Break-even analysis: the formula, worked step by step
Break-even analysis explained with real numbers: contribution margin, break-even units and revenue, margin of safety, and the multi-product trap.
Break-even is the sales level where contribution exactly covers fixed costs. Break-even units = fixed costs ÷ (price − variable cost per unit). With $477,000 of fixed costs, a $145 price and $92 variable cost, contribution is $53 per unit and break-even is 9,000 units, or $1,305,000 of revenue.
Key takeaways
- Break-even units = fixed costs ÷ contribution per unit, where contribution per unit = price − variable cost per unit.
- Break-even revenue = fixed costs ÷ contribution margin ratio. Both routes give the same answer; use whichever inputs you trust.
- Margin of safety = (actual − break-even) ÷ actual. It is the percentage sales can fall before you lose money.
- Break-even is more sensitive to price than to any other input. A 5% price cut raised break-even by 15.9% in the worked example; a 5% variable-cost rise raised it by 9.5%.
- With more than one product, break-even depends on mix. Use a weighted average contribution per unit and state the mix you assumed.
A break-even analysis answers one question with one number: how much do we have to sell before we stop losing money? It is the first calculation on any new product, the sanity check on any price change, and the number a lender asks for when you have none of the others. It also takes about four minutes once you know which costs go where.
- Break-even point
- The sales volume at which total contribution exactly equals fixed costs, so profit is zero. Below it every unit deepens the loss; above it every unit adds its full contribution straight to profit.
The three formulas you need
Contribution per unit = Price − Variable cost per unit
Break-even units = Fixed costs ÷ Contribution per unit
Break-even revenue = Fixed costs ÷ Contribution margin ratio
Contribution margin ratio = Contribution per unit ÷ PriceContribution is the engine. Each unit sold contributes price minus its variable cost toward the fixed cost pile. Once the pile is covered, contribution becomes profit. That is why fixed and variable have to be separated properly before anything else happens — get the split wrong and every downstream number is wrong by the same amount.
How to do a break-even analysis
- 01
Split every cost into fixed or variable
Variable costs move with each unit: materials, direct labour if it genuinely flexes, freight out, per-transaction fees, sales commission. Fixed costs do not move with the next unit: rent, salaried headcount, software, insurance, depreciation. Semi-variable costs like utilities or a supervisor's overtime get split — estimate the step, do not guess the whole line.
- 02
Compute contribution per unit
Price minus variable cost per unit. In our example the price is $145 and variable cost is $92, so contribution is $145 − $92 = $53 per unit. Express it as a ratio too: $53 ÷ $145 = 36.55%. The ratio is what you use when you only have revenue, not units.
- 03
Divide fixed costs by contribution per unit
Annual fixed costs are $477,000. Break-even units = $477,000 ÷ $53 = 9,000 units. Always round up to the next whole unit: 8,999 units leaves you short. If the division is not exact, the rounded-up figure produces a tiny profit rather than a tiny loss, which is the side you want to be on.
- 04
Convert to revenue and check it two ways
Break-even revenue = 9,000 × $145 = $1,305,000. Cross-check with the ratio route: $477,000 ÷ (53 ÷ 145) = $477,000 × 145 ÷ 53 = $1,305,000. The two agree exactly, which confirms the contribution ratio was built from the same price. Use the unrounded ratio for this check — rounding 36.55% to two decimals shifts the answer by a few hundred dollars.
- 05
Compare it to actual or forecast sales
Forecast volume is 11,500 units, or $1,667,500 of revenue. Profit = (11,500 − 9,000) × $53 = $132,500. Verify the long way: revenue $1,667,500 − variable costs (11,500 × $92 = $1,058,000) = $609,500 contribution, minus $477,000 fixed = $132,500. Both routes agree.
- 06
Calculate the margin of safety
Margin of safety = (actual − break-even) ÷ actual = (11,500 − 9,000) ÷ 11,500 = 2,500 ÷ 11,500 = 21.7%. In revenue terms: ($1,667,500 − $1,305,000) ÷ $1,667,500 = $362,500 ÷ $1,667,500 = 21.7%. Sales can fall 21.7% before this business posts a loss.
- 07
Add the target profit you actually need
Break-even at zero profit is rarely the real decision point. Units for a target profit = (fixed costs + target profit) ÷ contribution per unit. For $200,000 of profit: ($477,000 + $200,000) ÷ $53 = $677,000 ÷ $53 = 12,773.6, so 12,774 units and $1,852,230 of revenue. Check: 12,774 × $53 = $677,022, less $477,000 fixed = $200,022 profit.
