How to Calculate Discount and Sale Prices
Whether you are shopping in a sale, comparing online prices, or calculating VAT-exclusive costs from a receipt, knowing how to work with discount percentages is an essential everyday skill. The arithmetic is straightforward, but confusing which value to apply the percentage to — the original price or the discounted price — leads to common errors. This guide explains the formulas for discount and sale price calculations, shows how to find the original price from a discounted one, and covers how retailers use percentage-based pricing to your advantage and disadvantage.
Basic Discount Calculation
A discount is a percentage subtracted from the original (full) price. Three related calculations cover every common shopping scenario. Calculation 1: Finding the discount amount. Discount amount = Original price × (Discount percentage / 100) Example: A £80 jacket is 25% off. Discount = £80 × 0.25 = £20. Calculation 2: Finding the sale price. Sale price = Original price × (1 − Discount percentage / 100) Or equivalently: Sale price = Original price − Discount amount Example: £80 − £20 = £60 sale price. Or directly: £80 × (1 − 0.25) = £80 × 0.75 = £60. Calculation 3: Finding what percentage discount was applied. Discount % = ((Original price − Sale price) / Original price) × 100 Example: An item was £95 and is now £71.25. Discount = ((95 − 71.25) / 95) × 100 = (23.75 / 95) × 100 = 25%. In our percentage calculator, Calculations 1 and 2 use the 'X% of Y' mode. Calculation 3 uses the 'X is what percent of Y?' mode with the discount amount as X and the original price as Y — or equivalently, the percent change from the original price to the sale price. Note: always apply the discount percentage to the original price. A mistake often made in mental arithmetic is to calculate the discount on the wrong value, particularly when adding a subsequent discount.
Stacked Discounts: When Two Percentage Offs Are Not Additive
Retail promotions frequently combine multiple discounts: a 20% off sale, plus an additional 10% for loyalty card holders. Many shoppers assume this is 30% off in total. It is not. Stacked discounts are applied sequentially, each to the most recent price. The result is a discount smaller than the sum of the percentages. Example: A £100 item at 20% off gives £80. An additional 10% off the £80 gives £72. Total paid: £72. Effective total discount: (100 − 72) / 100 × 100 = 28% — not 30%. Formula for the effective discount when two percentage discounts D1 and D2 are stacked: Effective discount = 1 − (1 − D1/100) × (1 − D2/100) For 20% and 10%: 1 − (0.80 × 0.90) = 1 − 0.72 = 0.28 = 28%. This principle extends to any number of stacked discounts. Three discounts of 10%, 15%, and 5%: Effective discount = 1 − (0.90 × 0.85 × 0.95) = 1 − 0.7268 = 0.2733 = 27.33%. Retailers know that '20% off + extra 10% off' sounds better than '28% off' even though they are identical. Being able to calculate the true effective discount lets you compare offers that use different stacking structures. To use our calculator for stacked discounts: find the price after the first discount, then enter that price as the base for the second discount. Or use the formula above to find the effective single discount and apply it to the original price directly.
Finding the Original Price from a Discounted Price
Reverse discount calculation is useful when you see a sale price and want to verify the claimed original price, or when you need to find the pre-discount value for accounting or comparison purposes. Formula: Original price = Sale price / (1 − Discount percentage / 100) Example: A product is on sale for £51 at 15% off. Original price = £51 / (1 − 0.15) = £51 / 0.85 = £60. A common mistake is to add 15% back to the sale price: £51 × 1.15 = £58.65. This gives the wrong answer because 15% of £51 is not the same as 15% of £60 (the original). The 15% was applied to the original £60, not to the sale price of £51. This reversal calculation is also essential for VAT and tax calculations: - A bill is £144 including 20% VAT. The pre-VAT base = £144 / 1.20 = £120. VAT amount = £24. - A price includes 10% sales tax. Pre-tax price = Total / 1.10. And for gross salary calculations: - Net (take-home) pay is £2,400 after 20% income tax deducted. Gross = £2,400 / 0.80 = £3,000. (This is simplified — real tax calculations involve marginal rates and thresholds.) Use the 'reverse percentage' mode in our calculator. Enter the final price and the percentage that was applied (as a subtraction for discounts; as an addition for tax). The calculator returns the original value and the percentage amount.
Evaluating Deals: Is That Discount Actually Good?
Not every sale represents good value, and retailers use pricing psychology to make moderate discounts appear impressive. Knowing how to evaluate deals helps you shop smarter. The 'Was £199, Now £99' trap: a 50% discount is genuinely significant. But this claim is only meaningful if the £199 price was the real market price, charged for a substantial period, and not an inflated 'reference price' set specifically to create the impression of a large discount. In many jurisdictions, retailers are required to have sold at the higher price for at least 28–30 days before claiming a 'was' price — but enforcement is inconsistent. Comparing across retailers: use the discount percentage to calculate the absolute amount saved, then compare that saving across different retailers. A 40% off £80 item saves £32. A 20% off £110 item saves £22. Even though 40% sounds bigger than 20%, the first item is cheaper in absolute terms only if the base products are equivalent. Unit price comparisons: for consumable goods sold in different sizes, calculate the price per unit (per 100g, per litre, per sheet) to identify the true value. A 20% off large pack vs. a 10% off small pack may or may not be better value depending on the base prices and unit sizes. Most supermarkets now display unit pricing on shelf labels. Cashback and rewards as additional discount: if your credit card offers 2% cashback, add that to the posted discount to get your effective saving. A 15% sale price + 2% cashback = effectively 16.7% off (the cashback is applied to the already-discounted price, so the rates are not perfectly additive). Total cost of ownership: for large purchases, the discount on the initial price may be dwarfed by ongoing costs. A 30% discount on an inefficient appliance may cost more over five years in electricity than a full-price energy-efficient model.
Frequently Asked Questions
- How do I calculate a percentage discount on a price?
- Discount amount = original price × (discount percentage / 100). Sale price = original price × (1 − discount percentage / 100). Example: 30% off £120 → discount = £120 × 0.30 = £36; sale price = £120 × 0.70 = £84. In the calculator, enter 30% and £120 in the 'X% of Y' mode to get the £36 discount amount, then subtract from £120 for the sale price.
- What is the effective discount when two discounts are combined?
- Stacked discounts are not simply added. The formula is: effective discount = 1 − (1 − D1/100) × (1 − D2/100). For a 20% discount followed by a 10% discount: 1 − (0.80 × 0.90) = 1 − 0.72 = 28% effective discount, not 30%. Each subsequent discount is applied to the already-reduced price, not the original.
- How do I find the original price if I only know the sale price and the discount percentage?
- Original price = sale price / (1 − discount percentage / 100). Example: an item costs £68 after a 15% discount. Original = £68 / (1 − 0.15) = £68 / 0.85 = £80. Never simply add the discount percentage back to the sale price — that gives the wrong answer because the percentage was applied to the original price, not the sale price.