. It’s worth checking the sums first, because a discount cuts your profit by a larger percentage than it cuts your price.

Say an item costs you 700 and sells for 1,000. You make 300, which is a 30% margin on the selling price (and a markup of about 43% on your cost). Now you offer 20% off. The price falls to 800, but your cost is still 700, so profit drops to 100 and the margin to 12.5%. A 20% price cut has removed two thirds of your profit per item. You would need to sell three times as many just to earn the same total.

A useful rule: work out your cost and your margin first (a margin is profit as a share of the selling price, a markup is profit as a share of cost), and then decide how much room you have. Small discounts on slow lines, or bundles that raise the basket size, often protect margin better than a big across-the-board cut. This is general guidance, not business advice.

11. Quick mental-math tricks for 10%, 15%, 20%, 25% and 50%

These shortcuts get you close in seconds. 10%: move the decimal point one place left, so 10% of 3,450 is 345. 20%: find 10% and double it, which gives 690. 15%: take 10% and add half of that, so 345 + 172.50 = 517.50. 25%: halve the price, then halve it again, so 3,450 becomes 1,725 and then about 862.50. 50%: simply halve it.

To get the price you pay rather than the saving, subtract: a 20% discount on 3,450 leaves 3,450 − 690 = 2,760.

12. Common mistakes

Adding stacked percentages together is the big one, and we’ve covered it. Next is the reverse trap, adding the discount back onto the sale price. A third is dividing by the wrong price when working out a percentage, which gives 25% instead of 20% in the phone example above.

People also forget that tax, delivery or a service fee can change the final bill, so a lower tag price isn’t always a lower total. Another slip is comparing a percentage with a fixed amount without looking at the price, as in the table above. And finally, rounding too early: round at the end, or at each step if your shop does, so the numbers match the receipt. Splitting the bill afterwards? Try the Tip & Bill Split calculator.

13. Frequently asked questions

14. Method, sources and disclaimer

Method. Every result comes from the formulas in this guide. Final price = original × (1 − d÷100). Discount % = (original − sale) ÷ original × 100. Original = sale ÷ (1 − d÷100). Successive discounts are applied one after another to the running price, and an amount-off coupon is capped so the price never goes below zero. Combined discount = (starting price − final price) ÷ starting price. For “buy X get Y free”, every full group of X + Y items costs the price of X items, and a partial group costs the lesser of the leftover items and X. Rounding is half-up and is applied only to money values.

Sources. These are standard arithmetic definitions of percentage, percentage change and successive percentage change, as taught in school and consumer-maths textbooks. No external data, shop prices or tax rates are used or stored.

More tools are on the Calculators hub.

Disclaimer. Results are estimates for general information. Shops may round, apply offers or calculate tax in their own way. Always check the final price at checkout. This page is not financial, tax or legal advice.