250 with 20% then 10% off
- I want to find
- Price after discounts
- Original price
- 250
- Discounts (%)
- 20, 10
- Final price
- 180.00
- Amount off
- 70.00
- Effective discount
- 28%
Checked against: 250 × 0.8 × 0.9 = 180; 1 − 0.72 = 28%
Discount, markup and margin calculator
Sale price after one or more percent-off discounts, and selling price from cost using a markup or a profit margin, with each converted to the other.
By AdminDrafted with AI writing toolsUpdated Checked examples: 7
Final price
$
Final price: $180.00
- Amount off
- $70.00
- Effective discount
- 28%
You pay $180.00, saving $70.00: an effective discount of 28%. That is less than the 30% you get by adding the discounts, because each one applies to an already reduced price.
Price after each discount
How it's calculated S
Apply each discount to the running price
In the formula, P is the original price, P_f the final price, d_i each discount percentage, m the markup rate and g the margin rate. Enter percentages in the fields; m and g in the formula are decimal fractions.
Effective discount
Multiplying the successive price factors gives a 28% discount. Adding the rates 20% + 10% gives 30%.
About the discount, markup and margin calculator
Each discount multiplies the running price by (1 − d/100), so stacked discounts compound rather than add. For pricing, markup is profit as a percentage of cost and margin is profit as a percentage of the selling price. The calculator finds the selling price from either one and converts between them with margin = markup ÷ (1 + markup).
With the defaults, 20% off 250 followed by a further 10% off leaves 180: an effective discount of 28%, not 30%. In the pricing modes, an item that costs 80 and is marked up 25% sells for 100, which is a 20% margin.
A margin must stay below 100%, since a 100% margin would mean the item cost nothing, while a markup has no upper limit. All figures are per item, before any sales tax or VAT.
How to calculate a discount
To take a percentage off a price, multiply the price by (1 − discount ÷ 100). For 30% off 80, you pay 80 × 0.7 = 56 and save 80 × 0.3 = 24. That covers one discount; a second discount on top multiplies again instead of adding.
For mental math, find 10% by moving the decimal point one place left and build from it. 15% of 40 is 4 + 2 = 6, so 15% off 40 leaves 34.
How to find the percent off or the original price
Divide the saving by the price before the cut. A price cut from 60 to 45 saves 15, and 15 ÷ 60 = 25% off. Dividing by the new price instead gives 33.3%, which is the rise from 45 back to 60.
To recover the price before a discount, divide the sale price by the fraction that remains. An item selling for 42 after 40% off kept 60% of its price, so it was 42 ÷ 0.6 = 70.
Stacked discounts: why 20% then 10% off is 28%
The second discount applies to the price the first one already reduced, so multiply the fractions you keep. 20% off keeps 0.8 and a further 10% keeps 0.9 of that: 0.8 × 0.9 = 0.72, an effective discount of 28%, not 30%.
The order of percentage discounts makes no difference, because the product is the same in any order. Two 50% discounts keep 0.5 × 0.5 = 0.25 of the price: 75% off, not free.
| Scenario | Final price | Amount saved | Effective discount, % |
|---|---|---|---|
| Default | 180.000000 | 70.000000 | 28.000000 |
| Two half discounts | 25.000000 | 75.000000 | 75.000000 |
| No discount | 250.000000 | 0.000000 | 0.000000 |
| Full discount | 0.000000 | 250.000000 | 100.000000 |
| Reversed order | 180.000000 | 70.000000 | 28.000000 |
Every row starts from 250 except two half discounts, which starts from 100. Default takes 20% and then 10% off; reversed order takes 10% and then 20%. No discount and full discount are single reductions of 0% and 100%.
Coupons worth a fixed amount
A coupon for 10 off and a 10% discount are equal only on a price of 100. On 250, the coupon saves 10 and the percentage saves 25.
Combine a fixed coupon with a percentage and the order matters. With 20% off and a 10 coupon on 250, the coupon first gives (250 − 10) × 0.8 = 192. The percentage first gives 250 × 0.8 − 10 = 190. The store's terms decide which applies.
How to calculate markup and margin
Both compare the same profit with a different base: markup is profit ÷ cost, and margin is profit ÷ selling price. An item that costs 30 and sells for 40 earns 10, a 33.33% markup but only a 25% margin.
Use the formula that matches the percentage you were given:
- Price from a markup: cost × (1 + markup ÷ 100). A 25% markup on 30 gives 37.50, which is a 20% margin.
