What is a chain discount?

A chain or series discount is two or more percentage reductions applied one after the other. The combined effect is always less than the simple sum of the discounts.

Compound Percentage Calculator

Q: Is 20% off and then 10% off the same as 30% off?

No. 20% off $100 = $80, then 10% off $80 = $72. That's a 28% saving, not 30%. The second discount applies to the already-reduced price.

Q: Why does a 50% loss need a 100% gain to recover?

Lose 50%: $100 becomes $50. To return to $100 from $50 you need to double your money — a 100% gain. The percentages work on different base values.

Find the true combined effect of two percentage changes applied one after the other.

Discounts (reductions) Increases

First discount: % Second discount: %

Original value (optional):

Enter two percentages and click Calculate. Add an original value to also see the final amount.

Why stacked percentages don't add up

When two percentage changes are applied one after the other, the second one acts on the already-changed value, not the original. This makes the combined result different from simply adding the two percentages together.

The formula

Combined discount = 100 − (1 − A÷100) × (1 − B÷100) × 100
Combined increase = (1 + A÷100) × (1 + B÷100) × 100 − 100

Worked examples

First %	Second %	Simple addition	True combined effect
20% off	10% off	30% (wrong)	28% off
50% off	50% off	100% (impossible)	75% off
10% off	10% off	20% (wrong)	19% off
5% raise	5% raise	10% (close)	10.25% increase
25% off	20% off	45% (wrong)	40% off

When does this matter?

Sales with coupon codes — a store may advertise "40% off, plus extra 20% with code". The real saving is 52%, not 60%.
Wholesale trade pricing — suppliers sometimes quote a "double discount" like 30%+10%. This equals 37% off, not 40%.
Annual salary raises — two consecutive 5% raises give a 10.25% total increase, slightly above a flat 10%.
Investment returns — a 20% gain followed by a 20% loss does not break even; the result is a 4% net loss.

The investment trap

This asymmetry is especially important in investing. A 50% loss requires a 100% gain to break even — not 50%. A 20% gain followed by a 20% loss leaves you at 96% of your starting value (a 4% net loss).

Also on this site

Discount Calculator — find the sale price after a single percentage off
Percentage Change Calculator — measure increase or decrease between two values
Percentage Calculator — all three core percentage tools in one place
Why 20% + 10% is not 30% off — the full explanation

FAQ

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

No. 20% off $100 = $80, then 10% off $80 = $72 — a combined saving of $28, or 28% off, not 30%. The second discount is calculated on the already-reduced price.

What is a "series discount" or "chain discount"?

These are other names for stacked or compound discounts — two or more percentage reductions applied one after the other. The formula is: net factor = (1 − d1) × (1 − d2) × …

Can I stack more than two percentages?

Yes. Multiply the factors together: for three discounts A, B, C the combined effect is 100 − (1 − A/100) × (1 − B/100) × (1 − C/100) × 100.

Why does a 50% loss require a 100% gain to recover?

If you lose 50%, your $100 becomes $50. To get back to $100 from $50 you need to double your money — a 100% gain. The percentages work on different base values.