How to calculate a discount (and why stacked ones don't add up)

The discount formula

A discount is just a percentage applied to a price. The saving is:

Saving = Price × Discount ÷ 100

and the final price is what is left:

Final = Price − Saving, or in one step Final = Price × (1 − Discount ÷ 100)

A 2,000 item at 25% off saves 500 and costs 1,500. At 40% off it saves 800 and costs 1,200.

The single-step version is the one worth remembering: a 25% discount is the same as paying 75% of the price.

Finding the discount from two prices

Working backwards is just as common — you know the old and new price and want the percentage:

Discount % = (Original − Final) ÷ Original × 100

Something marked down from 2,000 to 1,500 is (2,000 − 1,500) ÷ 2,000 × 100 = 25% off. This is the same percentage-change formula used for any price move, which is why it is worth learning once and reusing everywhere.

The stacked-discount trap

This is where most people guess wrong. 25% off, then a further 10% off, is not 35% off.

The second discount applies to the already-reduced price, not the original:

• 2,000 − 25% = 1,500
• 1,500 − 10% = 1,350

So the total saving is 650, which is 32.5% off — not 35%. Discounts multiply, they do not add:

Combined = 1 − (1 − d1) × (1 − d2)

The more discounts you stack, the further the real total falls below their sum. A 50% + 50% double discount is 75% off, not 100%.

The same asymmetry runs in reverse for increases — a 25% rise then a 25% fall does not return to the start. We broke that pattern down in how to calculate percentages.

Run the numbers before you buy

The mental estimate almost always overshoots. Put the real price into the discount calculator and it returns the exact final price and saving, so a "30% off" badge can be checked in a second. For the underlying formulas — and the discount-versus-markup confusion that trips up pricing — the percentage calculator covers the rest.

The rule: trust the arithmetic, not the badge. A discount is only as good as the number you actually pay.