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Pricing & margin

Break-even calculator — units, revenue and margin of safety

Calculate break-even units and revenue from fixed costs and contribution margin. Includes margin of safety and the volume needed for a target profit.

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Short answer

Break-even units equal fixed costs divided by contribution per unit, where contribution is selling price minus variable cost per unit. With $1,850,000 of fixed costs and $43.75 of contribution on a $125.00 price, break-even is 42,286 units or $5,285,714 of revenue. Every unit above that adds $43.75 of operating profit.

A break-even calculator answers the question behind every pricing and capacity decision: how much must you sell before the fixed costs are covered? Divide fixed costs by contribution per unit and you have it in units; divide by the contribution margin ratio and you have it in revenue.

Enter fixed costs, price, variable cost per unit, the volume you expect and the profit you want. You get break-even units and revenue, the margin of safety at your expected volume, the volume required for the target profit, and operating leverage — how hard profit swings when volume moves.

Your numbers

$

Rent, salaried payroll, insurance, depreciation, software. Fixed only over the horizon you are modelling.

$

Realised price after discounts and rebates, not list price.

$

Materials, piece-rate labour, packaging, outbound freight, commission — costs that only exist when a unit ships.

units

The plan or forecast volume. Sets the margin of safety.

$

Added to fixed costs to find the volume that delivers it.

Result

Break-even volume
42,286 units

$5,285,714 of revenue at $125.00 per unit

Contribution per unit$43.75
Contribution margin ratio35.0%
Operating profit at 52,000 units$425,000
Margin of safety18.7% · 9,714 units
Units for $750,000 profit59,429 units · $7,428,571
Degree of operating leverage5.4×
Contribution is $43.75 a unit; fixed costs of $1,850,000 are deducted in full at every volume.
ScenarioUnitsRevenueContributionOperating profit
Break-even42,286$5,285,714$1,850,000-$0
90% of plan46,800$5,850,000$2,047,500$197,500
Expected volume52,000$6,500,000$2,275,000$425,000
Target profit59,429$7,428,571$2,600,000$750,000
contribution per unit = $125.00 − $81.25 = $43.75
contribution margin ratio = $43.75 ÷ $125.00 = 35.0%
break-even units = $1,850,000 ÷ $43.75 = 42,285.7 → 42,286
break-even revenue = $1,850,000 ÷ 0.350 = $5,285,714
target volume = ($1,850,000 + $750,000) ÷ $43.75 = 59,429 units (7,429 above plan)
Break-even is 42,286 units, so at 52,000 units you have a 18.7% margin of safety — 9,714 units or $1,214,286 of revenue — and $425,000 of operating profit. Every point of price you discount is a point of that cushion.

Single-product break-even. With a product range this holds only while the sales mix stays constant — recompute with the weighted average contribution per unit whenever mix moves.

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The formula

Break-even units = Fixed costs ÷ (Price − Variable cost per unit) · Break-even revenue = Fixed costs ÷ Contribution margin ratio
Fixed costs
Costs that do not move with volume over the period: rent, salaried payroll, insurance, depreciation, software.
Price
Average net selling price per unit, after discounts and rebates. Use realised price, not list.
Variable cost per unit
Materials, piece-rate labour, packaging, freight out, commission — everything that only exists when a unit ships.
Contribution per unit
Price minus variable cost. What each unit contributes towards fixed costs, then to profit.
Target profit
Operating profit you want. Add it to fixed costs before dividing.

This is the single-product break-even. With more than one product it holds only while the sales mix stays constant, because the weighted contribution per unit changes the moment mix moves. State that assumption out loud whenever you present a break-even chart — a mix shift can move the break-even point further than a price change.

Worked example

Fixed costs
$1,850,000
Selling price per unit
$125.00
Variable cost per unit
$81.25
Expected volume
52,000 units
Target operating profit
$750,000
Result
42,286 units · $5,285,714 revenue · 18.7% margin of safety

Contribution per unit is $125.00 − $81.25 = $43.75, a contribution margin ratio of 35.0%. Break-even is $1,850,000 ÷ $43.75 = 42,286 units, or $1,850,000 ÷ 0.350 = $5,285,714 of revenue. At the expected 52,000 units you clear break-even by 9,714 units — an 18.7% margin of safety and $425,000 of operating profit. Reaching $750,000 of profit needs 59,429 units.

