Math walkthrough · single-discount arithmetic

How to calculate 20 percent off

One formula covers every single-discount price tag, and 20% is the case you'll meet most. Here's the formula, two mental-math routes that work without a phone, worked examples at the price points where it matters, and a calculator to check yourself.

The formula

The price you pay is the original price times (1 − the discount as a decimal). For 20% off:

sale price = original price × (1 − 0.20) = original price × 0.8

Multiplying by 0.8 is the same as taking a fifth off. That's the whole method — and the reason it works is worth one sentence: the discount is 20% of the original price, so what remains is 80% of the original price.

Mental math shortcuts

• The 10% step. 10% of a number is the number with the decimal moved one left ($60 → $6). 20% off = take two of those off: $60 − $6 − $6 = $48. Same route works for 30% (three steps), 40% (four)…
• The fifth. 20% is one fifth. $45 ÷ 5 = $9 off → pay $36. Fastest when the price divides by 5 cleanly.
• Multiply by 0.8. The direct route: $129.99 × 0.8 = $103.99 (and if the tag says $129.99, remember the real "20% off" answer is $103.99 — the .99 carries through, it doesn't round away).

Worked examples

Other percentages are the same method with a different multiplier: 30% is ×0.7, 40% is ×0.6 — the full price-point chart is a separate reference. What changes everything is a second discount: stacked percentages multiply instead of add, so check any multi-coupon price in the main calculator instead of extending the mental math.

Went the other direction and need the price before the discount — a "was" anchor or a receipt to reconcile? That's the reverse formula, in how to find the original price before a discount, and the stacked case is worked through in the successive discount formula.

Arithmetic is arithmetic; retailer rounding at the register (and how gift-card or tax interplay is handled) can differ by a cent from the pure figure.