- Price from a target margin: cost ÷ (1 − margin ÷ 100). A 25% margin on 30 needs a price of 40.
- Markup to margin: markup ÷ (100 + markup) × 100.
- Margin to markup: margin ÷ (100 − margin) × 100.
Markup needed for common margins
- 10% margin: 11.11% markup
- 20% margin: 25% markup
- 25% margin: 33.33% markup
- 30% margin: 42.86% markup
- 40% margin: 66.67% markup
- 50% margin: 100% markup
- 60% margin: 150% markup
- 75% margin: 300% markup
Read a line from right to left to turn a markup into a margin: doubling the cost, a 100% markup, gives a 50% margin.
AccountingTools' explanation uses an item that costs 70 and sells for 100. The profit of 30 is a 30% margin and a markup of about 42.9%.
Common mistakes
- Pricing with a markup when the target is a margin. Adding 30% to a cost of 70 gives 91, only a 23.08% margin. A 30% margin needs 70 ÷ 0.7 = 100.
- Reversing a percentage with the same percentage. 20% off 100 is 80, and adding 20% back gives 96. On a cost of 80, a 25% markup followed by 25% off leaves 80 × 1.25 × 0.75 = 75. To undo a discount, divide by the fraction it kept: 80 ÷ 0.8 = 100.
- Dividing by the wrong base. Percent off divides by the original price, markup by the cost and margin by the selling price.
- Leaving costs out. A margin is only as complete as the cost behind it. If shipping, card fees or returns matter, add them to the per-item cost first.
What to enter
- Discounts as a comma-separated list in the order they apply, such as
20, 10: up to 10 discounts, each from 0% to 100%. - Markup as a percentage of cost, with no upper limit.
- Margin as a percentage of the selling price, below 100%.
- Fixed-amount coupons are not modeled: subtract them from the price yourself at the step the store applies them.
- Prices stay unrounded between discounts, so a till that rounds to the cent after each step can differ by a cent.
Related calculators
The percentage calculator handles percent change and "what percent of" questions. The GST, VAT and sales tax calculator adds tax to a sale price.
To compare pack sizes once you know the discounted prices, use the unit price comparison calculator. To set a price that also covers fixed costs, use the break-even calculator.
Worked examples
Two 50% discounts are 75% off, not 100%
- I want to find
- Price after discounts
- Original price
- 100
- Discounts (%)
- 50, 50
- Final price
- 25.00
- Effective discount
- 75%
Checked against: 100 × 0.5 × 0.5 = 25
No discount
- I want to find
- Price after discounts
- Original price
- 250
- Discounts (%)
- 0
- Final price
- 250.00
- Effective discount
- 0%
Checked against: Definition: 0% off leaves the price unchanged
Cost 80 with 25% markup
- I want to find
- Price from cost and markup
- Cost
- 80
- Markup (on cost)
- 25%
- Final price
- 100.00
- Margin
- 20%
- Profit per item
- 20.00
Checked against: 80 × 1.25 = 100; 20/100 = 20% margin
Questions
How do you calculate a percentage discount?
Multiply the price by (1 − discount ÷ 100). 20% off 250 is 250 × 0.8 = 200, a saving of 50. To find the discount from two prices, divide the saving by the original price: an item cut from 250 to 180 is 70 ÷ 250 = 28% off.
Is 20% off plus an extra 10% off the same as 30% off?
No. The second discount applies to the already reduced price, so 20% then 10% off is 1 − 0.8 × 0.9 = 28% off in total. Two 50% discounts leave a quarter of the price, which is 75% off rather than 100%. The order does not matter: 10% then 20% also gives 28%.
What is the difference between markup and margin?
Markup is profit divided by cost; margin is profit divided by the selling price. An item that costs 70 and sells for 100 makes 30 profit: a 42.9% markup and a 30% margin, the pairing AccountingTools uses in its explanation. Margin is always the smaller of the two, and a markup m converts to a margin of m ÷ (1 + m).
What markup gives a 50% margin?
A 100% markup: doubling the cost makes the profit equal to the cost, which is half the selling price. In general markup = margin ÷ (1 − margin), so a 20% margin needs a 25% markup, a 40% margin needs 66.67%, and a 60% margin needs 150%.
How do you find the selling price from cost and margin?
Divide the cost by (1 − margin). A cost of 60 at a 40% margin sells for 60 ÷ 0.6 = 100. Adding 40% to the cost instead gives 84, which is only a 28.57% margin; confusing the two percentages underprices every item.
About this calculator
Sources
Checked against references
This calculator includes 7 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.