How Much Must Sales Rise to Offset a Discount? The Margin Math
October 21, 2026
When you discount a product, each unit earns less profit, so you must sell more units to earn the same total. The required increase in volume is d ÷ (m − d), where d is the discount and m is the original gross margin, both as fractions of the original price. With a 40% margin and a 20% discount, that is 0.20 ÷ 0.20 = 100%: you must double unit sales just to break even on profit.
Skip the math and get your answer instantly:
Open the Margin & Markup Calculator →The Worked Example
A product sells for $100 and costs $60, a $40 profit per unit (40% margin). After a 20% discount it sells for $80, so profit per unit is $20. To earn the same total profit, you need twice as many units: 2 × $20 = $40 per original unit.
The discount cut the price by 20% but halved the profit per unit, because the whole discount comes out of margin and none of it out of cost.
| Original margin | 10% discount | 20% discount | 30% discount |
|---|---|---|---|
| 20% | +100% | impossible (no profit) | impossible |
| 30% | +50% | +200% | none |
| 40% | +33% | +100% | +300% |
| 60% | +20% | +50% | +100% |
What the Table Shows
High-margin products can absorb discounts more easily. At a 60% margin, a 20% discount needs 50% more units. At a 20% margin, a 10% discount already requires doubling volume, and a 20% discount wipes out profit entirely.
These figures assume costs per unit stay constant. Fixed costs spread over more units can soften the effect, while extra shipping or support costs can worsen it.
Using This Before a Sale
Estimate whether the promotion can realistically lift volume by the required amount. Count the benefits beyond immediate profit, such as new customers or clearing old stock, but be honest about the cost. Consider alternatives such as bundles, free shipping thresholds, or loyalty perks that protect the price.
Frequently Asked Questions
What is the formula for break-even volume after a discount?
Required increase in units = discount ÷ (original margin − discount), with both as fractions of the original price.
Why do discounts hurt more than they seem?
Because the entire discount reduces profit per unit, which is only a fraction of the price.
Can a discount ever be worth it?
Yes, if volume rises enough, if it clears slow stock, or if it brings repeat customers.
What if the discount equals the margin?
Profit per unit falls to zero, and no volume increase can recover it.