The Discount Formula
Every discount calculation uses one simple formula. Once you understand it, you can do quick mental math while shopping.
Basic Discount Formula
Final Price = Original Price × (1 - Discount Rate)
Example: 25% off $80 → $80 × 0.75 = $60
Worked Example: Black Friday Shopping
You're buying a $249 pair of headphones at 30% off.
- Step 1: Convert 30% to decimal: 30 ÷ 100 = 0.30
- Step 2: Subtract from 1: 1 - 0.30 = 0.70
- Step 3: Multiply: $249 × 0.70 = $174.30
- You save: $249 - $174.30 = $74.70
The Double Discount Trap
When stores advertise "30% off + extra 20% off," most shoppers think they're getting 50% off. They're not.
Double Discount Reality
Total Discount = 1 - [(1 - First Discount) × (1 - Second Discount)]
30% + 20% = 1 - (0.70 × 0.80) = 1 - 0.56 = 44% (not 50%)
Worked Example: Clearance Sale
A $200 jacket is marked 40% off. You have a 15% off coupon.
- After 40% off: $200 × 0.60 = $120
- After additional 15%: $120 × 0.85 = $102
- Total discount: ($200 - $102) ÷ $200 = 49% (not 55%)
$20 Off vs. 20% Off: Which Is Better?
This depends entirely on the item's price. The break-even point tells you when they're equal.
| Item Price | $20 Off Saves | 20% Off Saves | Better Choice |
|---|---|---|---|
| $60 | $20 | $12 | $20 off |
| $100 | $20 | $20 | Equal |
| $150 | $20 | $30 | 20% off |
Quick rule: Break-even = Dollar amount ÷ Percentage. For "$20 off vs 20% off," break-even = $20 ÷ 0.20 = $100.
Finding the Original Price
You see a "Sale: $75" tag on a jacket with "25% off" sticker. What was the original price?
Reverse Discount Formula
Original Price = Sale Price ÷ (1 - Discount Rate)
$75 ÷ 0.75 = $100 original price
Unit Price Comparison
Bigger packages often advertise "better value," but not always. The unit price tells the truth.
Worked Example: Grocery Shopping
Laundry detergent comes in two sizes:
- 64 oz bottle: $11.99 → $11.99 ÷ 64 = $0.187/oz
- 100 oz jug: $16.99 → $16.99 ÷ 100 = $0.170/oz
The larger size saves $0.017 per ounce. Over 100 oz, that's $1.70 savings—but only if you'll actually use all 100 oz before it expires.
Frequently Asked Questions
How do I calculate a discount?
Multiply the original price by (1 - discount rate). For 20% off an $80 item: $80 × 0.80 = $64 final price. The savings is $80 × 0.20 = $16. Mental shortcut: 20% off means you pay 80% of the price. Just move the decimal and multiply: $80 × 8 = $640, then divide by 10 = $64.
How do I calculate what percentage I saved?
Divide savings by original price, multiply by 100. You bought a $150 jacket for $105. Savings = $45. Percentage = ($45 ÷ $150) × 100 = 30% off. This is useful for comparing deals between different stores or checking if a "sale" is actually good.
How do double discounts work?
They multiply, not add. "30% off + extra 20%" means: (1) Apply 30% → pay 70%. (2) Apply 20% to that → pay 80% of 70% = 56%. Total discount is 44%, not 50%. The formula: Total = 1 - (0.70 × 0.80) = 0.44 or 44%.
Which is better: $20 off or 20% off?
Calculate the break-even: $20 ÷ 0.20 = $100. Below $100, take $20 off. Above $100, take 20% off. At exactly $100, they're equal. Real example: $75 item → $20 off saves $20, 20% off saves $15. Take the $20 off.
How do I find the original price from a sale price?
Divide by (1 - discount). A bag costs $63 after 30% off. Original = $63 ÷ 0.70 = $90. Verify: $90 × 0.30 = $27 discount. $90 - $27 = $63. This helps you evaluate whether "original" prices are inflated.
How do I compare unit prices?
Divide total price by quantity. 12-pack of soda at $5.99 = $0.50 per can. 24-pack at $8.99 = $0.37 per can. The 24-pack saves $0.13 per can (26% savings). But only buy the larger size if you'll consume it all—wasted product erases any savings.