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Business planning · cost-volume-profit
Break-even units from fixed costs, price and variable cost
Find the unit volume where revenue first covers fixed costs, from the selling price, the variable cost per unit and the fixed costs — with the contribution margin and its ratio alongside.
Verified engine
What the engine returns
The contribution margin and its ratio are identical in both runs, because neither depends on the fixed costs. The required volume, though, scales in exact proportion to the fixed base — several times the overhead demands several times the units — and the break-even revenue scales with it. Reading the two runs together shows precisely which lever moved which output.
Inputs the result is built from
Fixed costs
Selling price per unit
Variable cost per unit
How the result is derived
MethodThe contribution margin per unit is the selling price minus the variable cost; the break-even volume divides the fixed costs by that contribution; the break-even revenue multiplies the volume back by the price, and the contribution-margin ratio divides the unit contribution by the price.
StandardCost-volume-profit break-even analysis in units and revenue
GuardNegative fixed costs are rejected as bad input — a subsidy larger than the overhead is not a cost figure, and folding it in here would corrupt the division.
Every unit contributes; the fixed costs count the units
The contribution margin per unit is the heart of the calculation: what one more sale adds toward the fixed costs after paying for its own materials, labour and other per-unit expenses. Fixed costs never enter it — a unit’s contribution is the same whether the rent is large or small.
The break-even volume divides the fixed costs by that contribution. The relationship is strictly proportional: multiply the fixed costs several-fold at the same price and variable cost, and the required volume multiplies by exactly the same factor. Rent, salaries and licences translate directly into units that must be sold before any profit exists.
The break-even revenue restates the same threshold in money — the volume times the selling price — which is often the easier figure to hold against a sales forecast. The contribution-margin ratio expresses the unit contribution as a fraction of the price, and it depends only on the price and the variable cost: two ventures with very different fixed costs but the same pricing structure share the same ratio while needing very different volumes.
Beyond the threshold, the same arithmetic keeps working in your favour: each additional unit’s contribution now falls through to profit rather than to the hole. The break-even point is not a verdict on the business — it is the exchange rate between overhead decisions and sales requirements.
The contribution margin per unit is the selling price minus the variable cost; the break-even volume divides the fixed costs by that contribution; the break-even revenue multiplies the volume back by the price, and the contribution-margin ratio divides the unit contribution by the price.
When this calculation is used
- Testing whether a realistic sales forecast clears the volume a lease, a hire or a licence commits you to.
- Pricing a new product by watching the required volume move as the candidate price moves.
- Comparing a high-fixed-cost, low-variable-cost setup against its opposite for the same product.
- Converting a cost increase — materials or overhead — into the extra units it silently demands.
Worked example
A product priced comfortably above its variable cost, first against a modest fixed-cost base, then against the same pricing with the fixed costs several times larger.
The contribution margin and its ratio are identical in both runs, because neither depends on the fixed costs. The required volume, though, scales in exact proportion to the fixed base — several times the overhead demands several times the units — and the break-even revenue scales with it. Reading the two runs together shows precisely which lever moved which output.
Every figure is computed by the certified engine when the page loads, from a release checked against the test vectors declared in the signed pack — the scenario here only describes what to look at, never what the numbers are.
What each input represents
Fixed costs
The costs of the period that do not move with volume — rent, salaries, insurance, depreciation. Zero is accepted, and the break-even volume is then zero units: with no hole to climb out of, the first sale is already profitable. Negative entries are rejected as bad input.
Selling price per unit
What one unit sells for. It must exceed the variable cost per unit — the whole construction rests on each sale contributing something — and it is also the denominator of the contribution-margin ratio.
Variable cost per unit
What one additional unit costs to produce and sell: materials, direct labour, per-transaction fees. Costs that would be paid regardless of volume belong in the fixed figure instead — misfiling them is the classic way this analysis goes wrong.
Assumptions and limits
- The selling price and the variable cost per unit are constant across the whole volume range — no volume discounts, no capacity steps.
- Every cost is cleanly either fixed or variable; semi-variable costs must be split before entry.
- Units made are units sold: no inventory builds up between production and revenue.
- The break-even volume is reported as the exact quotient, which need not be a whole number — rounding it up to sellable units is a decision left to you.
- Any target volume or margin of safety you compare against is your own planning input, not a benchmark this page asserts.
What the guards protect against
- Negative fixed costs are rejected as bad input — a subsidy larger than the overhead is not a cost figure, and folding it in here would corrupt the division.
- The selling price must exceed the variable cost per unit: at or below it, each sale contributes nothing or worse, no volume ever breaks even, and the calculation refuses rather than reporting an absurdity.
- That refusal is the analysis working, not failing — a price at or under variable cost is the finding itself, and no unit count can repair it.
Provenance
Cost-volume-profit break-even analysis in units and revenue
The contribution margin per unit is the selling price minus the variable cost; the break-even volume divides the fixed costs by that contribution; the break-even revenue multiplies the volume back by the price, and the contribution-margin ratio divides the unit contribution by the price.
A planning instrument under deliberately linear assumptions — its refusals mark the edge of the model, not an error. The signed pack carries its own citation; the page reports the verification state of the release it mounted rather than asserting one.