Mathematical Audit LogVerified against standard business economics cost-volume-profit equations and GAAP principles.Last Audited: 2026-07-12
Mathematical Formulas
Contribution Margin: CM = Price - Variable Cost
Break-Even Units: BEU = ceil( Fixed Costs / CM )
Break-Even Revenue: Revenue = BEU × Price
Core Assumptions
Assumes unit price and unit variable cost are linear and remain constant across all sales volumes.
Assumes zero inventory accumulation (all units manufactured are sold immediately).
Limitations & Exclusions
Does not support multiple different products with separate margins or blended margins.
Does not account for non-linear scale pricing models or step-fixed overhead costs.
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About the Break-Even Calculator
A break-even calculator finds the point where a business stops losing money. Give it your fixed costs, your selling price and the variable cost of each unit, and it returns how many units you must sell, and what revenue that represents, before the first dollar of profit appears.
The idea rests on one distinction: fixed costs do not move with sales, variable costs do. Rent, salaries and software subscriptions carry on whether you sell one unit or a thousand. Materials, packaging, shipping and payment fees arrive only when something sells. Every sale contributes the gap between price and variable cost towards the fixed pile, and break-even is the moment that pile is finally covered.
Two things about break-even are routinely misread. It is not a target - it is the floor, the point of earning nothing, and a plan that ends at break-even is a plan to work for free. And it is not stable: it moves the instant you hire someone, take a bigger unit, or discount. The most useful thing this page can tell you is not the number itself but how violently that number responds to a small change in price, which is covered below.
Mathematical Formula & Logic
Four relationships do the work.
1. Unit contribution margin
CM = Price - Variable Cost
What one sale contributes towards fixed costs. If this is zero or negative you can never break even, because selling more deepens the hole.
2. Break-even in units
Units = Fixed Costs / CM, rounded up
Rounded up because you cannot sell part of a unit, and rounding down would leave you fractionally short.
3. Break-even in revenue
Revenue = Fixed Costs / CM Ratio, where CM Ratio = CM / Price
Useful when you do not sell discrete units at all. A consultancy or a cafe can reach a revenue figure without ever defining what one unit is.
4. The volume for a profit target, not just survival
Units = (Fixed Costs + Target Profit) / CM
Break-even is simply this equation with a target of zero. Treating profit as another fixed cost to be covered is the shift from surviving to planning.
Two further measures make the result usable.
Margin of safety = (Actual Sales - Break-Even Sales) / Actual Sales. It answers how far trade can fall before you are losing money. A business breaking even at 500 units and selling 700 has a 28.57% margin of safety.
Degree of operating leverage = Total Contribution Margin / Operating Profit. It measures how amplified your profit is. That same business has a DOL of 3.50, so a 10% rise in sales produces a 35% rise in profit - and a 10% fall produces a 35% collapse. Close to break-even this figure runs towards infinity, which is the formal way of saying that the nearer you sit to the floor, the more every small movement matters.
Step-by-Step Example
A business has $10,000 in monthly fixed costs, sells at $50 and pays $30 per unit in materials and shipping.
1. Inputs: Fixed = $10,000, Price = $50, Variable = $30.
2. Contribution margin: 50 - 30 = $20 per unit.
3. CM ratio: 20 / 50 = 40%.
4. Break-even units: 10,000 / 20 = 500 units.
5. Break-even revenue: 500 x 50 = $25,000, which also equals 10,000 / 0.40.
To earn $10,000 of profit rather than merely survive, the target becomes (10,000 + 10,000) / 20 = 1,000 units. Doubling the fixed burden doubles the volume, because contribution per unit has not changed.
Now the part that decides pricing strategy. Two apparently equal improvements are not equal at all.
Raise the price 10%, from $50 to $55. Contribution rises to $25 and break-even falls from 500 units to 400 - a 20% reduction.
Cut the variable cost 10% instead, from $30 to $27. Contribution rises only to $23 and break-even falls to 435 units - a 13% reduction.
The price increase wins, and it always will, because 10% of the price is a larger sum than 10% of the variable cost - and the variable cost is necessarily the smaller of the two in any business that can break even at all. This is the arithmetic behind the advice that a small price rise beats a hard-won supplier discount. It is also why discounting is so costly here: the same lever that lowers break-even fastest when pushed up raises it fastest when pulled down.
At 700 units the business earns 700 x 20 - 10,000 = $4,000, sits 28.57% above its break-even point, and carries a degree of operating leverage of 3.50.
Reference Data & Values
fixed costs
price
variable cost
CM
CM ratio
break-even units
break-even revenue
units for $10k profit
$10,000
$50.00
$30.00
$20.00
40.00%
500
$25,000
1,000
$5,000
$100.00
$50.00
$50.00
50.00%
100
$10,000
300
$25,000
$250.00
$175.00
$75.00
30.00%
334
$83,500
467
$60,000
$40.00
$10.00
$30.00
75.00%
2,000
$80,000
2,334
$100,000
$15.00
$10.00
$5.00
33.33%
20,000
$300,000
22,000
Frequently Asked Questions
The break-even point is the level of sales where total revenues equal total costs, resulting in zero profit and zero loss for the business.
Divide total fixed costs by the unit contribution margin (Price per Unit minus Variable Cost per Unit). Round up to the nearest whole unit.
Break-even sales revenue is calculated as: Fixed Costs divided by the Contribution Margin Ratio (expressed as a decimal). Alternatively, multiply break-even units by the selling price.
Contribution margin is the selling price per unit minus the variable cost per unit. It represents the amount of money each unit sale contributes to covering fixed overheads.
If variable cost exceeds the selling price, the contribution margin is negative. This means every sale increases your losses, and the business can never break even.
Yes, if you intend to be paid. Leaving the founder out is the most common way break-even gets understated, because the business then appears to cover its costs at a volume that leaves you personally earning nothing. Put the wage you would have to pay someone to do your job into fixed costs, and the number you get is the point where the business genuinely stands on its own.
Use a weighted average contribution margin based on your sales mix. If 60% of units sold are product A at $20 contribution and 40% are product B at $30, the weighted CM is (0.6 x 20) + (0.4 x 30) = $24. With $12,000 of fixed costs that is 500 units in total, split 300 and 200 in the same proportions. The result only holds while the mix holds - a shift towards the lower-margin product raises the break-even point without any cost changing.
The distance between current sales and the break-even point, as a percentage of current sales: (Actual - Break-Even) / Actual. Breaking even at 500 units while selling 700 gives a margin of safety of 28.57%, meaning trade could fall by roughly a quarter before losses begin. It is the single most useful figure to track alongside break-even, because break-even alone tells you nothing about how much room you have.
Because the percentage applies to a larger number. On a $50 price with $30 variable costs, a 10% price rise adds $5 to contribution and drops break-even from 500 units to 400. A 10% cut in variable cost adds only $3 and drops it to 435. Price always wins, since variable cost is necessarily lower than price in any business capable of breaking even at all.
No. Break-even is zero profit - the floor, not a goal. It also ignores anything below the operating line, so interest, tax and loan repayments still have to be found from somewhere. Use the target-profit form of the formula, adding your intended profit to fixed costs, to get a number worth actually aiming at.