Work out the final price and your savings from any percentage off, including stacked discounts and sales tax.
If you sell anything, from an online store to a market stall to freelance services, three percentages decide whether you make money: markup, margin and discount. They’re easy to confuse, and confusing them is expensive.
Definitions
- Markup: how much you add to your cost to set a price.
Markup % = (Price − Cost) ÷ Cost × 100 - Margin (gross margin): how much of the selling price is profit.
Margin % = (Price − Cost) ÷ Price × 100 - Discount: how much you take off the selling price.
Discount % = (List − Sale) ÷ List × 100
The key difference: markup divides by cost, while margin and discount divide by price.
One product, three numbers
You buy a lamp for $40 and sell it for $60.
- Profit: $20
- Markup: 20 ÷ 40 = 50%
- Margin: 20 ÷ 60 = 33.3%
Same lamp, same $20, two very different percentages. If a supplier says “we sell at 50%,” ask whether they mean markup or margin.
Converting between markup and margin
Margin = Markup ÷ (1 + Markup)
Markup = Margin ÷ (1 − Margin)
| Markup | Margin |
|---|---|
| 25% | 20% |
| 33.3% | 25% |
| 50% | 33.3% |
| 66.7% | 40% |
| 100% | 50% |
| 150% | 60% |
| 200% | 66.7% |
How discounts eat your margin
A discount comes straight out of profit, so its effect on margin is magnified.
Back to the lamp: price $60, cost $40, profit $20. Run a 20% off sale:
- Sale price: $48
- Profit: $8, down 60% from $20
- Margin: 8 ÷ 48 = 16.7%
A 20% discount wiped out 60% of the profit. The discount calculator shows the sale price; subtract your cost from it to see what’s left.
How much more must you sell?
To earn the same total profit after a discount:
Required sales increase = Old margin ÷ (Old margin − Discount) − 1
For a 33.3% margin and a 20% discount: 0.333 ÷ (0.333 − 0.20) − 1 ≈ 150% more units. You’d need to sell two and a half lamps for every one you sold before. Many promotions don’t hit that.
Pricing rules of thumb
- Set prices from margin, not markup. Decide the margin you need, then
Price = Cost ÷ (1 − Margin). For a 40% margin on a $40 cost: 40 ÷ 0.6 = $66.67. - Know your discount ceiling. Never discount beyond your margin, or you’re selling at a loss.
- Prefer fixed-amount or bundle offers for low-margin items. “Free shipping over $50” often costs less than a percentage off.
- Stacked promotions compound. See Stacked Discounts Explained: Why 20% + 10% Isn't 30% Off.
Quick reference
| Question | Formula |
|---|---|
| Price from cost and markup | Cost × (1 + Markup) |
| Price from cost and margin | Cost ÷ (1 − Margin) |
| Sale price from discount | Price × (1 − Discount) |
| Percent change in profit | (New profit − Old) ÷ Old |
For any percentage that isn’t covered here, the percentage calculator handles “what percent of” and percentage-change questions directly.
Work out the final price and your savings from any percentage off, including stacked discounts and sales tax.