Break-Even Point

In one sentence: The break-even point says how many items you must sell before the money from sales has paid back all your fixed costs, so you stop losing money.

$Q = \frac{F}{P - V}$

Read it out loud: “Q equals F divided by P minus V. Q is the number of units you must sell to break even. F is the fixed costs for the period. P is the price for one unit. V is the variable cost for one unit. P minus V is the contribution margin, the money each sale adds towards the fixed costs.”

Before you start

The ideas and signs this page uses, explained from zero. For powers of ten, Greek letters and other notation in general, see Math basics.

Fixed costs and variable costs: A fixed cost is a bill that does not change with how many items you sell, such as rent, insurance or a loan payment. A variable cost rises with each item you make, such as the flour and eggs for each loaf. Costs are usually counted over a set period, like one month. The formula needs the fixed costs for the period and the per-unit costs for one item, both in dollars.
Unit, price and cost per unit: A unit is one item you sell, such as one loaf of bread or one repaired bike. The price is the amount a customer pays for one unit, and the variable cost is what it costs you to make and sell that one unit. Both are measured in dollars per unit, which means dollars for each loaf or each repair. Keeping these per-unit figures separate from the fixed total is the key to the formula.
Contribution margin, $P - V$: The contribution margin is the price minus the variable cost, written $P - V$ . It is the money each sale leaves over to pay the fixed costs. If a loaf sells for 5 dollars and costs 2 dollars in flour, eggs and packaging, it contributes 3 dollars toward the rent and the other fixed costs. Every sale adds its margin to the pile that must cover the fixed costs.
Break-even: To break even means your profit is exactly zero, so revenue covers all of your costs. Below the break-even quantity you lose money, and above it you make a profit. The break-even point is the number of units at which this turning point happens, and it is the first number a new business should work out before it sets its plans.

What each symbol means

Symbol	Meaning
$Q$	The quantity of units you must sell to break even. It is a plain count of items, such as loaves per month, and it has no money unit. In the example Q comes out to 1000 loaves per month, which is the answer the formula gives.
$F$	The fixed costs for the period, in dollars, such as the monthly rent, the oven loan payment and the insurance. They must be paid whatever the number of sales. In the example F is 3000 dollars per month.
$P$	The price per unit, in dollars per unit, which is what a customer pays for one item. In the example P is 5 dollars per loaf.
$V$	The variable cost per unit, in dollars per unit, the cost of making and selling one more item, such as the ingredients and the bag. In the example V is 2 dollars per loaf.

The formula piece by piece

$P - V$: Start with the margin on one sale. The price minus the variable cost is the money each unit leaves over to pay the fixed costs, which is the contribution margin.
$F$: The fixed costs, the total bills for the period that must be paid whatever the sales turn out to be, such as rent and loan payments.
$\frac{F}{P - V}$: Divide the fixed costs by the margin per unit. This counts how many units it takes to earn back all of the fixed costs.
$Q = \frac{F}{P - V}$: The whole formula in one sentence: the break-even quantity equals the fixed costs divided by the price minus the variable cost per unit.

What the formula is doing, and why

The break-even formula answers one question: how many units must I sell before I stop losing money? Each sale brings in the price $P$ , but it also costs the variable amount $V$ , so each sale leaves $P - V$ behind. That left-over money pays the fixed costs $F$ . Once enough units have been sold to pay off all the fixed costs, every extra sale is profit.

Why subtract? The variable cost comes out of every sale, so only the difference between the price and the variable cost is free to go toward the fixed costs. A loaf that sells for 5 dollars and costs 2 dollars in ingredients leaves 3 dollars. The bigger that gap, the fewer sales are needed to cover the fixed costs.

Why divide? The fixed costs $F$ are a total that has to be covered, and the margin $P - V$ is what one sale covers. Dividing the total by the amount each unit covers gives the number of units needed: $Q = \frac{F}{P - V}$ . If the fixed costs double, you need twice as many units. If the margin doubles, you need only half as many.

What it means for profit. If you sell exactly $Q$ units, revenue equals all the costs and profit is zero. Sell more, and each extra unit adds $P - V$ to profit. Sell fewer, and each missing unit leaves $P - V$ of the fixed costs uncovered. The break-even point is the line between the two.

Limits of the formula. It assumes that the price, the variable cost per unit and the fixed costs all stay the same however many units you sell. Real businesses sometimes offer discounts or buy ingredients in bulk, so the formula is a good first estimate rather than an exact plan.

