Break-even analysis: the formula, a worked example, and a break-even chart in Excel

Break-even analysis finds the sales volume at which revenue exactly covers fixed and variable costs, so profit is zero. A product selling at $90 with a variable cost of $54 contributes $36 a unit; with fixed costs of $540,000 a year it breaks even at 15,000 units, or $1,350,000 of revenue. Every unit beyond that adds $36 of profit.

The break-even formula

Contribution per unit = Price − Variable cost per unit

Break-even units = Fixed costs / Contribution per unit

Break-even revenue = Fixed costs / Contribution margin ratio, where the ratio = Contribution per unit / Price

Contribution is what each sale leaves after the costs that rise with volume; it pays for the fixed costs first and becomes profit only once they are covered. OpenStax's managerial accounting text defines the break-even point as the dollar amount or production level "at which the company has recovered all variable and fixed costs", and gives both the unit and the sales-dollar versions. The ratio itself, and the contribution margin income statement behind it, are worked in full on the contribution margin ratio page; the contribution margin glossary entry has the short definition.

The figures you need

Three numbers for the period, all from the ledger:

• Fixed costs: rent, salaried staff, systems, depreciation, insurance. They do not change when one more unit is sold.
• Price per unit: the net price after discounts and rebates, not the list price.
• Variable cost per unit: materials, per-unit labor, commission, freight out, payment fees.

Many costs are part fixed and part variable: a utility bill with a standing charge, a sales team on salary plus commission. Split them before you start. The high-low method takes the months with the highest and lowest volume; the change in cost divided by the change in volume is the variable rate, and what is left is fixed. A regression of monthly cost on monthly volume does the same with every month. Allocating shared costs by driver, as in cost to serve per customer in Excel, is the same exercise one level down.

Worked example

One product, one year, in USD:

Step by step:

1. Contribution per unit = 90 − 54 = $36.
2. Contribution margin ratio = 36 / 90 = 40%.
3. Break-even units = 540,000 / 36 = 15,000 units.
4. Break-even revenue = 540,000 / 0.40 = $1,350,000, which is also 15,000 × 90.
5. Units for a target profit of $180,000 = (540,000 + 180,000) / 36 = 20,000 units.
6. Profit at the planned 18,500 units = 18,500 × 36 − 540,000 = $126,000.
7. Margin of safety = (18,500 − 15,000) / 18,500 = 18.9%, or 3,500 units and $315,000 of revenue.

The margin of safety is the difference between current or planned sales and break-even sales: here sales could fall by 18.9% before the product stops making money.

Build it in Excel, with a chart

Put price in B1, variable cost per unit in B2 and fixed costs in B3. Then:

Break-even units:    =B3/(B1-B2)
Break-even revenue:  =B3/((B1-B2)/B1)
Target-profit units: =(B3+180000)/(B1-B2)

For the chart, list volumes from 0 to 25,000 in A8:A13 and fill these down from row 8:

Revenue (B8):     =A8*$B$1
Total cost (C8):  =$B$3+A8*$B$2
Profit (D8):      =B8-C8

Select A7:C13 and insert a line chart (or a scatter with straight lines, so the units sit on a true numeric axis). Revenue starts at zero and rises $90 a unit; total cost starts at $540,000 and rises $54 a unit. The lines cross at 15,000 units and $1,350,000. The vertical gap between them to the right of the crossing is profit; to the left it is loss.

What moves the break-even point

Change one input at a time against the worked example:

Units are whole, so the two fractional answers round up: 13,334 and 16,217 units. A 5% price rise cuts break-even by 1,667 units; a 5% rise in variable cost adds 1,216. Price moves break-even more because it acts on $90, not $54. To compare several changes at once, keep each case in its own column of inputs.

The check that proves it

At break-even, profit must be exactly zero:

15,000 × 90 − 15,000 × 54 − 540,000 = 1,350,000 − 810,000 − 540,000 = 0

Then prove it a second way. Put profit in a cell, =B10*(B1-B2)-B3 with a trial volume in B10, and run Goal Seek: set the profit cell to 0 by changing B10. Microsoft's guide to Goal Seek notes that the cell it changes must feed the formula you set. It returns 15,000. If the formula and Goal Seek disagree, an input cell is wrong. Goal Seek in Excel covers the tool in more depth.

Break-even for a multi-product business

With more than one product, break-even uses the weighted contribution margin ratio at the current sales mix. Suppose the same $540,000 of fixed costs supports two products:

The weighted ratio is 552,000 / 1,560,000 = 35.4%, and break-even revenue is 540,000 / (552,000 / 1,560,000) = $1,526,087. Swap the volumes, 8,000 of A and 12,000 of B, and revenue falls to $1,440,000, contribution to $468,000, the ratio to 32.5% and break-even rises to $1,661,538. The fixed costs did not change; the mix did. The contribution margin ratio page works the same effect on four products. Break-even for a business is only as stable as its mix.

Where it goes wrong

• Semi-variable costs treated as all fixed or all variable. Split them first, by high-low or regression, or break-even is wrong before the arithmetic starts.
• One break-even for several products while the mix shifts. The weighted contribution margin moves with the mix, and break-even moves with it.
• Constant price and unit cost assumed at every volume. Volume discounts lower price; overtime and expedited freight raise unit cost. The straight lines in the chart hold only over a relevant range.
• Fixed costs that step up at capacity. A second shift or a second warehouse adds a block of fixed cost and creates a second break-even point.
• Break-even read as a target. It is the floor. A plan that sits 5% above break-even has almost no room for a bad quarter.

Break-even by customer

A business-wide break-even hides customers who never cover the cost of serving them. Covirage's tools compute contribution per customer from your ledger, delivery and order files; the external AI model explains the ranking and never does the arithmetic. See Covirage for customer profitability, and margin by account for the same contribution test run customer by customer. To split a cost into its fixed and variable parts first, see fixed vs variable costs; for testing the inputs, scenario analysis in Excel; for price against cost, markup vs margin.