# 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.

## 输入

- **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**

## 结果

- Break-even units (units) — 主要结果
- Break-even units (exact) (units)
- Break-even revenue
- Contribution margin per unit
- Contribution margin ratio
- Units for target profit (units)
- Revenue for target profit

## 公式

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

## 计算示例

### 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%**
- 核验来源：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%**
- 核验来源：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%**
- 核验来源：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**
- 核验来源：Python decimal: (50000 + 20000) / 10 = 7000 units; × 25 = 175000

## 常见问题

### 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”有多准确？

准确性取决于输入值和方法的假设。十进制运算使用50位有效数字，但估算、数值方法和源数据的精度可能较低；显示时的舍入并不能消除这些限制。 已按独立来源核验的计算示例：4。 例如，“Fixed 50,000, price 25, variable cost 15”根据Python decimal: 50000 / (25 − 15) = 5000 units; 5000 × 25 = 125000进行核验。

### 这种方法出自哪里？

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

## 来源

- [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)

_仅用于规划。贷款机构、税务机关和市场采用各自的舍入方式、费用和规则；作出承诺前，请向相关机构确认数值。_