How to calculate the break-even point, step by step
The break-even point is one division that answers one question: how much must you sell before you start making money? A business owner who knows the answer can see whether the price covers the costs. The calculation needs three numbers: the fixed costs, the price per unit and the variable cost per unit. The answer is a count of units, and a second figure in sales revenue: on $50,000 of fixed costs, a $25.00 price and a $15.00 variable cost, the contribution margin is $10.00 per unit and the break-even point is 5,000 units — $125,000.00 of sales.
The formula is break-even units = fixed costs ÷ (price − variable cost). The fixed costs are rent, salaries and everything that does not change with sales. The price is what you charge for one unit. The variable cost is what one unit costs you to make or buy. The difference between the price and the variable cost is the contribution margin: the amount each sale contributes toward the fixed costs. The break-even revenue is the units times the price.
The worked example, line by line. Step 1 — the fixed costs: $50,000. Step 2 — the price: $25.00. Step 3 — the variable cost: $15.00. Step 4 — the contribution margin: $25.00 − $15.00 = $10.00 per unit. Step 5 — the break-even units: $50,000 ÷ $10.00 = 5,000 units. Step 6 — the break-even revenue: 5,000 × $25.00 = $125,000.00. Step 7 — the meaning: at 5,000 units sold the business has covered every fixed cost and made exactly zero profit, and the 5,001st unit is the first one that is pure profit. Work it yourself in the break-even point calculator.
What the number means
A point of 5,000 units means 5,000 units sold covers every fixed cost and makes exactly zero profit, so on $50,000 of fixed costs the business keeps nothing until the 5,001st unit — for every unit before it, the sale is still paying off the rent and salaries, and for every unit after it, the sale is profit. A higher point means more units to sell before profit starts. A lower point means fewer units to sell before profit starts. The point on its own never says whether 5,000 units is healthy or thin — that depends on how many units the business can actually sell. A point of 5,000 units against demand for 6,000 is a business that clears the line, and the same point against demand for 4,000 is a business that never gets there.
What moves the break-even point
Three things move the point: the fixed costs, the price and the variable cost. Raise the fixed costs and the point rises, because there is more to cover before profit starts: with the price held at $25.00 and the variable cost at $15.00, $60,000 of fixed costs puts the point at 6,000 units. Cut the fixed costs and the point falls. Raise the price and the point falls, because each sale now contributes more: with the fixed costs held at $50,000, a $27.50 price holds the point at 4,000 units — the smallest price for the units to stay at or below 4,000. Cut the price and the point rises. Raise the variable cost and the point rises, because each sale now contributes less: with the fixed costs held at $50,000, a $16 variable cost holds the point at 5,555.56 units — the largest whole-dollar variable cost for the units to stay at or below 6,000. The revenue target moves too: with the fixed costs held at $50,000, a $22.50 price holds the revenue at $150,000.00 — the largest price for the revenue to stay at or above $150,000.00. Note: a small rise in the variable cost pushes the point up fast when the margin is thin.
When the break-even point is undefined
If the price equals the variable cost, the point is undefined — the contribution margin is $0.00 per unit, and dividing by zero has no answer. A business that sells at exactly its variable cost adds nothing with every sale, so no sales volume ever covers the fixed costs: on a $15.00 price and a $15.00 variable cost the point is undefined, not zero. If the price is below the variable cost, the point goes negative — a real figure, not undefined: on a $10.00 price and a $15.00 variable cost the margin is −$5.00 per unit, the point is −10,000 units and the revenue is −$100,000.00, because each sale loses money and there is no volume that breaks even. If the fixed costs are zero, the point is 0 units — a real figure, not undefined: with nothing to cover, the first sale is already profit.
The rounding trap
The units are displayed to two decimals, half-up, and a one-dollar move in the fixed costs moves the units by about a tenth — so the neighbour’s displayed figure can differ from the target even though it looks close. At $59,999 of fixed costs the point is 5,999.90 units, not 6,000 — a hair below the line. At $50,001 of fixed costs the point is 5,000.10 units, not 5,000 — a hair above the line.
Margin of safety
The margin of safety is how far current sales sit above the break-even point — the cushion between the sales you make and the sales you must make. On a point of 5,000 units, selling 6,000 units leaves 1,000 units of cushion: the business can lose 1,000 units of sales before it stops making money. The cushion grows when the point falls — a lower variable cost, a higher price, or lower fixed costs all widen it — and it shrinks when the point rises.
Common mistakes
The first mistake is confusing the break-even point with the contribution margin — the margin is an input to the point, not the point itself. The same $50,000 of fixed costs, $25.00 price and $15.00 variable cost give a margin of $10.00 per unit and a point of 5,000 units. The second is forgetting the fixed costs, and the point comes out far too low. The third is using the wrong price — the list price instead of the price after discounts — and the point is wrong before it starts. The fourth is rounding the point down to a whole number and treating it as exact — a point of 5,999.90 units is not 6,000. Work it out in the break-even point calculator, and check the contribution margin calculator and the customer acquisition cost calculator before you decide what the point means.