- 08
Stress-test the two inputs you are least sure about
Break-even is a ratio of two estimates, so it inherits both errors. Re-run it with price 5% lower and variable cost 5% higher and see whether the answer still clears your forecast. The table below shows what those swings do.
Enter fixed costs, price and variable cost per unit for break-even units, break-even revenue, margin of safety and the volume needed for a target profit.
Price moves break-even more than anything else
A 5% change in price and a 5% change in variable cost do not have equal effects, because the price change moves contribution by the full 5% of price while the cost change moves it by only 5% of cost. Same baseline, four single-variable changes:
| Scenario | Price | Variable cost | Contribution | Break-even units | Change |
|---|---|---|---|---|---|
| Baseline | $145.00 | $92.00 | $53.00 | 9,000 | — |
| Price −5% | $137.75 | $92.00 | $45.75 | 10,427 | +15.9% |
| Price +5% | $152.25 | $92.00 | $60.25 | 7,918 | −12.0% |
| Variable cost +5% | $145.00 | $96.60 | $48.40 | 9,856 | +9.5% |
| Fixed costs +$60,000 | $145.00 | $92.00 | $53.00 | 10,133 | +12.6% |
Read the second row carefully. Discounting by 5% raises the volume you must sell just to stay level by nearly 16%. That is the same arithmetic as the discount table in margin vs markup, seen from the volume side: a small price concession is a large volume commitment. Before you agree to a stacked discount schedule, run it through the discount cascade calculator and put the resulting break-even next to the promised volume.
Contribution margin is not gross margin
This trips up break-even calculations more often than the formula does. Gross margin subtracts cost of goods sold. Contribution margin subtracts every variable cost, including ones that sit below the gross profit line: outbound freight, sales commission, credit card fees, per-order packaging.
| Measure | Subtracts | Answers |
|---|---|---|
| Gross margin | COGS only | How profitable is the product before running the business? |
| Contribution margin | All variable costs, wherever they sit in the P&L | What does one more unit add to profit? |
| Operating margin | All costs, fixed and variable | Is the whole business making money at this volume? |
Using gross margin in place of contribution margin is a systematic error in one direction: it makes contribution look bigger and break-even look lower. If commission is 4% of price and freight out is $6 a unit, that is $11.80 of contribution per unit at a $145 price — over a fifth of the $53 figure. The contribution margin calculator keeps the two apart and shows contribution by line so you can see which product is actually carrying the fixed costs.
Break-even with more than one product
A single-product break-even is exact. A multi-product one is conditional on the sales mix, and you have to say so. The standard approach uses a weighted average contribution per unit based on the unit mix you expect.
Two lines, same $477,000 of fixed costs. Line A: price $145, variable cost $92, contribution $53, expected to be 70% of units. Line B: price $210, variable cost $155, contribution $55, 30% of units.
- Weighted contribution = (0.70 × $53) + (0.30 × $55) = $37.10 + $16.50 = $53.60 per unit
- Break-even = $477,000 ÷ $53.60 = 8,899.3, so 8,900 units total
- Split at the assumed mix: 6,230 units of A and 2,670 units of B
- Check: (6,230 × $53) + (2,670 × $55) = $330,190 + $146,850 = $477,040 — fixed costs covered with $40 to spare
Now change nothing except mix. At a 50/50 split the weighted contribution is $54.00 and break-even falls to 8,834 units. At 90% A it rises to $53.20 and 8,967 units. The whole answer moved 133 units on mix alone, with every price and cost identical. That is why a multi-product break-even is a statement about a scenario, not a fact about the business.
Where break-even analysis quietly breaks
- Fixed costs are only fixed inside a range. Add a second shift or a third warehouse and fixed costs step up. Break-even is valid only within the relevant range you built it for; note the volume at which the next step occurs.
- Depreciation is not cash. If you need a cash break-even, strip non-cash fixed costs out. With $84,000 of depreciation in the $477,000, cash fixed costs are $393,000 and cash break-even is $393,000 ÷ $53 = 7,415.1, so 7,416 units — 1,584 units below the accounting break-even.
- Volume changes price. The formula assumes one price at all volumes. If reaching break-even requires discounting to a larger customer, the price in the formula is no longer the price you will get, and you must re-run it at the realised price.
- Inventory build hides losses. Under absorption costing, producing more than you sell moves fixed overhead into inventory and flatters the P&L. Break-even in sales units is the honest measure; production units are not.
- Commission on gross profit is a feedback loop. If commission is a percentage of margin rather than revenue, contribution depends on price in two places. Model it explicitly rather than folding it into an average rate.
