Stacking Discounts: How the Math Actually Works

The Question Everyone Gets Wrong

If a store offers 20% off, then applies an extra 10% off at checkout — is that 30% off total?

No. It is 28% off.

This surprises most people. Here is exactly why, and how to calculate any stacked discount correctly.

Why Discounts Compound, Not Add

The second discount applies to the already-reduced price — not the original.

Example: 20% then 10% off a $100 item

• Step 1: 20% off $100 = $80
• Step 2: 10% off $80 = $72

Total saving: $28 on $100 = 28% total discount

If the discounts simply added, you would pay $70. You actually pay $72. The difference is $2 — small here, but significant on large purchases.

The Formula for Any Two Stacked Discounts

Combined discount = 1 − (1 − d1) × (1 − d2)

Where d1 and d2 are the discounts as decimals.

Example: 20% and 10%

1 − (1 − 0.20) × (1 − 0.10)
= 1 − 0.80 × 0.90
= 1 − 0.72
= 0.28 = 28%

Example: 30% and 15%

1 − (1 − 0.30) × (1 − 0.15)
= 1 − 0.70 × 0.85
= 1 − 0.595
= 0.405 = 40.5%

Three or More Discounts

The formula extends naturally:

Combined = 1 − (1−d1) × (1−d2) × (1−d3)

Example: 20% + 10% + 5% off

1 − 0.80 × 0.90 × 0.95
= 1 − 0.684
= 0.316 = 31.6%

Not 35%. The gap grows wider with each additional discount stacked.

Common Real-World Stacking Scenarios

Sale + Coupon code

A site offers 25% off, and you have a 10% newsletter coupon.

1 − 0.75 × 0.90 = 1 − 0.675 = 32.5% total saving

Not 35%. On a $150 order, the difference is $3.75.

Two 20% codes applied sequentially

1 − 0.80 × 0.80 = 1 − 0.64 = 36% total

Not 40%. Two 20% codes equal 36% off.

Stacked Discount Reference Table

For Businesses: The Maximum Safe Discount

If you mark up a product at 40% above cost, the maximum discount you can offer without losing money is:

Max discount = Markup ÷ (1 + Markup) = 0.40 ÷ 1.40 = 28.6%

Stacking two “small” discounts that together exceed 28.6% can quietly destroy your margin.

Use our discount calculator to check the real combined saving on any stacked offer.