Accounting Break-Even Point Per-Unit Formula
Learn how to calculate the unit sales and revenue needed to cover fixed costs using contribution margin per unit.
A per-unit break-even calculation estimates the minimum whole number of units a business must sell for sales to cover fixed costs and variable costs. It is useful for pricing, sales-volume planning, and assessing how changes in costs affect profitability.
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Break-Even Units
Where:
First find how much each unit contributes after its variable cost. Then divide fixed costs by that contribution and round up because a fraction of a unit does not fully cover costs.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| fixedCosts - Fixed Costs | Costs for the chosen period that generally do not change directly with unit sales, such as rent, salaries, or insurance. | currency |
| sellingPricePerUnit - Selling Price per Unit | Average revenue received from one unit sold, normally before sales taxes. | currency |
| variableCostPerUnit - Variable Cost per Unit | Average direct cost that changes with each unit sold, such as materials, packaging, or sales commission. | currency |
| contributionMarginPerUnit - Contribution Margin per Unit | Amount from each sale available to cover fixed costs and then profit. | currency |
| targetProfit - Target Profit | Optional profit amount to add to fixed costs when calculating a sales goal above break-even. | currency |
Step-by-Step Calculation
Calculate contribution margin per unit
Subtract the variable cost of one unit from its selling price.
contributionMarginPerUnit = sellingPricePerUnit - variableCostPerUnit
Calculate contribution margin ratio
Express the contribution from each sale as a percentage of its selling price.
contributionMarginRatio = (contributionMarginPerUnit / sellingPricePerUnit) * 100
Calculate unrounded break-even units
Divide fixed costs by the amount each unit contributes.
unroundedBreakEvenUnits = fixedCosts / contributionMarginPerUnit
Round up to whole break-even units
Round upward so the required sales volume fully covers fixed costs.
breakEvenUnits = ceil(unroundedBreakEvenUnits)
Calculate break-even revenue
Multiply the rounded unit requirement by the selling price per unit.
breakEvenRevenue = breakEvenUnits * sellingPricePerUnit
Calculate units for a target profit
Add the desired profit to fixed costs, divide by contribution per unit, and round up.
unitsForTargetProfit = ceil((fixedCosts + targetProfit) / contributionMarginPerUnit)
Product business break-even calculation
Contribution margin per unit
$50 - $30
$20 per unit
Contribution margin ratio
($20 / $50) * 100
40%
Unrounded break-even units
$10,000 / $20
500 units
Break-even revenue
500 * $50
$25,000
Units for target profit
($10,000 + $5,000) / $20
750 units
Final Result
The business needs 500 units and $25,000 in revenue to break even. It needs 750 units to reach a $5,000 target profit.
Assumptions
- ✓Fixed costs apply to the same period as the sales volume being measured.
- ✓Selling price and variable cost are average amounts that remain constant for every unit.
- ✓All units counted in the calculation are sold during the period.
- ✓The selling price and costs are measured consistently, commonly excluding sales taxes collected for tax authorities.
- ✓Contribution margin per unit is greater than zero.
Limitations
- !Actual prices, discounts, material costs, and commissions may vary by customer, product, or order.
- !A business selling multiple products needs a sales-mix assumption rather than one single per-unit result.
- !The calculation does not automatically include financing costs, taxes, inventory changes, or unentered overhead.
- !Rounding to whole units can make break-even revenue slightly higher than the exact mathematical threshold.
- !This estimate does not forecast demand or guarantee that the required units can be sold.
Common Mistakes to Avoid
Using total variable costs for the period instead of the variable cost for one unit.
Including sales tax in revenue while excluding it from the related costs.
Forgetting to include recurring fixed costs that apply to the selected period.
Rounding break-even units down instead of up.
Treating contribution margin as the same as gross profit without checking which costs have been included.
Using a selling price that ignores expected discounts, returns, or commissions.
Related Formulas
Frequently Asked Questions
What is the per-unit break-even formula?
Break-even units equal fixed costs divided by selling price per unit minus variable cost per unit, rounded up to a whole unit.
Why is contribution margin used in break-even analysis?
Contribution margin is the portion of each sale left after variable costs. That amount is what pays fixed costs and, after fixed costs are covered, creates profit.
How do I calculate break-even revenue from break-even units?
Multiply the rounded break-even unit figure by the selling price per unit.
Can break-even units be a decimal?
The raw calculation can be a decimal, but the operational result is usually rounded up because selling fewer than the calculated number would not fully cover costs.
What if variable cost equals selling price?
Contribution margin is zero, so no unit sale contributes toward fixed costs. A conventional break-even point cannot be calculated.
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