How to read the margin of safety
Margin of safety is the number to report alongside break-even, because break-even alone has no scale. At 21.7%, our example tolerates a meaningful downturn. A business at 4% is one lost customer from a loss, and a business at 45% has room to absorb a bad quarter without a covenant conversation.
Judge it against your own volatility rather than a published target. If your quarterly revenue routinely swings 15%, a 10% margin of safety is thin regardless of what any benchmark says. This is directional, not a standard: the useful comparison is margin of safety against the size of your typical bad quarter.
One caution on the price input. Break-even uses realised price, not list price. If rebates, freight allowances and credit notes take 6% off list, then a $145 list price is a $136.30 realised price, contribution drops from $53.00 to $44.30, and break-even rises from 9,000 to $477,000 ÷ $44.30 = 10,768 units — a 19.6% increase from a number that never appears on an invoice. The gross margin calculator is the quickest way to confirm what your realised price and unit margin actually are before you divide by them.
Getting the inputs out of your ERP
The formula is one division. The work is upstream: which cost elements are genuinely variable, which overhead is absorbed into unit cost, what the realised price actually was after discounts and credit notes, and how all of it looks by product line rather than in total. In most ERPs that means a saved search per input and a spreadsheet to reconcile them.
This is the kind of question is built to answer. Ask "what was average realised price and variable cost per unit by product line last quarter, excluding intercompany?" and get the figures computed live from your own account, with the query shown underneath so you can confirm which cost elements it treated as variable before you divide by them.
Frequently asked questions
What is the break-even point formula?
Break-even units = fixed costs ÷ (price − variable cost per unit). The denominator is contribution per unit. For break-even revenue, divide fixed costs by the contribution margin ratio instead. With $477,000 fixed, a $145 price and $92 variable cost, break-even is $477,000 ÷ $53 = 9,000 units, or $1,305,000 of revenue.
How do you calculate margin of safety?
Margin of safety = (actual sales − break-even sales) ÷ actual sales. It works in units or revenue and gives the same percentage when price is constant. At 11,500 units against a 9,000-unit break-even, that is 2,500 ÷ 11,500 = 21.7%. Sales can fall 21.7% before the business moves into a loss.
What is the difference between contribution margin and gross margin?
Gross margin subtracts only cost of goods sold. Contribution margin subtracts every variable cost, including selling costs below the gross profit line such as outbound freight, commission and payment fees. Break-even requires contribution margin. Substituting gross margin overstates contribution and understates the volume you need to break even.
How do you do a break-even analysis for multiple products?
Weight contribution per unit by the expected unit mix, then divide fixed costs by that weighted figure. At 70% of a $53-contribution product and 30% of a $55 one, the weighted contribution is $53.60 and break-even is 8,900 units. The answer is only valid for that mix, so always publish the mix assumption alongside it.
How many units do I need to sell for a target profit?
Units = (fixed costs + target profit) ÷ contribution per unit. Treat the profit target as extra fixed cost to cover. For $200,000 of profit on $477,000 of fixed costs and $53 contribution: $677,000 ÷ $53 = 12,774 units. If the target is after tax, gross it up by dividing by (1 − tax rate) before adding it.
Should depreciation be included in break-even fixed costs?
Include it for accounting break-even, exclude it for cash break-even. Both are useful and they answer different questions. With $84,000 of depreciation inside $477,000 of fixed costs, cash fixed costs are $393,000 and cash break-even is 7,416 units against 9,000 on the accounting basis — a 1,584-unit difference worth knowing during a cash squeeze.
Calculators for this
Calculate break-even units and revenue from fixed costs and contribution margin. Includes margin of safety and the volume needed for a target profit.
Calculate contribution margin per unit and as a ratio, split contribution across product lines, and see which line to push against a capacity constraint.
Calculate gross margin from revenue and COGS. Get gross profit, margin %, markup %, margin per unit, and the price you need for a target margin.
Chain up to four sequential discounts to see the net price, the effective single discount, and the gross margin left at every step of the cascade.
Keep reading
Margin vs markup, settled: both formulas, a checked conversion table, and the pricing error that quietly costs you dollars per unit.
Price volume mix analysis with a fully worked example: an additive decomposition where price, volume and mix sum exactly to the revenue change.
Build a NetSuite item profitability report that ties out: estimated versus actual COGS, landed cost allocation, and why item margin never equals GL margin.
Build a budget vs actual variance analysis that holds up: materiality thresholds, price/volume/mix drivers, and timing versus permanent.