If a store advertises "20% off, plus an extra 10% off", what is the total discount?

The effective discount is 28%, not 30%. The 20% brings the price to 80% of the original, and the extra 10% then takes 10% off that reduced amount. The combined survival rate is 0.80 × 0.90 = 0.72, meaning you pay 72% of the original price and save 28%.

How do I calculate the effective percentage for three stacked discounts?

Multiply the three survival rates: if the discounts are a%, b%, and c% off, the effective rate is 1 − (1 − a/100)(1 − b/100)(1 − c/100). For 20%, 10%, and 5% that is 1 − 0.80 × 0.90 × 0.95 = 1 − 0.684 = 31.6% off, compared to 35% if you added the rates.

Does it matter whether the store applies the coupon before or after the sale percentage?

For two percentage discounts the order does not change the final price because multiplication is commutative. For a mix of a percentage discount and a fixed-dollar coupon the order can matter slightly when comparing effective savings, but the final dollar price is the same as long as both are applied sequentially to the running price.

Is the tax calculated on the discounted price or the original price?

Tax is calculated on the discounted price. Retailers apply all eligible discounts first and then compute tax on the reduced amount, which is why the calculator always discounts before adding tax.

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

By DiscountLab · Published June 10, 2026 · Updated June 10, 2026

No — sequential discounts multiply rather than add, so 20% off followed by 10% off a $120 item saves $33.60 and gives a 28% effective discount, not 30%.

Why discounts multiply instead of add

When a retailer takes 20% off a $120 item the new price is $96. A second discount of 10% then applies to that $96 price, not the original $120, so it removes $9.60 rather than $12. The two steps together save $33.60 in total — equivalent to 28% off the original price, two full percentage points below the 30% you might expect by adding the two rates.

This is not a trick; it is ordinary arithmetic. Each discount is a fraction of whatever price it encounters, and by the time the second discount arrives the price is already smaller. The general formula is 1 minus the product of the two survival rates: 1 − (1 − 0.20) × (1 − 0.10) = 1 − 0.80 × 0.90 = 0.28, or 28%. The additive shortcut of simply summing the two percentages over-counts the saving by the overlap — here 20% × 10% = 2 percentage points.

Step-by-step on a $120 item

Starting price: $120. First discount, 20% off: the calculator returns a sale price of $96 and an amount saved of $24. Second discount, 10% off the $96 sale price: the calculator returns a final price of $86.40 and a further $9.60 saved. Running total saved is $33.60, and $33.60 divided by $120 equals exactly 28%. The mythical 30% off would have produced an $84.00 final price and $36 saved — $1.60 more than actually on offer.

To use the calculator for this yourself, enter $120 and 20% to get $96, then enter $96 and 10% to get $86.40. The effective-percentage readout on each step shows 20% and 10% respectively, but dividing the cumulative saving by the original price reveals the true 28%.

Does the order of the discounts matter?

No. Applying 10% first and then 20% reaches the same final price. Starting at $120 with 10% off gives $108; 20% off $108 gives $86.40 — identical to the previous order. Multiplication is commutative: 0.80 × 0.90 equals 0.90 × 0.80, so the sequence a retailer applies its promotions cannot change how much you pay. What does vary between retailers is whether both discounts are genuinely applied to the price or whether only the larger one is honoured.

This commutativity means you can use the simpler formula first: multiply the two survival rates, subtract from one, and convert to a percentage. For any pair of discounts a and b the effective rate is 1 − (1 − a)(1 − b). Three successive discounts extend the pattern to 1 − (1 − a)(1 − b)(1 − c), and so on.

Coupon-plus-sale combinations

The same principle applies when a percentage sale and a fixed-dollar coupon are both in play, because the coupon still reduces a price that has already been cut. On a $100 item with a 25% sale and a $15 coupon applied after, the calculator shows: 25% off $100 is $75, then $15 off $75 is $60. That is 40% off the original price — better than the 25% sale alone, but the $15 coupon now represents 20% of the $75 sale price rather than 15% of the original.

Reading the effective-percentage figure for each step makes the real value of a coupon visible. A "$15 off" coupon is worth proportionally more when the item is already on sale at a higher price and the base for the coupon calculation is therefore smaller. Check whether the retailer applies the coupon to the pre-sale or post-sale price, as different checkout systems handle this differently.

How sales tax interacts with stacked discounts

Sales tax is applied to the final discounted price, not the original sticker price. After taking both discounts on the $120 item the taxable amount is $86.40. At an 8% tax rate that adds $6.91, bringing the checkout total to $93.31. If tax were mistakenly applied to the original $120 before discounting the arithmetic would reach the same $93.31 in this particular case — but that is a coincidence of rounding, not a rule. For other discount and tax combinations the two orders diverge, and the correct sequence is always discount first, then tax on the reduced amount.

Tax rates vary by state, county, and product category, so treat the tax-inclusive total from the calculator as a close estimate of what you will see at the register. Some items such as groceries or clothing are exempt from sales tax in certain states, and some discount types such as manufacturer rebates may be taxed differently from store promotions. The calculator accepts any tax rate you enter so you can plug in the rate for your location and item type.

Questions

If a store advertises "20% off, plus an extra 10% off", what is the total discount?: The effective discount is 28%, not 30%. The 20% brings the price to 80% of the original, and the extra 10% then takes 10% off that reduced amount. The combined survival rate is 0.80 × 0.90 = 0.72, meaning you pay 72% of the original price and save 28%.
How do I calculate the effective percentage for three stacked discounts?: Multiply the three survival rates: if the discounts are a%, b%, and c% off, the effective rate is 1 − (1 − a/100)(1 − b/100)(1 − c/100). For 20%, 10%, and 5% that is 1 − 0.80 × 0.90 × 0.95 = 1 − 0.684 = 31.6% off, compared to 35% if you added the rates.
Does it matter whether the store applies the coupon before or after the sale percentage?: For two percentage discounts the order does not change the final price because multiplication is commutative. For a mix of a percentage discount and a fixed-dollar coupon the order can matter slightly when comparing effective savings, but the final dollar price is the same as long as both are applied sequentially to the running price.
Is the tax calculated on the discounted price or the original price?: Tax is calculated on the discounted price. Retailers apply all eligible discounts first and then compute tax on the reduced amount, which is why the calculator always discounts before adding tax.