The discount formula
Two numbers matter in every sale: how much you save and what you pay.
saving = price × discount ÷ 100 · sale price = price − saving
Worked example: $120 jacket at 25% off.
- Saving: 120 × 25 ÷ 100 = $30
- Sale price: 120 − 30 = $90
Shortcut: sale price = price × (1 − discount ÷ 100). So $120 × 0.75 = $90 in one step.
Finding the discount percent from two prices
Sometimes the tag shows old and new prices but not the percent: $120 now $90 — what percent off?
Formula: ((original − sale) ÷ original) × 100
Worked: (120 − 90) ÷ 120 × 100 = 30 ÷ 120 × 100 = 25% off. Useful for comparing “was/now” labels and checking whether a claimed discount is honest.
Stacked discounts: the mistake everyone makes
“Extra 10% off already-reduced items” — if an item is 20% off and you get another 10% off, is that 30% off? No.
The second discount applies to the already-reduced price:
- $100 item → 20% off → $80
- Extra 10% off $80 → $72
- Total saving: $28, i.e. 28% off — not 30%.
General rule: multiply the “keep” fractions. 20% + 10% stacked = 0.80 × 0.90 = 0.72 → you pay 72%. Retailers know most shoppers just add the percentages — now you know better.
The 10% mental-math trick
For quick in-store estimates, master 10%:
- 10%: move the decimal one place left. 10% of $85 = $8.50.
- 20%: double it → $17 off, pay $68.
- 30%: triple it → $25.50 off, pay $59.50.
- 5%: halve the 10% → $4.25.
- 15%: 10% + 5% → $12.75 off, pay $72.25.
Combine with fractions for common sales: 25% = quarter off, 50% = half, 75% = pay a quarter. You'll beat the calculator to the answer most of the time.
Real-life uses beyond shopping
- Negotiating: translate “can you do 15% better?” into dollars instantly.
- Business: trade discounts, early-payment discounts, bulk pricing tiers.
- Finance: bond prices quoted at a discount to face value.
- Verification: check a store's claimed “70% off” with the two-price formula above.
For exact figures without the mental gymnastics, the discount calculator gives sale price and savings in one tap — and the percentage calculator handles any other percent problem.
How stores use discounts to influence you
Knowing the math also helps you see through pricing psychology:
- Anchoring: a high “was” price makes the sale price feel like a steal — even if the item never sold at the “was” price. Compute the real discount percent yourself.
- Charm pricing: $99.99 instead of $100. Your brain reads “ninety-something” — the discount math is identical, the perception isn't.
- “Up to 70% off”: legally, only one item needs the full 70%. Most of the store may be 10–20% off. Check individual tags.
- Urgency timers: countdowns push fast decisions. A genuine deal will still be a deal after you do the math calmly.
- Loyalty “extra 10%”: usually stacks on the sale price (see stacked discounts above), so it's worth less than it sounds — still worth taking, just calculate it properly.
The defense is always the same: convert every claim into actual dollars saved before deciding. Percentages are marketing; dollars are reality.
Try it now: Discount Calculator
Enter the original price and discount percent to see the sale price and your exact savings instantly.
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