Break-even point in units vs in revenue

There are two standard ways to state a break-even point: the number of units you must sell, or the sales revenue you must reach. They come from the same model and give consistent answers, but each fits different businesses.

The two formulas

Both appear in OpenStax Managerial Accounting §3.2 and in the SBA's break-even guidance. Because the contribution margin ratio is contribution per unit divided by price, break-even revenue always equals break-even units multiplied by price.

Example 1: a single product (illustrative)

Price $40, variable cost $25, fixed costs $5,000 per month. Contribution per unit is $15 and the ratio is 37.5%.

• Break-even units = $5,000 ÷ $15 = 333.33…
• Break-even revenue = $5,000 ÷ 0.375 = $13,333.33 (= 333.33 × $40)

Why you round units up

You cannot sell a third of a unit, and rounding down leaves a small loss. At 333 units, operating income is 333 × $15 − $5,000 = −$5; at 334 units it is +$10. So the practical break-even is 334 units, or $13,360 of revenue at $40 each. Always round up, even when the decimal is small.

Example 2: a service business with no natural unit (illustrative)

A small design studio sells projects of very different sizes, so "units" mean little. Its monthly fixed costs (rent, software, salaried staff) are $12,000. Contractor fees and payment processing run at about 40% of revenue, so the contribution margin ratio is 60%.

Here revenue is the only sensible form. If the studio's average project were $2,500, you could translate that into roughly 8 projects, but the revenue figure is the reliable one.

Which version should you use?

Example 3: break-even with a sales mix (illustrative)

Suppose the business sells two products in a steady 3-to-1 ratio: product A at $40 with $15 contribution, and product B at $60 with $30 contribution. Fixed costs stay at $5,000.

1. Treat one "package" as 3 A + 1 B. Package contribution = 3 × $15 + 1 × $30 = $75; package revenue = 3 × $40 + $60 = $180.
2. Weighted-average contribution per unit = $75 ÷ 4 units = $18.75. Weighted contribution ratio = $75 ÷ $180 ≈ 41.67%.
3. Break-even units = $5,000 ÷ $18.75 ≈ 266.67 units in total: 200 of A and 66.67 of B.
4. Break-even revenue = $5,000 ÷ ($75 ÷ $180) = $12,000 ($8,000 from A + $4,000 from B).

Check: 200 × $15 + 66.67 × $30 = $3,000 + $2,000 = $5,000 of contribution, exactly covering fixed costs. If the mix shifts toward the lower-contribution product A, the break-even point rises even though nothing else changed, which is the central warning of OpenStax §3.4.

Assumptions behind both versions

• Price per unit and variable cost per unit are constant across the volume range.
• Fixed costs are truly fixed within that range (see fixed vs variable costs).
• For a mix, the proportions stay stable.
• Inventory levels do not change, so units produced equal units sold.

When any of these break, re-run the numbers for each scenario instead of stretching one answer.

Educational arithmetic only. Results do not set prices, forecast sales or establish suitability for any lending, investment or business decision. See Use & limitations.