Break-Even Analysis: Formula, Chart and Worked Examples
Find the sales you need to cover your costs, hit a profit target, and judge your safety margin.
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The idea: contribution pays for fixed costs
Each unit you sell earns a contribution: selling price minus variable cost. That contribution first pays off the fixed costs. The break-even point is the number of units needed to cover them in full. Every unit sold beyond that point adds its full contribution to profit.
Worked example
A product sells for 50. The variable cost is 30 per unit and fixed costs are 20,000.
- Contribution per unit = 50 − 30 = 20.
- Break-even units = 20,000 ÷ 20 = 1,000 units.
- Break-even sales value = 1,000 × 50 = 50,000.
- Contribution margin ratio = 20 ÷ 50 = 40%. Check: 20,000 ÷ 0.40 = 50,000 ✓.
Margin of safety. If the firm expects to sell 1,400 units, its margin of safety is 1,400 − 1,000 = 400 units, or 400 ÷ 1,400 = 28.6%. Sales can fall by that proportion before a loss occurs. See margin of safety.
The break-even chart
The chart plots revenue and total cost against units sold. They cross at the break-even point. To the left the business makes a loss, and to the right it makes a profit.
Units needed for a target profit
With the same figures, to earn a profit of 8,000: (20,000 + 8,000) ÷ 20 = 1,400 units. Check: 1,400 × 20 = 28,000 of contribution, less 20,000 fixed costs, leaves 8,000 profit ✓.
What-if table: how changes move the break-even point
| Scenario | Contribution per unit | Fixed costs | Break-even units |
|---|---|---|---|
| Original (price 50, variable cost 30) | 20 | 20,000 | 1,000 |
| Price rises to 55 | 25 | 20,000 | 800 |
| Fixed costs rise to 25,000 | 20 | 25,000 | 1,250 |
| Variable cost falls to 27 | 23 | 20,000 | 870 (869.6 rounded up) |
Higher prices and lower variable costs lower the break-even point. Higher fixed costs raise it. Round up to whole units, because you cannot sell part of a unit and still break even.
Limitations of break-even analysis
- It assumes the selling price and variable cost per unit stay constant at every volume.
- It assumes fixed costs stay fixed, although they can step up when capacity is exceeded.
- For several products it assumes a constant sales mix.
- It assumes everything produced is sold.
Quick check
1. Fixed costs are 30,000, the selling price is 40 and the variable cost is 25. What is the break-even point in units?
Contribution = 40 − 25 = 15. Break-even = 30,000 ÷ 15 = 2,000 units.
2. How many units are needed to earn a profit of 15,000?
(30,000 + 15,000) ÷ 15 = 3,000 units.
More practice: Problem 7 (break-even, target profit and margin of safety). You can also try the free calculators.
Frequently asked questions
How do you calculate the break-even point in sales value?
Divide fixed costs by the contribution margin ratio, or multiply break-even units by the selling price. In the example, 20,000 ÷ 0.40 = 50,000.
What does the margin of safety show?
How far sales can fall below the expected level before the business reaches break-even.
How can a business lower its break-even point?
Raise the selling price, reduce variable cost per unit, or cut fixed costs.
Keep learning
- Cost Accounting learning path
- Management Accounting learning path
- Cost classification
- Free templates
- Break-even in 8 slides
- Break-even calculator
This lesson is for general learning. Terminology and layouts vary by syllabus and country.
