How the result is calculated
Break-even is the volume at which a business stops losing money and has not yet started making any: sales exactly pay for every cost of the period. Below it each extra sale shrinks the loss, above it each extra sale adds to profit, and the size of that step is the same on both sides. That step is the contribution margin, what one unit brings in after the cost of making and delivering it.
The calculation splits costs into two kinds. Fixed costs do not change with how much you sell in the period: rent, salaries, insurance, software, the repayment on a loan. Variable costs arrive with each sale: materials, packaging, postage, the commission a marketplace or card processor takes. Each sale's contribution goes first towards the fixed costs, and once they are covered, into profit.
Contribution marginP − V
Contribution margin ratio(P − V) ÷ P
Break-even unitsF ÷ (P − V)
Break-even salesF ÷ contribution margin ratio
Units for a target profit(F + T) ÷ (P − V)
Margin of safety(Q × P − break-even sales) ÷ (Q × P)
- F
- fixed costs for the period
- P
- selling price per unit, without VAT or sales tax
- V
- variable cost per unit
- T
- the profit you want for the period, before income tax
- Q
- the units you expect to sell
A unit count is rounded up, because 333.4 units means the 333rd sale still leaves you short and only the 334th covers the costs. The sales figure is not rounded, since it is the point where revenue and cost meet in money.
Worked example
The calculator opens on a small manufacturer used in an open accounting textbook: a birdbath that sells for $100, costs $20 a unit to make and carries $18,000 a month of fixed costs. In a normal month it sells 300.
| Item | Amount | How it is obtained |
|---|---|---|
| Contribution margin | $80 | 100 − 20 |
| Contribution margin ratio | 80% | 80 ÷ 100 |
| Break-even units | 225 | 18,000 ÷ 80 |
| Break-even sales | $22,500 | 18,000 ÷ 0.80 |
| Profit at 300 units | $6,000 | 300 × 80 − 18,000 |
| Margin of safety | 25% | (30,000 − 22,500) ÷ 30,000 |
| Units for a $16,000 profit | 425 | (18,000 + 16,000) ÷ 80 |
A flood that cut one month's sales to 175 units would cost the business $4,000: 175 × 80 is 14,000 of contribution against 18,000 of fixed costs. The margin of safety says the same thing in advance: sales could fall by a quarter, 75 units, before the month made a loss.
A service business works the same way. A tax practice charging $400 a return, with $150 of variable cost per return and $14,000 of monthly fixed costs, has a contribution margin of $250 and a ratio of 62.5%.
| Item | Amount | How it is obtained |
|---|---|---|
| Break-even returns | 56 | 14,000 ÷ 250 |
| Break-even sales | $22,400 | 14,000 ÷ 0.625 |
| Returns for a $10,000 profit | 96 | (14,000 + 10,000) ÷ 250 |
Reading the result
The headline is the number of units that covers the period's fixed costs, with the sales value beside it. The contribution margin tile says how much each sale above that point adds to profit; it is the most useful single number on the page, because it tells you what one more customer is worth and what one lost customer costs.
The margin of safety only appears once you enter expected sales. A negative one means your expected volume is below break-even, and the calculator says how many units short you are. The chart draws revenue and total cost from zero units: the cost line starts at your fixed costs and rises by the variable cost per unit, the revenue line starts at zero and rises by the price, and the gap between them to the right of the crossing is profit.
What changes the result
Price moves break-even more than cost does
A price rise goes straight into the contribution margin. In the birdbath example a $10 increase lifts the margin from $80 to $90 and pulls break-even from 225 units to 200. A $10 cut to variable cost does the same arithmetic, but a price change also moves sales volume, which is why the two are not interchangeable in practice.
Fixed costs scale break-even in proportion
Doubling fixed costs doubles the break-even volume, whatever the margin. A business taking on a second premises at the same rent needs twice the sales to stand still, so the question before signing is whether the extra space brings in at least that much.
Thin margins make break-even sensitive
When price and variable cost are close, a small change in either swings the result a long way. At a $10 margin, a $1 rise in variable cost moves break-even by about 11%; at an $80 margin the same rise moves it by little more than 1%. If the price falls to the variable cost, no volume breaks even, and the calculator says so rather than showing a number.
What is not included
The model is linear: one price, one variable cost per unit and one block of fixed costs across the whole range of volume. Real businesses get volume discounts on materials, give discounts to large customers, and hit capacity limits where another machine or another person is needed, which makes fixed costs jump in steps. If your expected volume crosses one of those steps, run the calculator twice, once each side.
A business selling several products needs a weighted contribution margin, each product's margin multiplied by its share of unit sales, used as one figure. Income tax is not deducted: the target profit is before tax. Break-even is also a profit measure, not a cash one. Stock bought ahead of sales, customers who pay late and equipment paid for up front all mean the bank balance can run below zero in a month the accounts show at break-even.
Using the result
Use break-even as a test of whether a plan is plausible, not as a forecast. Compare the volume against what you can physically make, deliver or staff: a salon that needs 200 cuts a month from one chair is planning about eight a day, six days a week. Then compare it against the market: if break-even means taking a share of local demand no competitor has managed, the plan needs a higher price or lower costs before it needs more marketing.
The margin of safety is the figure to watch over time. Recalculate it whenever rent, wages or supplier prices change, and set prices so that it stays comfortably above the swing between your best and worst months. When you sell through a marketplace or take cards, put the per-sale fees in the variable cost: the Etsy, eBay, Shopify, Stripe and PayPal fee calculators on this site give the figure for one sale.