Break-Even Analysis: The Formula, a Worked Example and a Free Calculator

Every business decision about price, costs or a new product eventually comes back to one question: how many do we need to sell before we stop losing money? That number is the break-even point. Below it, every sale reduces the loss; above it, every sale adds profit.

This guide gives you the break-even formula in units and in revenue, works through a full example, shows what happens when you change the price, and explains where the model stops being reliable. The free Break-Even & Sensitivity Model does all of it for you and exports an Excel-compatible workbook.

Key takeaways

• Break-even units = fixed costs ÷ (price per unit − variable cost per unit).
• The amount each sale contributes towards fixed costs, price minus variable cost, is the contribution margin. It drives everything else.
• Break-even revenue = fixed costs ÷ contribution margin ratio.
• Price cuts are expensive: in the example below, a price 17% lower needs 38% more sales just to break even.
• The margin of safety tells you how far sales can fall before you reach break-even.

The break-even formula

Costs come in two kinds. Fixed costs stay the same whatever you sell in the period: rent, salaries, insurance, software, marketing you have already committed to. Variable costs rise with every unit sold: materials, delivery, payment processing fees, sales commission.

Each sale brings in its price and costs its variable cost. What is left over, the contribution margin, goes towards paying the fixed costs. Once enough sales have covered them, you have broken even:

• Contribution margin per unit = price − variable cost per unit
• Break-even units = fixed costs ÷ contribution margin per unit
• Contribution margin ratio = contribution margin ÷ price
• Break-even revenue = fixed costs ÷ contribution margin ratio

A worked example

Suppose you run a premium workshop. For the season, the venue, promotion and your team cost 30,000 whether you sell one seat or three hundred. Each seat sells for 300, and each attendee costs you 120 in materials, catering and payment fees.

• Contribution margin per seat: 300 − 120 = 180
• Break-even seats: 30,000 ÷ 180 = 166.7, so you need 167 seats, because you cannot sell two thirds of a seat
• Contribution margin ratio: 180 ÷ 300 = 60%
• Break-even revenue: 30,000 ÷ 0.60 = 50,000, or 50,100 once you round up to 167 whole seats

From there, profit is simple arithmetic. Sell 200 seats and profit is 200 × 180 − 30,000 = 6,000. Want a 9,000 profit? Add it to the fixed costs: (30,000 + 9,000) ÷ 180 = 216.7, so 217 seats.

What a price change does to break-even

The most useful thing a break-even model does is show you how sensitive the target is to price. Here is the same workshop at five different prices, with fixed costs and variable costs unchanged:

Dropping the price from 300 to 250, about 17% cheaper, cuts the contribution per seat by 28%, so you need 231 seats instead of 167, 38% more, just to get back to zero. Raising it to 350 means 36 fewer seats. This asymmetry is why discounting to win volume so often backfires: the volume has to grow much faster than the price falls. Our guide to margin vs markup shows the same effect on service projects.

Margin of safety

Once you know break-even, compare it with the sales you actually expect. The margin of safety is the gap, as a share of expected sales:

Margin of safety = (expected sales − break-even sales) ÷ expected sales

If you expect 220 seats, the margin of safety is (220 − 167) ÷ 220 = 24%. Sales could fall almost a quarter short of the plan before the season makes a loss. A thin margin of safety is a warning even when the plan shows a profit.

Break-even in Excel

With fixed costs in B1, the price in B2 and variable cost per unit in B3:

• Break-even units: =ROUNDUP(B1/(B2-B3),0)
• Break-even revenue: =B1/((B2-B3)/B2)
• Units for a target profit in B4: =ROUNDUP((B1+B4)/(B2-B3),0)
• Profit at a given volume in B5: =B5*(B2-B3)-B1

A price sensitivity table is just the break-even formula copied down a column of prices. Excel's Goal Seek can also find the price that gives a target profit at a given volume.

How to split fixed and variable costs

The model is only as good as the split. Some practical rules:

• Ask whether the cost would change if you sold one more unit this month. If not, it is fixed for this purpose.
• Payment processing fees, packaging, delivery and commission are almost always variable.
• Some costs are semi-variable, such as a phone plan with a base fee plus usage. Split them into a fixed part and a per-unit part.
• Watch for step costs: fixed until a capacity limit, then a jump. A second venue or another hire changes the fixed costs, so run the model again for the next level of capacity.

Where break-even analysis stops working

• It assumes the price and the variable cost stay the same at every volume. Bulk discounts and volume pricing break that assumption.
• With several products, you need a weighted average contribution margin, which only holds while the sales mix stays roughly the same.
• It says nothing about timing. You can be above break-even for the year and still short of cash in a particular month. A 12-month cash flow forecast answers that question.
• It ignores capacity. Break-even at 400 seats in a 300-seat room is not a plan.

Use the free break-even calculator

The Break-Even & Sensitivity Model takes a product or service name, your fixed costs, variable cost per unit, a default sale price, a test price to compare it with, and an optional target profit. It returns:

• a volume outcomes table showing revenue, variable cost, total cost, profit or loss, margin and status at each volume;
• a break-even chart and a volume-versus-profit view;
• a side-by-side answer for your test price, so you can see what a price change does before you make it;
• an Excel-compatible XLSX download in which the calculations are live formulas, and a recap image you can share.

It runs in your browser, and nothing you enter is uploaded. For pricing a project rather than a product, try the Service Pricing Calculator.

Frequently asked questions

What is contribution margin?

It is what each sale leaves over after its own variable costs, price minus variable cost per unit. It is the amount each sale contributes towards fixed costs and, after break-even, towards profit.

What is a good margin of safety?

There is no universal figure. The steadier and more predictable your sales, the thinner a margin of safety you can live with. New products, seasonal businesses and plans that depend on a few large customers deserve a wide one.

How do I calculate break-even with several products?

Work out a weighted average contribution margin using your expected sales mix, then divide fixed costs by it. If the mix changes, the break-even point changes too, so rerun it when it does.

Is break-even the same as payback period?

No. Break-even is the sales volume that covers the costs of a period. Payback period is how long it takes for cumulative cash inflows to repay an up-front investment.

Why does my break-even number have a decimal?

Because the formula divides fixed costs by the contribution margin. You cannot sell part of a unit, so always round up to the next whole unit.