Break-Even Point Calculator

Contribution-margin view of operating break-even.

Worked example — Break-Even Point Calculator

Gross margin	60%

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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Lesson

The theory — Break-Even Point Calculator

The break-even point is the sales volume at which revenue exactly covers total cost — the last unit before profit begins. It exists because costs split into two kinds that behave completely differently: some you pay once whatever you sell, and some you pay again for every unit.

What each symbol means

FC: fixed costs — rent, tooling, the things that do not care how many you sell. 1800 at the defaults.
p: the price each unit sells for. It is what the contribution margin is measured from, and the leverage is not obvious: raising it by 1 adds 1 to the margin of every unit, so a small price move shifts break-even far more than the same move in fixed costs.
VC: the variable cost per unit — materials, packing, the cost that repeats. 2.4.
CM: the contribution margin, p − VC = 3.6. This is the real engine: what each unit contributes toward paying off the fixed costs.

Where the formula comes from

Write revenue and cost as functions of volume Q: revenue is p·Q, total cost is FC + VC·Q.
Break-even is where they meet: p·Q = FC + VC·Q. Collect the Q terms: Q(p − VC) = FC.
Divide by the contribution margin: Q* = FC / (p − VC). At the defaults, 1800 / 3.6 = 500 units — and revenue there is 500 × 6 = 3000.

Assumes: One product, a single price, and costs that are perfectly linear — no bulk discount on materials, no overtime premium, and every unit made is sold. Real businesses break at least one of those.
Breaks when: Push the variable cost above the price and the model does not merely give a large answer — it stops having one. Set VC = 8 against a price of 6 and the margin becomes −2, with the readout returning no break-even: each unit sold now deepens the loss, so no volume can ever recover the fixed costs. Volume cannot fix a negative margin, and that is the most useful thing this model has to say.

why break-even is not your goal 🖖

Break-even is the floor, not the target. The number tells you how many units you must sell to stop losing money — but it says nothing about how fast you accumulate profit beyond it. That speed is called operating leverage: if fixed costs are a large share of total costs, profit grows steeply once you cross Q*. A SaaS business with 85% gross margin scales dramatically; a low-margin retailer needs huge volume just to stay solvent. The contribution margin (p − VC) is the real lever: raise price, cut variable cost, or both. Fixed costs set the threshold, but contribution margin sets the slope.

where the two lines cross 🖖

Every business has two running totals: money coming in (price times units sold) and money going out (fixed cost plus variable cost times units). Break-even is simply the point where those two lines meet. Sell one unit fewer and you are in the red; one more and you are in the black. The formula Q* = fixed cost / (price − variable cost) just locates that crossing directly, so you can see your target before spending a cent.

airlines break even by the seat 🖖

Airlines rarely count units. Instead they track the break-even load factor: the share of seats that must be sold for a flight to cover its costs, typically around 70–80%. It reframes break-even not as a count of items but as a percentage of a fixed capacity — the same algebra, asked as "how full must we be?" A route with 65% break-even is a money machine; one at 95% is one bad week from disaster.

Practice

Check yourself

Predict the answer first, then use the controls above to find out. Reveal only after you have committed to a guess — that is what makes it practice.

Fixed costs are 1800 and the margin is 3.6, giving 500 units. Double the fixed costs to 3600 — what happens to the break-even volume?

Show answer

It doubles, to 1000 units. Q* = FC / CM is linear in the fixed costs, so they scale straight through. This is the least interesting of the three levers, and the one people reach for first.
Now instead raise the price from 6 to 7, leaving everything else alone. Predict whether that helps more or less than halving the fixed costs.

Show answer

The price moves by only a sixth, but the margin goes from 3.6 to 4.6 — a 28% jump — because the variable cost is subtracted first. Break-even falls from 500 to about 391 units. Halving the fixed costs would give 250, so it is not a clean win either way; the point is that a small price change is amplified by the margin.
Set the variable cost to 8, above the price of 6. What volume breaks even?

Show answer

There is no such volume, and the readout says so: it returns no break-even. The margin is 6 − 8 = −2, so every unit sold widens the loss and no amount of volume recovers the fixed costs. That is the most useful thing this model has to say, and the reason contribution margin matters more than price or cost alone.

Problem solved in full

Break-even volume for fixed costs 1800 and price 6 6 steps
Fixed costs 1800, price 6, variable cost 2.4. Find the break-even volume — then find out which of the three numbers you should least like to be wrong about.
1. Profit is contribution times volume, less the fixed costs. Setting it to zero and solving for volume is the whole model.
  
  $profit = (p - V C) Q - F C = 0 ⟹ Q^{*} = \frac{F C}{p - V C}$
2. The contribution margin is what each unit adds after paying for itself. Fixed costs divided by it is the count you need before anything is earned.
  
  $C M = p - V C = 6 - 2.4 = 3.6, Q^{*} = \frac{1800}{3.6} = 500, R^{*} = 500 \times 6 = 3000$
3. Gross margin is the same contribution expressed as a share of price, which is the form that lets you compare a café with a software company.
  
  $gross margin = \frac{C M}{p} = \frac{3.6}{6} = 60%$
4. Now perturb the price by 10% and re-solve. The margin absorbs the whole change, so the percentage move in the margin is larger than the move in the price.
  
  $p \to 5.40 (- 10%) : C M = 3.00, Q^{*} = \frac{1800}{3.00} = 600 (+ 20%)$
5. Do the same to the variable cost. The change is identical in currency terms and its effect is a third as large, because it starts from a smaller base.
  
  $V C \to 2.16 (- 10%) : C M = 3.84, Q^{*} = \frac{1800}{3.84} = 469 (- 6.25%)$
6. The asymmetry has a name and a number: the ratio of price to margin is the leverage on every price decision.
  
  $\frac{\partial Q ^{*}}{Q ^{*}} = - \frac{\partial C M}{C M} = - \frac{p}{C M} \cdot \frac{\partial p}{p} : \frac{p}{C M} = \frac{6}{3.6} = 1.67$
Answer

500 units, and the number to be careful with is the price. Break-even moves as the reciprocal of the contribution margin, and the margin is a difference, so a small change in price is a large change in the difference. Cut the price by 10% and the margin falls by 17%, which pushes break-even from 500 to 600 units — you must sell 20% more to stand still. Cut the unit cost by the same 10% and break-even improves by only 6.25%. The amplification factor is p/CM = 1.67 here, and it grows without limit as the margin thins: a business running on a 10% gross margin amplifies every price change tenfold. That is the whole argument against discounting to fill capacity, in one ratio.

$Q^{*} = \frac{F C}{p - V C} = 500; a 10% discount costs 20% more volume$

References (2)

The break-even chart as originally set out: W. L. Fill, "The Break-Even Chart." The Accounting Review 27(2), 202–209, 1952.
On the linearity the model assumes and where real cost behaviour departs from it: A. W. Patrick, "Some Observations on the Break-Even Chart." The Accounting Review 33(4), 573–580, 1958.

By the 42Math team · Updated 2026-06-22

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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