Where the Lines Cross
Break-even is the quantity at which total revenue finally overtakes total cost — the point where the rising revenue line crosses above the cost line. · 12 min
The last folio found the money a single sale leaves behind: price minus the cost of making one unit, its contribution margin. This folio asks the next question a founder loses sleep over — how many sales before the whole month pays for itself. That number has a name and a picture, and once you can find both, you know exactly when a venture stops bleeding and starts earning.
Guess before you learn
A market booth costs you $300 a month. Each candle sells for $8 and costs $3 in materials to make. How many candles must you sell in a month before you start making money?
The number that matters is what one candle clears after its own materials — $8 minus $3 is $5. Divide the fixed $300 booth rent by that $5 and you get 60. Candle number sixty is the first one that leaves you ahead. If you guessed 38, keep the pencil mark: counting the whole $8 against the rent is the most common first move, and the next section is exactly about why only the $5 counts.
9–12
3–5
You spend $12 on supplies for a bake sale. Each cookie earns you $2 after what it cost to make. Count the cookies: after six, you have your $12 back. Cookie seven is your first real profit. That break-even count tells you whether the sale was even worth setting up.
6–8
Costs come in two kinds. Fixed costs stay the same whether you sell one candle or a hundred — the $300 booth rent. Variable costs rise with each unit — the $3 of wax and wick in every candle. What one candle earns after its own variable cost is its contribution margin: $8 − $3 = $5. Break-even is the count where those $5 slices have finally paid off the whole fixed cost: $300 ÷ $5 = 60 candles. Below sixty you are still paying off the booth. Above it, each candle's $5 is yours to keep.
9–12
Write total cost as a line: fixed cost + (variable cost × quantity), here 300 + 3q. Write revenue as another line: price × quantity, here 8q. Both climb as you sell more, but they start in different places — revenue from zero, cost from $300. Break-even is the quantity where they meet: set 8q = 300 + 3q, so 5q = 300, and q = 60. That 5 is the contribution margin, and the shortcut is always the same: break-even quantity = fixed cost ÷ contribution margin per unit.
K–2
You spend six dollars on lemons. Each cup you sell earns one dollar back. So you must sell six cups just to get your six dollars back. Cup six is when you stop losing money.
Undergrad
The same crossing reads in dollars, not just units: break-even revenue equals fixed cost divided by the contribution margin ratio — here $5/$8, so $300 ÷ 0.625 = $480. Two extensions matter in practice. The margin of safety is how far current sales sit above break-even, the cushion before losses begin. And operating leverage rises with fixed costs: a booth-heavy, low-material venture breaks even later but earns more from each sale past that point. The model assumes price and unit cost hold steady across the range — usually true enough near your current volume, and worth checking when it is not.
Postgrad
Cost-volume-profit analysis generalizes this. With several products, break-even uses a weighted-average contribution margin across the expected sales mix; shift the mix and the break-even point moves even when no single price changes. The linear model is a first-order approximation — real cost curves have step jumps (a second booth, a hired helper) and real demand bends the price line, so the true profit region is a band, not a clean wedge. Its enduring value is diagnostic: it isolates the three levers — fixed cost, price, and unit variable cost — and shows exactly how a change in each moves the quantity at which the venture stops losing money.
break-even
The sales quantity where total revenue equals total cost. Sell one more and you profit; one fewer and you lose. Found as fixed cost ÷ contribution margin per unit.
Why is this true?
Why does dividing the fixed cost by one unit's contribution margin land exactly on break-even?
Because each unit sold hands over its contribution margin toward the fixed cost, and nothing else touches that fixed cost. When enough units have each handed over their margin to cover the whole fixed amount, it is exactly paid off — and that count is break-even. So fixed cost ÷ margin per unit gives it directly.
The arithmetic is worth doing by hand until it is automatic. Two numbers go in — the fixed cost you owe no matter what, and the margin one sale clears — and the break-even quantity falls out. Work the candle booth through, step by step.
Break-even for the candle booth — the steps fade as you master them
$8 − $3 = $5
$300 ÷ $5
60 candles a month
The number is only half of it. Draw the same situation and break-even stops being a formula and becomes a place — the spot where two climbing lines cross. Revenue starts at zero and rises by the full price of each sale. Total cost starts high, at the fixed $300, and rises only by the materials in each sale. Because revenue climbs faster, it eventually catches the cost line, and the point where it does is break-even.
Break-even is the honest floor of a venture: the sales you must reach just to owe nothing. Everything above it is profit, and everything below it is a bill you are quietly paying yourself. The next folio adds the twist that ruins founders who track only this number — a month can show a profit here while the bank account still falls.
Practice — new ink and old, interleaved
1.A warm referral is standing in front of you. You have named the price. What do you do?
2.A defensible first price should sit—
3.Your unit cost is $16 and you want to keep $20 per sale. What price is that?
4.You raise the candle price from $8 to $10, materials unchanged at $3. What happens to the break-even quantity?
5.In one sentence, why can a $100 sale leave less behind than a $20 sale?
6.Order one turn of the build-measure-learn loop.
- Idea
- Build the smallest test
- Customers use it
- Measure what they did
- Decide the next step
7.Without looking back: what is the formula for the break-even quantity?
Break-even quantity = fixed cost ÷ contribution margin per unit, where the margin is the price minus the variable cost of one unit.
How close were you? Grade yourself honestly — it sets your review date.
8.A potter rents a kiln for $600 a month. Each mug sells for $25 and costs $10 in clay and glaze. How many mugs must sell to break even?
9.A candle sells for $8; the wax, wick, and jar cost $3. What is the contribution margin per candle?
10.Which of these is a fixed cost for the candle booth?