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Break-Even Quantity

Also known as break even point · units to break even

Q=Fp−vQ = \frac{F}{p - v}

Units aren’t used in this calculation — every value is a plain number.

Worked example: $12,000 fixed, $40 price, $25 variable → 800 units — press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value.

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Break-Even Quantity explained

pvFQ

Fixed costs arrive whether you sell anything or not: rent, insurance, the shop truck payment, the phone. Every unit you do sell contributes its price minus its own variable cost toward that pile, and break-even is simply the point where the contributions finish covering it. With $12,000 of monthly fixed cost and units that sell for $40 while costing $25 in material and labour, each one contributes $15, and 12000/15=80012000/15 = 800 units clears the month.

The quantity p−vp - v is called the contribution margin, and it deserves the attention rather than the price. Raising the price by $5 lifts the contribution from $15 to $20 and drops break-even from 800 units to 600, a 25% cut in the work needed to survive. Shaving $5 off the variable cost does exactly the same thing. Neither is intuitive until you see that both act on a denominator.

If the price does not exceed the variable cost, no quantity ever breaks even and the solver refuses the question. This is not a technicality. A shop losing money on every job cannot make it up in volume, and the formula is the most honest way to demonstrate that to someone who believes otherwise.

Break-Even Quantity formula

Q=Fp−vQ = \frac{F}{p - v}
Where
  • QQ= Break-even quantity
  • FF= Fixed cost for the period ($)
  • pp= Selling price per unit ($)
  • vv= Variable cost per unit ($)

Missing one of these? Work it out first, then come back

Part of this formula set

Pricing and profit

5 formulasMarkup, margin, break-even and ROI — the four numbers that decide whether the work is worth doing.