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Triple Discount Calculator

Stack three discounts, as percentages or fixed amounts off, and see the final price, the single discount they add up to and your profit per sale. Or start from your cost and margin and find the list price to set.

What is a triple discount?

A triple discount is three discounts applied in turn, each to the price the one before it left. They multiply rather than add, so three discounts of 10% take 27.1% off in total, not 30%. The final price is the list price x (1 - d1) x (1 - d2) x (1 - d3).

Optional

Start from your store

Enter your Shopify or WooCommerce store's address and we'll read the prices it shows publicly. Product costs, ad spend and returns are never public, so those stay yours to fill in.

Stack three discounts

Start from a list price or from your cost and margin, then enter the three discounts in the order they apply.

The price

The price before any discount, and optionally what the item costs you.

The regular price, before any discount.
What one unit costs you to buy or make. Adds the profit per sale and the margin.

The discounts

In the order they apply. Each one can be a percentage or a fixed amount off. Leave one empty for no discount.

Applies to the list price.
Applies to the price left after discount 1.
Applies to the price left after discount 2.

The formulas

How a triple discount is calculated

Final price = List price x (1 - d1) x (1 - d2) x (1 - d3); Combined discount = 1 - (1 - d1) x (1 - d2) x (1 - d3)

Each discount applies to the price the one before it left, so the three multiply rather than add.

d1, d2, d3
The three discounts as decimals, in the order they apply: 20% is 0.20.
Fixed amount off
Taken off the price left at its step: Price after = Price before - Amount, never below zero.
Profit per sale
Final price - Unit cost.
Margin after discounts
Profit per sale / Final price.
List price for a target margin
Unit cost / (1 - Target margin), then each discount undone in reverse order: divide by (1 - d) for a percentage, add the amount for a fixed amount.
  • Three percentage discounts give the same price in any order. With a fixed amount in the stack the order changes the price, so the calculator shows percentages first and fixed amounts first.
  • The list price is rounded up to the smallest unit of your currency, so the margin after discounts is never below the target.

Worked examples

Three triple discounts, worked through

Example 1

Three 10% discounts

An item listed at 100.00 gets 10% off in a sale, 10% for members and 10% with a code.

Inputs

List price
100.00
Discounts
10%, 10% and 10%

Working

  1. After the first discount: 100.00 x 90% = 90.00
  2. After the second discount: 90.00 x 90% = 81.00
  3. After the third discount: 81.00 x 90% = 72.90
  4. Combined discount: 1 - 0.90 x 0.90 x 0.90 = 27.1%

Final price

72.90

The customer saves 27.10, not 30.00. Each 10% is worth less than the one before because it applies to a smaller price.

Example 2

Sitewide, collection and email discounts

A pair of shoes listed at 150.00 is in a 20% sitewide sale, the collection has another 10% off and an email code takes 5%. The shoes cost 40.00.

Inputs

List price
150.00
Discounts
20%, 10% and 5%
Unit cost
40.00

Working

  1. After the first discount: 150.00 x 80% = 120.00
  2. After the second discount: 120.00 x 90% = 108.00
  3. After the third discount: 108.00 x 95% = 102.60
  4. Combined discount: (150.00 - 102.60) / 150.00 = 31.6%
  5. Profit per sale: 102.60 - 40.00 = 62.60, a 61.0% margin

Final price

102.60

Each sale still earns 62.60, against 110.00 at full price, so it takes 1.76 discounted sales to earn what one full-price pair does.

Example 3

A list price that survives three discounts

A product costs 24.00, and the store wants a 50% margin after 20%, 10% and 5% off.

Inputs

Unit cost
24.00
Margin to keep
50%
Discounts
20%, 10% and 5%

Working

  1. Lowest final price: 24.00 / (1 - 50%) = 48.00
  2. Share of the price left after all three: 80% x 90% x 95% = 68.4%
  3. List price: 48.00 / 68.4% = 70.1754, rounded up to 70.18
  4. Check: 70.18 x 68.4% = 48.00, leaving 24.00 over the cost, which is 50%

List price to set

70.18

Listed at 70.18, the product keeps half of what the customer pays even with all three discounts applied.