Which lever moves break-even most

Using the worked example, a 5% price rise beats a 5% cut in variable cost and beats a 10% cut in fixed costs. Price moves both the numerator's coverage and the contribution per unit, which is why it dominates.

LeverChangeBreak-even unitsMove
Price per unit+5% to $131.2537,000−12.5%
Variable cost per unit−5% to $77.1938,693−8.5%
Fixed costs−10% to $1,665,00038,057−10.0%
Volumeany42,286No change — volume moves the margin of safety, not the break-even point.
Base case: $1,850,000 fixed, $125.00 price, $81.25 variable cost, 42,286 units to break even.

Reading the margin of safety

Margin of safety is how far volume can fall before you post a loss, expressed as a percentage of expected volume. It is the number to quote in a board pack, because it converts break-even into risk.

Margin of safetyWhat it meansWhat to do
NegativePlanned volume is below break-even. The plan loses money.Fix price, mix or fixed cost before approving the plan.
0–10%A single lost customer or one soft quarter puts you under.Convert fixed cost to variable where you can; hold hiring.
10–25%Normal for a capital-intensive plant. The example sits here.Watch discounting — every point of price is a point of safety.
Over 25%Comfortable. Operating leverage is working for you.Consider whether the spare capacity is earning anything.

Break-even analysis assumptions to state out loud

  • Costs split cleanly into fixed and variable. Most do not. Supervision, utilities and maintenance are step costs that jump at capacity thresholds, so the real break-even line has kinks in it.
  • Price is constant at every volume. Higher volume usually arrives through deeper discounts, which lowers contribution exactly when you were counting on it.
  • Mix is constant. The most common reason a break-even forecast misses. Recompute the weighted contribution whenever mix moves more than a few points.
  • Variable cost per unit is constant. Volume brings purchase price breaks downwards and overtime premiums upwards; they rarely cancel out.
  • The period is fixed. Fixed costs are only fixed for a stated horizon. A twelve-month break-even and a three-year break-even are different calculations.

Getting fixed and variable costs out of the ledger

No chart of accounts labels costs fixed or variable, so the split is a judgement applied account by account — and it has to be applied the same way every time or the trend lies. Start from the contribution side with the contribution margin calculator, then reconcile to the operating profit in the GL.

Asking for "contribution margin by product line for the last four quarters using my fixed-cost account list" returns the figures with the query shown, so the classification is visible and arguable rather than buried in someone's spreadsheet.

Frequently asked questions

How do you calculate the break-even point?

Divide fixed costs by contribution per unit, where contribution is selling price minus variable cost per unit. $1,850,000 of fixed costs and $43.75 of contribution gives 42,286 units. For break-even revenue, divide fixed costs by the contribution margin ratio instead: $1,850,000 ÷ 0.350 = $5,285,714.

What is the break-even formula in revenue?

Break-even revenue equals fixed costs divided by the contribution margin ratio. The ratio is contribution per unit divided by price — $43.75 ÷ $125.00 = 0.350. So $1,850,000 ÷ 0.350 = $5,285,714. Use the revenue form when you sell many items and unit counts are not comparable.

What is a good margin of safety?

Above 25% is comfortable, 10–25% is normal for a plant with heavy fixed costs, and under 10% means one soft quarter produces a loss. Below zero the plan itself does not work. Judge it against your revenue volatility: a stable subscription base tolerates a thinner cushion than a project business.

How many units do I need for a target profit?

Add the target profit to fixed costs, then divide by contribution per unit. For $750,000 of profit on $1,850,000 of fixed costs and $43.75 of contribution: $2,600,000 ÷ $43.75 = 59,429 units. That is 7,429 units above the 52,000 in the plan.

Does break-even analysis work with multiple products?

Only at a constant sales mix. Compute a weighted average contribution per unit using the mix percentages, then divide fixed costs by it. The answer stops being valid the moment mix shifts, which is why multi-product businesses usually work in break-even revenue with a weighted contribution margin ratio.

Is depreciation a fixed cost for break-even?

Straight-line depreciation is fixed, so it belongs in fixed costs even though no cash moves. If you want a cash break-even instead, strip depreciation and other non-cash charges out of fixed costs — the volume it produces is lower, and it answers a different question about survival.

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