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
This lesson is for general learning. Terminology and layouts vary by syllabus and country.
