Break-Even Analysis Explained: Formula, Chart and Worked Examples

What break-even means

Break-even analysis answers one question before you spend money: how much do I have to sell for the business, product or project to stop losing money? Below that volume you make a loss; above it, every extra sale adds profit. It is used to test a new product, set a price, decide whether to rent a bigger shop, or judge a marketing target.

The idea rests on splitting costs in two kinds. Fixed costs stay the same however much you sell in the period. Variable costs rise with each unit sold.

Some costs are part fixed and part variable, such as an electricity bill with a standing charge and a usage charge. Split them before you enter them.

The break-even formula

The contribution margin is what each unit contributes toward paying the fixed costs: price minus variable cost. Break-even units are the fixed costs divided by that contribution.

• Contribution margin per unit = selling price − variable cost per unit.
• Break-even units = fixed costs ÷ contribution margin per unit.
• Break-even sales = break-even units × price, or fixed costs ÷ contribution margin ratio.

Worked example. A shop has fixed costs of 18,000 a month and sells a product for 80, paying 35 in variable cost per unit. The contribution margin is 45, which is 56.3% of the price. It breaks even at 18,000 ÷ 45 = 400 units, which is 32,000 in sales. Every unit after the 400th adds 45 to profit.

Round break-even units up to a whole unit. You cannot sell 399.4 units, and you have not covered your costs until you sell the next whole one.

How to read the break-even chart

The chart plots money against units sold. The revenue line starts at zero and climbs by the price with every unit. The total-cost line starts at the fixed costs, because you pay them even with no sales, and climbs more slowly by the variable cost per unit. A dashed horizontal line shows the fixed costs.

Where the revenue line crosses the total-cost line is the break-even point. To the left the cost line is on top, so you are in the loss zone; to the right the revenue line is on top, the profit zone. The gap between the two lines at any volume is the profit or loss at that volume. A steeper revenue line, a flatter cost line or a lower start moves the crossing point left and makes the business safer.

Planning for a profit target

Breaking even is the minimum. To earn a target profit, add it to the fixed costs. To make 4,000 a month in the example you need (18,000 + 4,000) ÷ 45 = 489 units.

If the target is after tax, you have to earn more before tax. With a 30% tax rate, a 3,500 after-tax profit means 5,000 before tax, so the units become (18,000 + 5,000) ÷ 45 = 512. Check the answer against your capacity: if you can only supply 450 units, a target that needs 489 is out of reach without changing price or cost.

Margin of safety and operating leverage

The margin of safety measures how far above break-even you expect to be: (expected units − break-even units) ÷ expected units. At 500 expected units and a break-even of 400, it is 20%, so sales can fall by a fifth before the business loses money. At 300 expected units the margin is -33.3%: negative means a loss, here -4,500.

Operating leverage is contribution divided by profit. At 500 units it is 5.0×: a 10% rise in sales lifts profit by about 50%, and a 10% fall cuts it by the same. A business with high fixed costs has high leverage, which is a strength in good months and a risk in bad ones.

What to change if you are below break-even

If you expect only 300 units, the same figures give a loss. To break even at 300 you could raise the price to 95, cut the variable cost to 20, or cut fixed costs to 13,500. The sensitivity table shows which lever moves the break-even most.

In this example a 10% price rise cuts break-even from 400 to 340 units, more than a 10% fall in either cost, because price changes the contribution on every unit.

More than one product

Most businesses sell a mix. Estimate each product’s share of units sold, take the weighted average price and variable cost, and treat that as one average product. If 70% of units are a Standard item at price 100 and cost 60, and 30% are a Premium item at price 200 and cost 100, the average price is 130 and the average variable cost 72. With 5,800 of fixed costs the break-even is 100 units in total, 70 Standard and 30 Premium.

The result is only as good as the mix. If customers shift toward the cheaper product, the real break-even rises, so re-run the numbers when the mix changes.

Break-even analysis in Excel

1. Put fixed costs, price and variable cost in three cells.
2. Contribution margin: price minus variable cost. Break-even units: fixed costs divided by it.
3. Make a column of units from 0 to about twice the break-even, a revenue column (units × price) and a total-cost column (fixed + units × variable cost).
4. Select the units, revenue and total-cost columns and insert a line chart. The lines cross at break-even.

The calculator’s Excel CSV does the layout for you: it has the inputs at the top and live formulas below, so changing the price or cost redraws the table.

Limits of break-even analysis

• It assumes a steady price and variable cost, but discounts and overtime change them.
• It assumes fixed costs stay fixed, but a bigger volume may need more space or staff.
• It says nothing about when cash arrives, so a business can break even and still run out of money.
• It treats demand as given and does not predict whether you can sell the units.

Use it as a planning aid beside a cash-flow forecast, not as a forecast of its own.

Common questions

How this guide was prepared

This guide uses the standard cost-volume-profit formulas taught in introductory managerial accounting. Every figure is computed by the same code that runs the break-even calculator, so you can reproduce each example by entering the same numbers.

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