An everyday picture

Think of a bike repair shop. Each repair pays for the spare parts and the mechanic’s time for that job, and the money left over from the repair, after the parts, is the contribution margin. The shop’s rent, insurance and loan payment are the fixed costs, and they come due whether or not any bikes arrive. Counting how many repairs must be finished each month to cover those bills is the break-even point. Once the margins from the repairs have covered the rent, each further repair is money the shop keeps.

Worked example: How many loaves must the bakery sell?

A small bakery has fixed costs of 3000 dollars each month. These cover the rent, the oven loan payment and the insurance. Each loaf sells for 5 dollars and costs 2 dollars in flour, eggs and packaging, so the variable cost is 2 dollars per loaf. All numbers are made up for illustration. We want the break-even quantity $Q$ , and then we check the profit at a higher level of sales.

Write the formula and the numbers. The formula is $Q = \frac{F}{P - V}$ , with fixed costs $F = 3000$ dollars per month, price $P = 5$ dollars per loaf and variable cost $V = 2$ dollars per loaf. The money figures are all per month or per loaf, so the answer will be a count of loaves per month.
Find the contribution margin. Each loaf brings in 5 dollars and costs 2 dollars to make, so it leaves $P - V = 5 - 2 = 3$ dollars toward the fixed costs. This 3 dollars is the margin that one sale adds, and it is the number we divide by.
Divide the fixed costs by the margin. The fixed costs are 3000 dollars, and each loaf covers 3 dollars of them, so $Q = \frac{3000}{3} = 1000$ loaves. Dividing a total by the amount each item covers counts how many items it takes to cover that total.
Check the units. Dollars per month divided by dollars per loaf leaves loaves per month, because the dollar signs cancel in the division. So 1000 is a count of loaves per month, which is the right kind of answer for a quantity of units.
Check the break-even by putting the answer back. At 1000 loaves the bakery takes in $1000 \times 5 = 5000$ dollars, and its variable costs are $1000 \times 2 = 2000$ dollars. Subtracting the variable costs from the sales leaves $5000 - 2000 = 3000$ dollars, which exactly pays the fixed costs. The profit is zero, as break-even should be.
See what happens above break-even. If the bakery sells 1200 loaves, the margin brings in $1200 \times 3 = 3600$ dollars. After the 3000 dollars of fixed costs, the profit is $3600 - 3000 = 600$ dollars. The extra 200 loaves above break-even added 600 dollars, which is 3 dollars each.

Answer: The bakery must sell 1000 loaves per month to break even. Each loaf above that adds 3 dollars of profit, so selling 1200 loaves in a month earns a profit of 600 dollars.

The numbers in this example are recomputed by script every time the site is built.

Common mistakes

Mixing time periods, such as using yearly fixed costs with a monthly count of sales. If F is a yearly total, Q is a yearly count too. Keep the fixed costs and the quantity on the same period.
Dividing by the price instead of the margin, so writing $F / P$ rather than $F / (P - V)$ . In the example that gives 600 loaves, which ignores the ingredient cost of every loaf.
Treating a fixed cost as if it changed with each loaf, or treating a per-loaf cost as if it were a monthly total. Fixed costs are totals and variable costs are per unit.
Thinking break-even means making a profit. At the break-even quantity profit is exactly zero. Only the units sold beyond Q add to profit.

Where you will meet it

Deciding whether a new product, menu item or service is worth launching, by checking how many units it must sell before it stops losing money.
Setting prices, since the price must be high enough that a realistic number of sales can cover the fixed costs.
Planning loans and budgets for a small business, where a lender wants to know the minimum sales needed to repay the debt.
Factory and workshop planning, where a new machine’s cost is compared with the margin earned on each product it makes.

Questions people ask

Why is the answer a number of units and not dollars?

Because the question is how many items must be sold. The formula uses dollars to work out the margin per unit, but the answer counts units. To find the break-even sales in dollars instead, multiply Q by the price P. In the example, 1000 loaves at 5 dollars each is 5000 dollars of sales.

What if the variable cost is bigger than the price?

Then P minus V is zero or negative, so each sale adds nothing to the fixed costs or loses money. No number of sales will ever cover the fixed costs, and the formula gives no sensible answer. The business must raise the price or cut the variable cost before the break-even point means anything.

Do I include my own pay in the fixed costs?

Yes, if you pay yourself a fixed salary. It does not change with the number of loaves you sell, so it is a fixed cost. If your pay depends on how much you sell, it behaves more like a variable cost, and it belongs in V instead.

Net Profit Margin: Net profit margin says how many cents of profit a business keeps from each dollar of sales, after every cost has been paid.
Markup: Markup says how much a seller adds on top of what an item cost, measured as a share of that cost.
Return on Investment (ROI): Return on investment says how much profit you made for each dollar you spent, so you can compare a small investment with a large one.