Break-Even Calculator

Enter your monthly fixed costs, the price you charge per unit and the variable cost of making or delivering each one. The calculator returns the number of units you must sell in a month before the business covers everything, the revenue that volume represents, the contribution each sale makes toward fixed costs, and that contribution expressed as a share of the price. The unit count is the headline: below it the month ends at a loss, above it every further sale drops its full contribution straight through to profit.

How the calculation works

Break-even arithmetic rests on splitting costs in two. Fixed costs — rent, salaries, insurance, software subscriptions — arrive whether you sell anything or not. Variable costs — materials, packaging, payment fees, per-unit labor — scale with each unit sold. Whatever remains of the price after variable costs is the contribution per unit, so called because it is the part of each sale that contributes toward paying the fixed block.

contribution = price − variable cost

break-even units = fixed costs ÷ contribution, rounded up

break-even revenue = fixed costs ÷ (contribution ÷ price)

The bracketed term in the third formula is the contribution margin ratio, the fraction of every unit of revenue left after variable costs. Dividing fixed costs by it converts the break-even point from a count of units into an amount of money, which is the more useful form when a business sells many products at once. The unit result is rounded up because part units cannot be sold, while the revenue result keeps the exact division. The calculator reports an error whenever the price does not exceed the variable cost, because in that case no volume of sales ever covers the fixed block.

A worked example

Take the defaults: fixed costs of 10,000 a month, a price of 25 and a variable cost of 15. Each sale contributes 25 − 15 = 10, so covering 10,000 of fixed costs takes 10,000 ÷ 10 = 1,000 units. The contribution margin ratio is 10 ÷ 25 = 0.40, which makes break-even revenue 10,000 ÷ 0.40 = 25,000, and the cross-check holds: 1,000 units at 25 each is exactly 25,000.

The rounding distinction appears as soon as the division stops coming out even. With fixed costs of 1,000, a price of 30 and a variable cost of 15, contribution is 15 and the exact break-even point is 1,000 ÷ 15 = 66.67 units, which is 2,000 of revenue. Since a 67th sale is needed to actually get past the line, the calculator reports 67 units — worth 2,010 — alongside the exact 2,000 revenue figure. The gap is simply the revenue of the fraction of that final unit lying beyond break-even.

The same arithmetic reproduces the standard textbook case. The OpenStax managerial accounting text works fixed costs of 18,000, a price of 100 and a variable cost of 20 to a contribution of 80 per unit, 225 units and 22,500 of break-even revenue, and entering those three figures here returns exactly that.

Where the chart came from

The picture behind this arithmetic — a straight revenue line climbing across a total cost line, with the crossing marking the point of zero profit — is older than its name. Histories of cost accounting generally begin with the engineer Henry Hess, who in 1903 published a chart relating profit to cost, volume and price; a 2023 survey of the technique in the journal Mercados y Negocios describes Hess's diagram as the crossing point graph and treats it as the clearest ancestor of the modern chart. The same survey points next to Charles E. Knoeppel's Graphic Production Control, a 1920 book from the Engineering Magazine Company, which set out the separation of a company's expenses into fixed and variable, and notes that some authors were still calling the diagram the Knoeppel graph as late as the 1960s. A 2024 literature review of budgeting history adds that Knoeppel's 1933 book Profit Engineering presented the flexible budget as a chart he called the profitgraph.

The name that stuck arrived in 1930. Walter Rautenstrauch, a professor of industrial engineering at Columbia University, used the term break-even point in his book The Successful Control of Profits to describe the relations of cost, volume, price and profit, and explained at length how the chart could guide management decisions. His Wikipedia biography credits him with coining the term, records that he developed the break-even chart together with Knoeppel, and adds that he was instrumental in creating Columbia's Department of Industrial Engineering, said in that account to be the first such department in the United States, where he taught until retiring in 1943. The same biography records a stranger detour: in 1932 he formed the Committee on Technocracy with Howard Scott, and it disbanded the following year over the two men's differing views.

That engineering lineage is not the only one on offer. Wikipedia's entry on the break-even point credits the economists Karl Bücher and Johann Friedrich Schär with developing break-even analysis, a reminder that the idea also grew up inside German-language business economics. The safest summary is that the chart emerged from turn-of-the-century efforts on both sides of the Atlantic to make factory costs visible, and that Rautenstrauch supplied the English name every textbook now uses.

The model behind the math

Break-even analysis is the zero-profit special case of cost-volume-profit analysis, the accounting model that treats profit as revenue minus variable costs minus fixed costs and asks how it moves as volume changes. Everything here inherits the model's straight-line assumptions: the price never changes with volume, the variable cost per unit is the same for the first unit and the ten-thousandth, fixed costs genuinely stay fixed, the business sells a single product or an unchanging mix, and everything produced is sold. Real businesses bend every one of those lines — bigger customers negotiate discounts, suppliers cut unit prices at volume, overtime raises labor costs near capacity, and fixed costs jump in steps when a second machine or a larger space becomes necessary. Accountants trust the straight lines only across a relevant range of output near current operations, and that is the right way to read this page: reliable near the volumes you actually expect, increasingly indicative the further from them you move.

