# Discount, markup and margin calculator

> Sale price after one or more percent-off discounts, and selling price from cost using a markup or a profit margin, with each converted to the other.

Интерактивная версия: https://www.calcopenly.com/ru/everyday/discount-and-markup-calculator
Тема: Повседневные калькуляторы

Each discount multiplies the running price by (1 − d/100), so stacked discounts compound rather than add. For pricing, markup is profit as a percentage of cost and margin is profit as a percentage of the selling price. The calculator finds the selling price from either one and converts between them with margin = markup ÷ (1 + markup).

With the defaults, 20% off 250 followed by a further 10% off leaves 180: an effective discount of 28%, not 30%. In the pricing modes, an item that costs 80 and is marked up 25% sells for 100, which is a 20% margin.

A margin must stay below 100%, since a 100% margin would mean the item cost nothing, while a markup has no upper limit. All figures are per item, before any sales tax or VAT.

## Входные данные

- **Что нужно найти** (варианты: Price after discounts, Price from cost and markup, Price from cost and margin)
- **Original price**
- **Discounts (%)**: Applied one after another: 20, 10 means 20% off, then 10% off the reduced price.
- **Cost**
- **Markup (on cost)**
- **Margin (on price)**

## Результаты

- Final price — основной результат
- Amount off
- Effective discount
- Profit per item
- Margin
- Markup

## Формула

$$
\begin{gathered}P_{\text{final}} = P\prod_i\left(1 - \frac{d_i}{100}\right) \\ \text{margin} = \frac{\text{markup}}{1 + \text{markup}} \\ \text{markup} = \frac{\text{margin}}{1 - \text{margin}}\end{gathered}
$$

## Примеры с решением

### 250 with 20% then 10% off

- Что нужно найти: Price after discounts
- Original price: 250
- Discounts (%): 20, 10
- **Final price: 180.00**
- **Amount off: 70.00**
- **Effective discount: 28%**
- Источник проверки: Python decimal: 250 × 0.8 × 0.9 = 180; 1 − 0.72 = 28%

### Two 50% discounts are 75% off, not 100%

- Что нужно найти: Price after discounts
- Original price: 100
- Discounts (%): 50, 50
- **Final price: 25.00**
- **Effective discount: 75%**
- Источник проверки: Python decimal: 100 × 0.5 × 0.5 = 25

### No discount

- Что нужно найти: Price after discounts
- Original price: 250
- Discounts (%): 0
- **Final price: 250.00**
- **Effective discount: 0%**
- Источник проверки: Definition: 0% off leaves the price unchanged

### Cost 80 with 25% markup

- Что нужно найти: Price from cost and markup
- Cost: 80
- Markup (on cost): 25%
- **Final price: 100.00**
- **Margin: 20%**
- **Profit per item: 20.00**
- Источник проверки: Python decimal: 80 × 1.25 = 100; 20/100 = 20% margin

### Cost 60 with 40% margin

- Что нужно найти: Price from cost and margin
- Cost: 60
- Margin (on price): 40%
- **Final price: 100.00**
- **Markup: 66.6667%**
- **Profit per item: 40.00**
- Источник проверки: Python decimal: 60 / 0.6 = 100; 40/60 = 66.67% markup

### Cost 70 sold at a 30% margin

- Что нужно найти: Price from cost and margin
- Cost: 70
- Margin (on price): 30%
- **Final price: 100.00**
- **Markup: 42.9%**
- Источник проверки: AccountingTools worked example: sells for 100, costs 70 → 30% margin, 42.9% markup

## Вопросы

### How do you calculate a percentage discount?

Multiply the price by (1 − discount ÷ 100). 20% off 250 is 250 × 0.8 = 200, a saving of 50. To find the discount from two prices, divide the saving by the original price: an item cut from 250 to 180 is 70 ÷ 250 = 28% off.

### Is 20% off plus an extra 10% off the same as 30% off?

No. The second discount applies to the already reduced price, so 20% then 10% off is 1 − 0.8 × 0.9 = 28% off in total. Two 50% discounts leave a quarter of the price, which is 75% off rather than 100%. The order does not matter: 10% then 20% also gives 28%.

### What is the difference between markup and margin?

Markup is profit divided by cost; margin is profit divided by the selling price. An item that costs 70 and sells for 100 makes 30 profit: a 42.9% markup and a 30% margin, the pairing AccountingTools uses in its explanation. Margin is always the smaller of the two, and a markup m converts to a margin of m ÷ (1 + m).

### What markup gives a 50% margin?

A 100% markup: doubling the cost makes the profit equal to the cost, which is half the selling price. In general markup = margin ÷ (1 − margin), so a 20% margin needs a 25% markup, a 40% margin needs 66.67%, and a 60% margin needs 150%.

### How do you find the selling price from cost and margin?

Divide the cost by (1 − margin). A cost of 60 at a 40% margin sells for 60 ÷ 0.6 = 100. Adding 40% to the cost instead gives 84, which is only a 28.57% margin; confusing the two percentages underprices every item.

### Насколько точен «Discount, markup and margin calculator»?

Точность зависит от введённых данных и допущений метода. Десятичная арифметика использует 50 значащих цифр, но оценки, численные методы и исходные данные могут быть менее точными; округление на экране не устраняет эти ограничения. Решённые примеры, проверенные по независимым источникам: 7. Например, «250 with 20% then 10% off» проверяется по источнику Python decimal: 250 × 0.8 × 0.9 = 180; 1 − 0.72 = 28%.

### Откуда взята методика?

AccountingTools — The difference between margin and markup; Corporate Finance Institute — Markup and markup percentage.

## Источники

- [AccountingTools — The difference between margin and markup](https://www.accountingtools.com/articles/what-is-the-difference-between-margin-and-markup.html)
- [Corporate Finance Institute — Markup and markup percentage](https://corporatefinanceinstitute.com/resources/accounting/markup/)