Discount Calculator — Sale Price, Savings and Stacked Offers

Calculate Sale Price, Savings & Final Price After Discount — Free & Instant

Two Ways to Get the Same Answer, and One Is Faster

A single discount can be worked out in two steps or one, and the one-step version is both quicker and less error-prone because it removes an intermediate figure you can mis-copy.

Two steps: saving = price × rate ÷ 100, then final = price − saving
One step: final = price × (1 − rate ÷ 100)

A 40 item at 25% off is 40 × 0.75 = 30. The multiplier is worth learning as a reflex: 10% off is × 0.9, 20% off is × 0.8, 25% is × 0.75, and 30% is × 0.7. Once you think in multipliers rather than subtractions, stacked offers become straightforward too.

Stacked Discounts Do Not Add Up

This is the one piece of discount arithmetic that genuinely costs people money, because the intuitive answer is always too generous.

"30% off, then an extra 20% off at the till" is not 50% off. The second discount applies to the already-reduced price, not to the original.

100 × 0.70 = 70
70 × 0.80 = 56

Total reduction: 44%, not 50%

The shortcut is to multiply the multipliers: 0.70 × 0.80 = 0.56, so you pay 56% of the original and save 44%. Stacking always produces less than the sum of the parts, and the gap widens as the discounts get larger.

The last row makes the principle unmistakable. Two halvings can never reach free, because each one only removes half of what remains.

A useful corollary: the order does not matter. Applying 30% then 20% gives exactly the same result as 20% then 30%, because multiplication is commutative. If a shop insists one order is better for you, the arithmetic disagrees.

Working Back to the Original Price

Knowing the sale price and the discount, the original is a division — never the discount added back on.

Original = Sale price ÷ (1 − rate ÷ 100)

An item at 63 after 30% off was 63 ÷ 0.70 = 90. Adding 30% to 63 gives 81.90, which is wrong because the 30% was calculated on the larger original figure rather than on the reduced one.

The same division answers the other common question — what percentage off is this? Divide the saving by the original price: an item reduced from 90 to 63 has saved 27, and 27 ÷ 90 = 30%.

Discount and Markup Are Not Symmetrical

Adding a percentage and then removing the same percentage does not return you to where you started, because the two percentages are calculated on different bases.

100 marked up 50% → 150
150 discounted 50% → 75

To reverse a 50% markup you need a 33.3% discount

This is worth knowing when a price is inflated before a sale. An item marked up 50% and then advertised at "50% off" ends up below its original price, but an item marked up 100% and then sold at 50% off is back exactly where it started while appearing to be half price.

Is It Actually a Good Deal?

The percentage tells you how the price changed, not whether the price is good. Three checks separate the two.

• Compare against the price elsewhere, not the reference price. The crossed-out figure on the label is set by the seller. The only meaningful comparison is what the same item costs somewhere else today.
• Work out the unit price. A larger pack at a discount is not automatically better value. Divide by weight, volume or count and compare the per-unit figures — this reverses the ranking more often than people expect.
• Include the cost of getting it. Delivery, a trip across town, or a minimum spend that pushes you into buying something else can absorb the whole saving.

The framing that helps most is that a discount is a reduction in what you spend only if you were going to buy the thing anyway. Spending 60 to save 40 on something you did not need leaves you 60 down, not 40 up.

For percentage arithmetic in other contexts — increases, reverse percentages, and the difference between percent and percentage points — see the percentage calculator. If the price includes sales tax that you need to separate out, the VAT calculator handles that.

Discount Questions