How to Calculate a Discount (and Spot a Fake One)

Sale math is designed to be done badly in your head — that's what "70% off up to 3 items" signage is counting on. The actual formulas take seconds, and knowing two of them (single discounts and stacked ones) covers every case you'll meet in a store or checkout page.

The basic formula

Sale price = original price × (1 − discount rate)

*Example:* a $89 jacket at 30% off: 89 × (1 − 0.30) = 89 × 0.70 = $62.30

The savings, if you want them separately: 89 × 0.30 = $26.70.

The multiplier form (×0.70 rather than "subtract 30%") is worth internalizing — it's faster, and it's the only form that works correctly when discounts stack.

Mental shortcuts at the rack

• 10%: move the decimal left. $89 → $8.90.
• 20%: double the 10% figure. $17.80.
• 25%: quarter the price. ~$22.
• 30%: 10% × 3. ~$26.70.
• Odd numbers like 35%: 25% + 10%, or just take 10% × 3.5.

Round the price first ($89 ≈ $90) — at the register you need the neighborhood, not the cents.

Stacked discounts don't add

"Extra 20% off already-reduced items" is the classic trap. A 30% markdown followed by an extra 20% is not 50% off — the second discount applies to the already-reduced price:

89 × 0.70 × 0.80 = $49.84, an effective 44% off, not 50%.

General rule: multiply the keep-multipliers. (1−0.30)(1−0.20) = 0.56, so you pay 56%. Stacking always yields less than the sum, and retailers phrase it as a sum. The Discount Calculator handles single and percentage-plus-fixed combinations directly.

Discounts and sales tax

Tax is charged on the price actually paid, after the discount, in nearly all jurisdictions. So the register math is:

Final = original × (1 − discount) × (1 + tax rate)

The $62.30 jacket at 8% tax rings up at $67.28. In VAT countries, sticker prices usually already include tax — the VAT Calculator extracts or adds it when receipts need dissecting.

Reading a markdown skeptically

A discount is only as real as the reference price. Three checks:

1. Anchor inflation: "Was $199, now $89" only means something if it actually sold at $199. Price-history tools on major retailers often show the "sale" price is the usual price.
2. Per-unit reframing: "3 for $25" against a $9 unit price is a 7.4% discount dressed as a bundle. Divide it out.
3. Effective rate: compute what you actually pay as a fraction of what you'd otherwise pay today, not against the printed anchor. That's the only percentage that belongs in your decision — and it's a plain percentage problem.

Reversing a discount

To recover the original price from a sale price, divide by the keep-multiplier (don't add the percentage back):

$62.30 ÷ 0.70 = $89 ✓ — whereas $62.30 × 1.30 = $80.99 ✗.

This asymmetry is the same one that governs all percentage changes: down 30% then up 30% doesn't round-trip.

FAQ

How do I calculate 20% off quickly? Take 10% (decimal left one place), double it, subtract. $45 → $4.50 → $9 off → $36.

Is 50% off then 50% off the same as free? No — it's 75% off. Each discount applies to the remaining price: 0.5 × 0.5 = you pay 25%.

How do I find the original price before discount? Sale price ÷ (1 − rate). Paid $36 at 20% off → 36 ÷ 0.80 = $45.

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*Check any deal in seconds with the free Discount Calculator — percentage, fixed, or stacked.*

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