How to Calculate Discounts and Percentages (Without Getting Fooled)
Sale season tricks shoppers all the time — '70% off then an extra 20%' is not 90% off. Here's how to work out discounts, the real final price, and how much you actually saved, with a free calculator.
Sale season is full of maths traps. "70% off, then an extra 20%" sounds like 90% off — it isn't. Here's how to work out discounts and percentages so you always know the real price.
The discounted-price formula
final price = original × (1 − discount%)
you save = original × discount%
Example: 30% off an item priced at 1,000 → 1,000 × 0.70 = 700, and you save 300. Don't want to calculate by hand? Our percentage / discount calculator gives you the final price and the savings together.
The trap: stacked discounts
This is where shops win. "70% off + an extra 20% off" is not 90% off. The discounts stack multiplicatively:
- 70% off → you pay 30%
- an extra 20% off that → 30% × 80% = 24% of the original
So you pay 24% — a 76% total discount, not 90%. Stacked discounts are always less than the sum of the percentages. Whenever you see "extra % off," multiply the remaining fractions instead of adding the percentages.
"What percentage is X of Y?"
Divide and multiply by 100:
percentage = part ÷ whole × 100
Saved 250 on a 1,000 item? 250 ÷ 1,000 × 100 = 25% off. The same formula works for a test score (45/50 = 90%) or any proportion.
Percentage increase: tax and tips
Going up instead of down? Multiply by (1 + percent):
- 5% tax on 1,000 → 1,000 × 1.05 = 1,050
- 15% tip on 800 → 800 × 1.15 = 920
To compare two numbers (this month vs last month), use (new − old) ÷ old × 100 for the percentage change.
The bottom line
Discounts come down to one formula — final price = original × (1 − discount%) — and one warning: stacked discounts multiply, so "extra % off" is always less than it sounds. For increases, multiply by (1 + percent). Keep the percentage calculator open while you shop and you'll never be fooled by a clever sale tag again.
FAQ
How do I calculate a discounted price?
Final price = original price × (1 − discount%). For 30% off an item at 1,000, that's 1,000 × (1 − 0.30) = 1,000 × 0.70 = 700. The amount you save is original × discount%, so 1,000 × 0.30 = 300. A calculator does both at once if you'd rather not do the maths.
Is '70% off plus an extra 20%' the same as 90% off?
No — and this is the most common trap. The two discounts stack multiplicatively, not additively. 70% off leaves you paying 30%; an extra 20% off that leaves 30% × 80% = 24% of the original. So you pay 24%, i.e. a 76% total discount — not 90%. Stacked discounts are always less than the sum of the percentages.
How do I find what percentage one number is of another?
Divide and multiply by 100: part ÷ whole × 100. If you saved 250 on a 1,000 item, that's 250 ÷ 1,000 × 100 = 25% off. The same method tells you a test score (45/50 = 90%) or any proportion.
How do I calculate a percentage increase, like tax or a tip?
Multiply by (1 + percent). For 5% tax on 1,000: 1,000 × 1.05 = 1,050. For a 15% tip on 800: 800 × 1.15 = 920. To find the percentage change between two numbers, use (new − old) ÷ old × 100.