Triple discounts explained

How three discounts combine

Common triple discounts

Each row applies the discounts in turn, each to what the one before it left. The last column shows what an item listed at 100 sells for.

DiscountsAdded upReal discount100 becomes
10% + 10% + 10%30%27.1%72.90
20% + 10% + 5%35%31.6%68.40
20% + 10% + 10%40%35.2%64.80
20% + 20% + 10%50%42.4%57.60
25% + 10% + 5%40%35.9%64.13
30% + 10% + 5%45%40.2%59.85
30% + 20% + 10%60%49.6%50.40
40% + 10% + 5%55%48.7%51.30
50% + 10% + 5%65%57.3%42.75
50% + 20% + 10%80%64%36.00

Three 10% discounts take 27.1% off, not 30%, because each one applies to a smaller price than the one before.

The formula

Combined discount = 1 - (1 - d1) x (1 - d2) x (1 - d3). For 20%, 10% and 5%: 1 - 0.80 x 0.90 x 0.95 = 1 - 0.684 = 0.316, or 31.6%. With percentages only, the order does not change the result.

Where triple discounts show up

A sitewide sale, a collection or loyalty discount on top, and a code at checkout. Trade pricing can stack the same way, with a distributor tier, a volume discount and an early payment discount. That series is also called a chain discount.

Quote the single equivalent discount

One combined figure is clearer for customers and safer for you, because three separate numbers invite the assumption that they add up. The table above gives the single equivalent for common stacks.

Watch the fixed amounts

If one of the three is a fixed amount off, its position changes the price. Taken last, it comes off the smallest price and gives away the largest share. The calculator shows the final price with percentages first and with fixed amounts first.

Make sure the third discount still pays

Each extra discount comes out of your margin, not your revenue. Use the list price mode above to set a price that keeps your margin after all three, test the extra volume you need with the discount impact calculator, and check what a discounted order leaves after ads and returns with the Black Friday profit calculator. Pricing a new product from scratch? Start with the product pricing calculator.

In MerchantFlow

See what every discount code really earns

MerchantFlow reads the discount codes on your Shopify and WooCommerce orders and shows gross revenue, discount cost, COGS, ad spend and gross margin for each one, so you can see which promotions made money and which only moved revenue.

See the real-time P&L

Common Questions

Triple discount questions

How do you calculate a triple discount?

Apply the three discounts one after another. For 100.00 with 10%, 10% and 10% off: 100.00 x 0.90 = 90.00, then 90.00 x 0.90 = 81.00, then 81.00 x 0.90 = 72.90.

Are three 10% discounts the same as 30% off?

No. Together they take 27.1% off, because each 10% applies to a smaller price: 1 - 0.90 x 0.90 x 0.90 = 0.271.

What is the formula for three successive discounts?

Combined discount = 1 - (1 - d1) x (1 - d2) x (1 - d3), with each discount as a decimal. For 20%, 10% and 5% that is 1 - 0.80 x 0.90 x 0.95 = 0.316, or 31.6%.

Does the order of three discounts matter?

Not when all three are percentages. Once one of them is a fixed amount off it does: a fixed amount taken last comes off the smallest price, so the total discount is larger.

What is the difference between a double and a triple discount?

Only the number of steps. Both multiply what each discount leaves of the price, and a triple discount adds a third step. For two discounts there is a shortcut, d1 + d2 - d1 x d2.

What is a chain discount?

Chain discount is the trade term for a series of discounts applied one after another, often written as 20/10/5. It works exactly like a triple discount: 20/10/5 is 31.6% off the list price.

How do I find the original price before three discounts?

Divide the final price by what each discount left. A final price of 102.60 after 20%, 10% and 5% off was 102.60 / 0.95 / 0.90 / 0.80 = 150.00 before the discounts.

Can three discounts take a product below cost?

Yes. A 31.6% combined discount on a product with a 30% margin sells it below cost. Enter your unit cost to see the profit per sale at the final price, or use the list price mode to set a price that keeps your margin.

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