# Break-even calculator

> Calculate the break-even point in units and sales revenue from fixed costs, price and variable cost, plus the volume needed for a target profit.

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The break-even point is the sales volume at which revenue equals total cost. Each unit sold contributes its price minus its variable cost, the contribution margin, toward fixed costs, so the break-even volume is Q = F ÷ (p − v). Break-even revenue is the fixed costs divided by the contribution margin ratio, (p − v) ÷ p.

With the defaults, fixed costs of 50,000, a price of 25 and a variable cost of 15 per unit, each unit contributes 10, a 40% margin ratio. Break-even comes at 5,000 units, or 125,000 of revenue, and a target profit of 20,000 would take 7,000 units.

The model is linear: price and variable cost per unit stay constant, and fixed costs do not step up as volume grows. Break-even units are rounded up, because one unit fewer would leave a small loss.

## 입력

- **Fixed costs**: Rent, salaries and other costs that don't change with volume, for the period
- **Price per unit**
- **Variable cost per unit**: Materials, packaging, commissions — costs that scale with each unit
- **Target profit**

## 결과

- Break-even units (units) — 주요 결과
- Break-even units (exact) (units)
- Break-even revenue
- Contribution margin per unit
- Contribution margin ratio
- Units for target profit (units)
- Revenue for target profit

## 공식

$$
Q_{BE} = \frac{F}{p - v},\qquad R_{BE} = \frac{F}{(p - v)/p}
$$

## 계산 예제

### Fixed 50,000, price 25, variable cost 15

- Fixed costs: 50,000
- Price per unit: 25
- Variable cost per unit: 15
- Target profit: 0
- **Break-even units: 5,000 units**
- **Break-even revenue: 125,000.00**
- **Contribution margin per unit: 10.00**
- **Contribution margin ratio: 40%**
- 검증 출처: Python decimal: 50000 / (25 − 15) = 5000 units; 5000 × 25 = 125000

### Fractional break-even rounds up

- Fixed costs: 10,000
- Price per unit: 7
- Variable cost per unit: 4
- Target profit: 0
- **Break-even units: 3,334 units**
- **Break-even units (exact): 3,333.3333 units**
- **Break-even revenue: 23,333.33**
- **Contribution margin ratio: 42.86%**
- 검증 출처: Python decimal: 10000 / 3 = 3333.33…, ceiling 3334; revenue 10000 / (3/7) = 23333.33

### Zero fixed costs

- Fixed costs: 0
- Price per unit: 12
- Variable cost per unit: 7.5
- Target profit: 0
- **Break-even units: 0 units**
- **Break-even revenue: 0.00**
- **Contribution margin per unit: 4.50**
- **Contribution margin ratio: 37.5%**
- 검증 출처: Python decimal: 0 / 4.5 = 0 — every unit sold is profit from the first

### Target profit 20,000

- Fixed costs: 50,000
- Price per unit: 25
- Variable cost per unit: 15
- Target profit: 20,000
- **Units for target profit: 7,000 units**
- **Revenue for target profit: 175,000.00**
- **Break-even units: 5,000 units**
- 검증 출처: Python decimal: (50000 + 20000) / 10 = 7000 units; × 25 = 175000

## 자주 묻는 질문

### How do you calculate the break-even point?

Divide fixed costs by the contribution margin per unit, price minus variable cost. With fixed costs of 50,000, a price of 25 and a variable cost of 15, break-even is 50,000 ÷ 10 = 5,000 units. When the division is not whole, round up: 10,000 ÷ (7 − 4) = 3,333.33, so 3,334 units are needed.

### What is the contribution margin?

The contribution margin is what each sale leaves after its variable costs, available to cover fixed costs and then profit: price − variable cost per unit. At a price of 25 and a variable cost of 15 it is 10 a unit. As a share of price, the contribution margin ratio, it is 10 ÷ 25 = 40%.

### How do you calculate break-even in sales revenue?

Divide fixed costs by the contribution margin ratio. With 50,000 of fixed costs and a 40% ratio, break-even revenue is 50,000 ÷ 0.40 = 125,000, the same as 5,000 units × 25. The revenue form is useful when a business sells many products with a similar margin ratio.

### How many units do I need to sell to make a target profit?

Add the target profit to the fixed costs and divide by the contribution margin: (F + target) ÷ (p − v). Earning 20,000 on top of 50,000 of fixed costs at a margin of 10 a unit takes 70,000 ÷ 10 = 7,000 units, or 175,000 of revenue at a price of 25.

### How does a price change affect the break-even point?

A small price change moves break-even a lot, because it changes the margin on every unit. With 50,000 of fixed costs and a variable cost of 15, raising the price from 25 to 27 lifts the margin from 10 to 12 and cuts break-even from 5,000 to 4,167 units; cutting the price to 23 raises it to 6,250 units.

### “Break-even calculator”의 정확도는 어느 정도인가요?

정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 4. 예를 들어 “Fixed 50,000, price 25, variable cost 15”은 Python decimal: 50000 / (25 − 15) = 5000 units; 5000 × 25 = 125000와 대조해 확인합니다.

### 이 계산 방법의 출처는 무엇인가요?

Corporate Finance Institute — Break-even analysis; Horngren, Datar & Rajan — Cost Accounting: A Managerial Emphasis, ch. 3 (cost-volume-profit analysis).

## 출처

- [Corporate Finance Institute — Break-even analysis](https://corporatefinanceinstitute.com/resources/accounting/break-even-analysis/)
- Horngren, Datar & Rajan — Cost Accounting: A Managerial Emphasis, ch. 3 (cost-volume-profit analysis)

_계획을 위한 참고용입니다. 대출기관, 세무당국과 시장은 자체 반올림 방식, 수수료와 규칙을 적용합니다. 계약 등의 결정을 내리기 전에 해당 기관에 수치를 확인하세요._