Business · By ListCalc Editorial Team · Jul 30, 2026 · 5 min read

Why 20% Then 10% Off Is Not 30% Off

Take 20% off, then another 10% off, and most people expect to pay 70% of the original price. You will actually pay 72%. The second discount is applied to a smaller number, and that one detail changes every stacked-offer calculation you will ever do.

Follow the money once

Start with $100. The first discount takes 20% of $100, which is $20, leaving $80. The second discount takes 10% of $80 — not of $100 — which is $8, leaving $72.

You paid $72, so the total discount was $28. Twenty-eight percent, not thirty. The missing 2% is 10% of the $20 you had already saved: a discount on money you were never going to spend.

The formula: combined discount = 1 − (1 − d₁) × (1 − d₂) × …
For 20% and 10%: 1 − (0.80 × 0.90) = 1 − 0.72 = 0.28

Discounts multiply because each one acts on whatever survived the last. Add more and the effect keeps compounding downward — you can stack a lot of percentages and never reach zero.

Order does not matter

Multiplication is commutative, so applying 10% first and 20% second gives exactly the same result:

Order	Step 1	Step 2	Final
20% then 10%	$80.00	$72.00	$72.00
10% then 20%	$90.00	$72.00	$72.00

If a cashier tells you the order of two percentage discounts matters, it does not — provided both are percentages. Fixed-dollar coupons are a different story, and that is covered below.

Common stacks

Advertised	Sounds like	Actually is	You pay
10% + 10%	20%	19%	81.0%
20% + 10%	30%	28%	72.0%
25% + 15%	40%	36.25%	63.75%
30% + 20%	50%	44%	56.0%
50% + 20%	70%	60%	40.0%
50% + 30% + 20%	100%	72%	28.0%

That last row is the clearest illustration: three discounts that add to 100% still leave you paying 28 cents on the dollar. Percentages taken in sequence can never reach free.

When order does matter

Mix a percentage with a fixed-dollar coupon and the sequence changes the total. Take a $200 order with 25% off and a $20 coupon:

Order	Working	You pay
Percentage first	$200 → $150 → −$20	$130.00
Coupon first	$200 → $180 → ×0.75	$135.00

Applying the percentage first is $5 better for the customer, because the fixed $20 comes off at full value instead of being shrunk by 25%. Retailer terms usually specify which goes first — and it is rarely the one that favours you.

Two more sequencing traps. Sales tax is normally calculated on the discounted subtotal, so discounts reduce the tax too. And a coupon with a minimum-spend threshold is usually tested against the pre-discount total, so stacking can quietly disqualify you from the very offer you were stacking.

The side sellers care about

From behind the counter the same arithmetic looks alarming, because a discount comes entirely out of profit. Take an item costing $60 and priced at $100 — a 40% gross margin:

Discount	Price	Profit	Margin	Profit change
None	$100	$40	40.0%	—
10%	$90	$30	33.3%	−25%
20%	$80	$20	25.0%	−50%
20% + 10%	$72	$12	16.7%	−70%

A 20% discount does not cost 20% of profit — it costs half. Stack another 10% on top and 70% of the profit is gone, which is why the extra 10% that looked small to the customer is the one that hurts. To stay whole on profit at 20% off, you need to sell twice as many units.

Checking an offer quickly

Multiply what you keep, not what you save. Two 20% discounts means keeping 0.8 × 0.8 = 0.64, so 36% off. It is one multiplication and it is always right.

Sources and method: the combined-discount identity 1 − ∏(1 − dᵢ) follows directly from applying each reduction to the remaining balance. Margin figures are gross margin, (price − cost) ÷ price. Sequencing of percentage and fixed-value offers, and minimum-spend qualification, are set by seller terms; US advertising of comparative prices is addressed by the FTC Guides Against Deceptive Pricing (16 CFR Part 233). Last reviewed 30 July 2026.

Run your own numbers

Discount Percentage Profit margin

FAQ

Is 20% off then 10% off the same as 30% off?

No — it works out at 28% off. The second discount applies to the already-reduced price, so on a $100 item you pay $80 after the first discount and $72 after the second. The general formula is 1 − (1 − d₁)(1 − d₂), which for 20% and 10% gives 1 − (0.8 × 0.9) = 0.28.

Does the order of two discounts change the price?

Not when both are percentages — multiplication is commutative, so 20% then 10% and 10% then 20% both land on $72 from $100. Order does matter when you combine a percentage with a fixed-dollar coupon: taking the percentage off first leaves the coupon at full value and gives the lower final price.

Can stacked percentage discounts ever reach 100% off?

No. Each discount only removes a fraction of what is left, so the price approaches zero without reaching it. Even 50% + 30% + 20% — which adds to 100% — leaves you paying 28% of the original price, because you keep 0.5 × 0.7 × 0.8 = 0.28 of it.

How do I calculate a stacked discount quickly?

Work with what you keep rather than what you save. Convert each discount to the fraction remaining, multiply them together, and subtract from 1. For 25% and 15%: 0.75 × 0.85 = 0.6375, so you pay 63.75% and the true discount is 36.25%.

How much does a 20% discount cost a business?

Far more than 20% of profit. On an item costing $60 and priced at $100, the $40 profit falls to $20 — a 50% cut — because the entire discount comes out of margin rather than being shared with cost. Stacking a further 10% drops profit to $12, down 70% from where it started.

Sources

Primary references used for the figures and rules on this page.

Guides Against Deceptive Pricing (16 CFR Part 233) — Federal Trade Commission
Advertising and Marketing Business Guidance — Federal Trade Commission