How to Calculate Discount Percentage — Sale Prices & Savings Guide

The Core Discount Formulas You Need to Know

All discount calculations revolve around three key values: Original Price, Discount Percentage, and Sale Price. Master these foundational equations to handle any scenario.

1. Calculating the Discount Amount and Sale Price

This is the most common calculation—finding how much you save and what you pay after a percentage discount.

Formulas:

• Discount Amount = Original Price × (Discount % ÷ 100)
• Sale Price = Original Price – Discount Amount
• Or directly: Sale Price = Original Price × (1 – Discount % ÷ 100)

Example: A £120 jacket is 25% off.

• Discount = £120 × 0.25 = £30
• Sale Price = £120 – £30 = £90
• Or: £120 × (1 – 0.25) = £90

💡 Pro Tip: For mental math, calculate 10% first (move decimal left once), then scale:
25% = 10% + 10% + 5% → £12 + £12 + £6 = £30

2. Finding the Original Price from Sale Price

Ever see a “Was £X, Now £Y” tag and wonder if it’s genuine? Reverse the calculation.

Formula:
Original Price = Sale Price ÷ (1 – Discount % ÷ 100)

Example: You paid £84 after a 30% discount.

• Original = £84 ÷ (1 – 0.30) = £84 ÷ 0.70 = £120

3. Calculating the Discount Percentage

Compare two prices to find the actual discount offered.

Formula:
Discount % = [(Original – Sale) ÷ Original] × 100

Example: A TV drops from £500 to £375.

• Discount = [(500 – 375) ÷ 500] × 100 = (125 ÷ 500) × 100 = 25%

4. Handling Multiple Discounts (Stacked or Sequential)

Stores often apply discounts in sequence (e.g., “20% off + extra 10% for members”). Never add percentages!

Formula:
Final Price = Original × (1 – D₁) × (1 – D₂) × …

Example: £100 item with 20% off, then 10% off:

• After first discount: £100 × 0.80 = £80
• After second: £80 × 0.90 = £72
• Total discount = 28% (not 30%!)

5. Including Sales Tax (VAT)

In the UK, VAT is typically 20%. Decide whether the discount applies before or after tax.

Pre-Tax Discount (most common):

1. Apply discount to pre-tax price
2. Add VAT to sale price
   Example: £100 item, 20% off, 20% VAT:

• Sale price = £80
• Total = £80 × 1.20 = £96

Post-Tax Discount (rare):

1. Add VAT to original
2. Apply discount to total
   Example: £100 × 1.20 = £120 → £120 × 0.80 = £96
   → Same result only if discount % = VAT %—usually not the case!

Pro Tips & Common Mistakes

• Beware of “Was” prices: Retailers inflate “original” prices to make discounts seem larger. Verify with price history tools.
• Bulk discounts ≠ percentage discounts: “Buy 2, get 1 free” = 33% off, not 50%. Calculate per-unit cost:
  3 items for price of 2 → Pay £20 for 3 → £6.67/unit vs. £10 → 33.3% savings.
• Use decimals, not percentages: 15% = 0.15 in formulas. Avoid the “%” button on basic calculators—it behaves differently.
• Round only at the end: Keep intermediate values precise to avoid compounding rounding errors.
• For e-commerce: Always display both discount % and savings amount—shoppers respond to both.

Practical Applications

• Shoppers: Compare “3 for £10” vs. “25% off” deals
• Sellers: Set competitive sale prices without eroding margins
• Businesses: Calculate bulk order savings for procurement
• Students: Solve real-world math problems involving percentages
• Travelers: Decode hotel or flight discounts in foreign currencies