What to do with the number

A break-even figure earns its keep in two decisions. The first is the launch question: compare the break-even unit count with the volume you can realistically sell. A stall with 8,500 of monthly fixed costs, selling coffee at 4.50 a cup with 1.20 of variable cost per cup, must sell 2,576 cups a month to cover itself; if foot traffic supports 1,500, no amount of optimism changes the arithmetic. Only three levers move the figure, and each shows up directly in the formula: raising the price to 5.00 lifts the contribution to 3.80 and cuts the target to 2,237 cups, trimming the variable cost to 1.00 brings it to 2,429, and negotiating the fixed block down to 7,500 brings it to 2,273. The gap between expected and break-even sales is also a cushion measure — the closer the two sit, the less room a bad month leaves.

The second is pricing. The variable cost per unit is the absolute floor for any price, and the calculator's error when the price fails to clear it is the bluntest statement of that floor, but the practical floor sits higher, at the price that lets attainable volume carry the fixed block. Working the formula backwards answers questions the forward version cannot: with volume fixed at what the market allows, what price breaks even, and what price leaves a margin worth having. Recompute whenever a lease renews, a salary is added or a supplier reprices.

Assumptions and conventions

The month is a labeling convention rather than a requirement: enter quarterly fixed costs and the unit answer becomes quarterly too. The contribution margin ratio is displayed as a percentage of the price. The currency selector relabels amounts without converting them. Costs that are partly fixed and partly variable — a phone plan with overage fees, wages with a commission element — must be split by hand before entry, the fixed part added to fixed costs and the per-unit part to variable cost. An owner's own pay counts only if it is entered as a fixed cost, an omission that flatters many small-business break-even figures. The comparison is strict: a price exactly equal to the variable cost is treated as an error, since each sale would then earn nothing toward fixed costs. Amounts above 1,000,000,000,000 are rejected rather than displayed inaccurately, and taxes, financing costs and depreciation are outside the model unless you fold them into the fixed block yourself.

Break-even math assumes straight lines that real costs and prices only approximate, so treat the result as a planning benchmark rather than a forecast. See the site disclaimer.

Frequently asked questions

How do you calculate the break-even point in units?

Divide monthly fixed costs by the contribution per unit, which is the selling price minus the variable cost of each unit. With fixed costs of 10,000, a price of 25 and a variable cost of 15, each sale contributes 10, and 10,000 ÷ 10 = 1,000 units. Because part units cannot be sold, any fractional answer is rounded up to the next whole unit.

What is the contribution margin ratio?

It is the contribution per unit divided by the price: the share of every unit of revenue left after variable costs to pay fixed costs. A price of 25 with a variable cost of 15 gives a ratio of 10 ÷ 25 = 40%. Dividing fixed costs by this ratio converts the break-even point from units into revenue, so 10,000 ÷ 0.40 = 25,000.

Why is break-even revenue different from break-even units times price?

The unit figure is rounded up because part units cannot be sold, while the revenue figure keeps the exact division. Fixed costs of 1,000 with a price of 30 and a variable cost of 15 break even at exactly 2,000 of revenue, which is 66.67 units; the calculator reports 67 units, and 67 sales bring in 2,010. The two agree whenever the division comes out whole.

Who invented break-even analysis?

No single inventor holds an undisputed claim. Histories of cost accounting point to a chart the engineer Henry Hess published in 1903 relating cost, volume, price and profit, Charles E. Knoeppel's 1920 book Graphic Production Control separated fixed from variable expenses, and Walter Rautenstrauch of Columbia University applied the name break-even point in his 1930 book The Successful Control of Profits. German-language accounting literature, as summarized on Wikipedia, separately credits the economists Karl Bücher and Johann Friedrich Schär with developing break-even analysis.

What happens if the variable cost is higher than the price?

There is no break-even point at any volume, because every additional sale widens the loss instead of narrowing it. The calculator shows an error whenever the price does not exceed the variable cost per unit, including the case where the two are equal and each sale earns nothing toward fixed costs. The fix is a higher price, a lower unit cost, or both.

Is break-even analysis accurate for real businesses?

It is a deliberately simplified model. The straight-line math assumes the price never changes with volume, the variable cost per unit stays constant, fixed costs really stay fixed, and everything produced is sold, and those assumptions hold only across a limited range of output. Treat the result as a planning benchmark to be recomputed when rent, wages or pricing change, not as a forecast.