The three core formulas
A discount takes a percentage off the starting price, so every formula comes down to multiplication. Sale price = original price Γ (1 β discount Γ· 100), discount rate = (original β sale price) Γ· original Γ 100, and original price = sale price Γ· (1 β discount Γ· 100). They are the same relationship solved in three directions. A $50 item at 30% off costs 50 Γ 0.7 = $35.00. Run it backwards: if you know $35 is the 30%-off price, the original was 35 Γ· 0.7 = $50.
The most common slip is working back to the original by adding 30% to the sale price. 35 Γ 1.3 = $45.50, but the real original was $50, because the discount percentage is measured against the original price, not the sale price. This "which number is the base?" question is the heart of most percentage mistakes and is also covered in the percentage calculator.
Why a discount is not the same as "getting more"
A discount tells you how much less you pay, not how much more you get. 50% off means the same money buys twice as much, and 20% off means it buys 25% more. The gap widens quickly as the discount grows. The table is calculated from the formulas when the page is built: the middle column is the buying-power multiple for the same money, and the last column is the price increase that would put the price back at the original.
| Discount | What the same money buys | Rise needed to return to original price |
|---|---|---|
| 10% | 1.11x | +11.1% |
| 20% | 1.25x | +25.0% |
| 25% | 1.33x | +33.3% |
| 30% | 1.43x | +42.9% |
| 40% | 1.67x | +66.7% |
| 50% | 2.00x | +100.0% |
| 60% | 2.50x | +150.0% |
| 70% | 3.33x | +233.3% |
The rise needed to undo a discount is always bigger than the discount. A 30% cut has to be followed by a 42.9% rise to get back to the old price, which is why a price that creeps back up after a sale can feel like a small change when it isn't.
Turning "buy N, get M free" into a discount rate
Offers such as "buy 1 get 1 free" have no percentage on the label, which makes them hard to compare. If you pay for N items and receive N + M, the effective discount is M Γ· (N + M). This assumes every item has the same price, so check that the unit price or pack size has not quietly changed.
| Offer | Effective discount |
|---|---|
| Buy 1 get 1 free | 50.0% |
| Buy 2 get 1 free | 33.3% |
| Buy 3 get 1 free | 25.0% |
| Buy 4 get 1 free | 20.0% |
| Buy 2 get 2 free | 50.0% |
When pack sizes differ, compare cost per unit with the unit price comparison calculator instead of relying on the headline offer.
Stacked discounts and coupons: order matters
Percentage discounts multiply, so their order does not matter. 20% off then 10% off equals 10% then 20%: price Γ 0.8 Γ 0.9 = price Γ 0.72, a 28% total, not 30%. A fixed-amount coupon changes that. Because it is a flat sum, the result depends on whether it comes off before or after the percentages. Which one a store applies depends on its own terms, so confirm using the total on the checkout screen. The "when the coupon applies" option lets you compare both.
Example 1: two percentages and a coupon. A $120 item with 30% off, a further 15% off and a $5 coupon: 120 Γ 0.7 = $84.00, then 84 Γ 0.85 = $71.40, then $5 off leaves $66.40. You saved $53.60, a real combined discount of 44.67%. Adding 30 + 15 would suggest 45%, plus the coupon, which is not how it works.
Example 2: coupon timing. With the same numbers but the coupon taken off first, (120 Γ 0.7 β 5) Γ 0.85 = $67.15, which is $0.75 more than the $66.40 above. Taking the coupon last is better for you because the full $5 comes off. The percentage then no longer shrinks it.
Example 3: three percentages. $200 with 20%, 10% and 5% applied in turn: 200 Γ 0.8 Γ 0.9 Γ 0.95 = $136.80, a combined 31.6%. Simply adding the numbers gives 35%, 3.4 points too high. The more small discounts you stack, the larger the gap between the sum and the truth.
Percentage coupon or fixed coupon?
If you can use only one of a 20% coupon and a $10 coupon, find the break-even price: break-even = fixed amount Γ· percentage = 10 Γ· 0.2 = $50. Above $50, the 20% coupon wins; below it, the $10 coupon wins. On an $80 purchase the percentage coupon saves $16, which is $6 more. On a $30 purchase it saves only $6, so the fixed coupon is $4 better. If a percentage coupon has a maximum discount, compare against that cap too, because it stops growing past the price where the cap is reached.
Spotting misleading price tags
- Inflated list prices: raise a $100 price to $150 and then mark it 40% off, and you pay $90. That looks like a 40% deal but is 10% above where it started. Compare with recent prices, not the "was" price.
- "Up to 70% off": this describes the best item in the sale, not a typical one. Plug the actual list and sale prices into the "price + sale price" tab.
- Coupon conditions: minimum spend, stacking rules and caps differ. A deal is not a deal if you buy things you do not need to qualify.
- Shipping: a lower sale price may drop your basket below a free-shipping threshold, and the shipping fee can cancel part of the saving.
What this calculator does not cover
This is plain arithmetic on the amounts you enter. It does not know whether sales tax or VAT is included in a price, and it does not apply any tax rate for you. If tax is added at checkout, add it separately with the sales tax calculator using the rate that applies where you shop. Card offers, points and store credit are not modeled either. Results are rounded to two decimal places at each step, and stores may round differently, so a difference of a cent or two is possible.
Putting the results to use
- Compare the final checkout price at different shops for the same product rather than the advertised percentage.
- If you have a target price, use the original-price tab to see how the current price relates to the real list price.
- For restaurant bills with a discount, work out the discounted total first, then split or add a gratuity using the tip calculator.
Frequently Asked Questions
Is 20% off plus another 10% off the same as 30% off?
No. The second discount applies to the already reduced price, so the total is price Γ 0.8 Γ 0.9 = price Γ 0.72, a 28% discount.
How do I find the original price from a sale price?
Divide the sale price by (1 β discount). If the 30%-off price is $35, then 35 Γ· 0.7 = $50. Multiplying 35 by 1.3 to get $45.50 is incorrect.
Is a fixed coupon better used before or after percentage discounts?
Usually after, because the whole coupon value comes off the lower price. If it is taken off first, part of its value is shaved away by the percentage that follows. The order a store really uses is set by its own terms.
Does this include sales tax or VAT?
No. It works on the amounts you enter and does not know whether tax is included. If tax is added separately at checkout, your total will differ from this result.
What if the sale price is higher than the original?
In the discount-rate tab, a sale price above the original is shown as a price increase instead of a negative discount.
What discount is "buy 1 get 1 free"?
You pay for one and take two, which equals 50% off. Buy 2 get 1 free is about 33.3% and buy 3 get 1 free is 25%, as long as the items share the same price.