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How break-even analysis works

Break-even units are fixed costs divided by the contribution margin, which is price minus variable cost per unit. With $24,000 of fixed costs, a $35 price and $20 of variable cost, each sale contributes $15, so you break even at 1,600 units, or $56,000 of sales.

Break-even volume

1,600 units

At $35.00 a unit that is $56,000.00 of sales. Each one puts $15.00 toward the $24,000.00 you have to cover.

Contribution margin per unit
$15.00
Margin as a share of price
42.86%
Sales needed
$56,000.00
$

Costs that arrive whether or not you sell: rent, insurance, salaried pay.

$
$

What one more sale costs you: materials, packaging, card fees.

$

Leave this at zero for the plain break-even point.

On this page

In short

  • Contribution margin is price minus variable costs per unit. On a $35 price and $20 of variable cost, that is $15 a unit, 42.86 percent of the price.
  • Break-even units are fixed costs over that margin. 24000/15=160024000 / 15 = 1600 units, which is $56,000 of revenue.
  • Add a $12,000 profit target and the same margin needs 2,400 units, or $84,000 of sales. The extra 800 units are the $12,000 divided by $15.
  • Raise the price to $38, hold costs still, and the margin is $18. Break-even falls to 1,333.33 units, which rounds up to 1,334 because you cannot sell a third of a unit. Revenue at that rounded count is not the 1,333.33 figure.
  • Break-even is a volume that covers a period's fixed costs. It is not a valuation and not a cash-flow timing model.

Fixed costs, then a margin, then a count

Break-even asks how many units you have to sell before a period's fixed costs are covered. Each unit contributes its price minus its variable cost:

Q=FP−VQ = \frac{F}{P - V}

With $24,000 of fixed costs, a $35 price and $20 of variable cost, the contribution margin is $15. The margin ratio is 42.86 percent. Units: 24000/15=160024000 / 15 = 1600. Revenue: 1,600 times $35 is $56,000. The other walk is fixed costs over the margin ratio, $24,000 / 0.4286, which is the same $56,000.

The break-even calculator on this page is that division. Every unit after 1,600 adds $15 of profit. Every unit short leaves $15 of the fixed costs unpaid.

How payback period works is a different clock: how long a project takes to hand back the cash it cost, not how many units cover a year's rent.

A profit target is more units of the same margin

Keep $24,000 of fixed costs, $35 and $20. Aim for $12,000 of profit. You now need the margin to cover the fixed costs plus the target. At $15 a unit that is 2,400 units, or $84,000 of sales.

The extra 800 units are the $12,000 target divided by $15. Nothing about the cost structure changed. The target did.

Price is the lever that cuts the count

Hold $24,000 of fixed costs and $20 of variable cost. Raise the price to $38. Contribution margin is $18. The margin ratio is 47.37 percent. Units: $24,000 / $18 = 1,333.33, which rounds up to 1,334 because a unit is whole. Revenue on the unrounded count is $50,666.67.

A three-dollar price rise cut the break-even count by hundreds of units, because it widened the margin that each unit contributes to the same $24,000. Volume still has to show up at the new price. The formula does not know whether it will.

What this page is not doing

It is not a discounted cash flow, not a tax model, and not a claim that 1,600 units will sell. The three sheets are $24,000 of fixed costs at a $35 price (1,600 units, $56,000), the same costs with a $12,000 profit target (2,400 units, $84,000), and a $38 price (1,333.33 units, rounding to 1,334). The cost-base shape on this page is operating leverage. Operating against financial leverage is why a low debt ratio does not make a high-fixed-cost firm safe, and why a high leverage ratio is not a break-even count.

This is educational material, not financial advice.

Worked examples

Fixed costs of \$24,000 at a \$35 price

Your fixed costs are $24,000 for the year. Each unit sells for $35 and costs $20 to make. How many units do you have to sell to break even?

  1. Find the contribution margin: $35 minus $20 leaves $15 a unit.
  2. As a share of the price that margin is 15/35=0.42857115/35 = 0.428571, so the margin ratio is 42.86 percent.
  3. Divide the fixed costs by the margin: 24000/15=160024000/15 = 1600 units.
  4. Turn units into money: 1600×35=560001600 \times 35 = 56000, so $56,000 of sales.
  5. Check it the other way, fixed costs over the margin ratio: 24000/(15/35)=5600024000/(15/35) = 56000. Same answer, different route.

You break even at 1,600 units, which is $56,000 of revenue. Every unit after that adds $15 of profit, and every unit short of it leaves $15 of the fixed costs unpaid.

The same costs with a \$12,000 profit target

Same $24,000 of fixed costs, same $35 price, same $20 variable cost. How many units cover the fixed costs and leave $12,000 of profit?

  1. A profit target behaves like extra fixed cost, so add it on top: 24000+12000=3600024000 + 12000 = 36000.
  2. The margin is unchanged at $15 a unit, because nothing about the product moved.
  3. Divide: 36000/15=240036000/15 = 2400 units.
  4. Revenue at that volume: 2400×35=840002400 \times 35 = 84000, so $84,000 of sales.

You need 2,400 units, which is $84,000 of revenue. That is 800 units past the break-even 1,600, and 800 units at $15 of margin is exactly the $12,000 you asked for.

Raising the price to \$38

Fixed costs stay at $24,000 and the unit still costs $20 to make, but you raise the price to $38. Where does break-even land, and what do you do with the fraction?

  1. The new margin is $38 minus $20, which is $18 a unit.
  2. As a share of the price that is 18/38=0.47368418/38 = 0.473684, a margin ratio of 47.37 percent.
  3. Divide the fixed costs by the margin: 24000/18=1333.3324000/18 = 1333.33 units.
  4. You cannot sell a third of a unit, and 1,333 units leaves part of the fixed costs unpaid, so round up to 1,334.
  5. Revenue at the exact crossing point: (24000/18)×38=50666.67(24000/18) \times 38 = 50666.67, or $50,666.67 of sales.

Break-even falls from 1,600 units to 1,334, which is 16.6 percent fewer, and the exact crossing point is 1,333.33 units on $50,666.67 of sales. A three dollar price rise did that, because all of it landed in the margin, taking it from $15 to $18 a unit.

Common questions

Is break-even the same as payback?

No. Break-even is a volume that covers a period's fixed costs. Payback is how long a project takes to hand back the cash it cost. On this sheet, 1,600 units at $35 is $56,000 of sales covering $24,000 of fixed costs. That is not a date.

Why round 1,333.33 up to 1,334?

Because you cannot sell a third of a unit. 1,333 units would still leave a slice of the $24,000 uncovered. The calculator reports both the exact 1,333.33 and the whole-unit 1,334.

What if some costs are mixed?

Split them. The part that does not move with the next unit is fixed. The part that does is variable. Mixing them in one line makes the $15 margin, and the 1,600 count, describe a firm that does not exist.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.