Discount math · worked examples

How to Calculate Two Discounts in a Row (the 30% + 20% Math)

Checkout says "30% off, plus an extra 20% off." Your brain says 50%. The register says 44% — and the register is right. Here's the math that stacked discounts actually follow, worked out step by step.

They multiply, not add

The instinct to add — 30% + 20% = 50% — fails because the second discount applies to a smaller number. The first discount takes 30% off the original price; the second takes 20% off what's left, not off the original. So the second discount is worth less than its face value.

On a $100 item: 30% off leaves $70. Then 20% comes off the $70 — that's $14, not $20 — leaving $56. You saved $44, so the two discounts together are 44% off, not 50%. The missing 6 points is exactly the shrinkage the second discount suffered.

The formula

Multiply the survival factors instead of adding the percentages:

final price = price × (1 − d₁) × (1 − d₂)

And if you want the single discount that would do the same job — the equivalent single discount:

equivalent % = 1 − (1 − d₁) × (1 − d₂)

For 30% and 20%: 0.70 × 0.80 = 0.56, so the equivalent single discount is 1 − 0.56 = 44%. Percentages under about 20% stack to just under their sum (20% + 20% = 36%); bigger ones diverge faster (50% + 20% = 60%, not 70%).

Worked examples

Example 1 — $100, 30% then 20%. $100 × 0.70 = $70.00; $70 × 0.80 = $56.00. Total saved: $44.00 (44%).

Example 2 — $249.99, 15% then 10%. $249.99 × 0.85 = $212.49; $212.49 × 0.90 = $191.24. A naive 15% + 10% = 25% guess would have said $187.49 — $3.75 too optimistic. The full guide to the multiplication is in the successive discount formula walkthrough.

Does the order matter?

No — multiplication is commutative. 30% then 20% lands on the same final price as 20% then 30%. Whatever order the cashier rings them, the number is identical.

What does depend on order is whether the second discount applies at all: some coupons exclude already-discontinued or clearance prices, and "extra % off sale items" rules differ from store to store. The math doesn't care about order; the coupon eligibility rules do. For category-level coupon structures (percent codes, category codes, dollar rewards applied in a specific sequence), see Kohl's four-coupon structure as a worked example.

Check your own numbers

The card above runs the same multiplication for up to four discounts. If a deal needs the full treatment — coupon limits, exclusions, per-retailer stacking rules — the stacked discount calculator home tool and the Black Friday stacking guide cover the rule side.

This page is arithmetic, not advice: retailer coupon rules decide whether a second discount applies at all. The retailer's own terms govern your checkout.