# 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.

Phiên bản tương tác: https://www.calcopenly.com/vi/everyday/discount-and-markup-calculator
Chủ đề: Máy tính hằng ngày

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.

## Dữ liệu đầu vào

- **Tôi muốn tính** (lựa chọn: 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)**

## Kết quả

- Final price — kết quả chính
- Amount off
- Effective discount
- Profit per item
- Margin
- Markup

## Công thức

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

## Ví dụ có lời giải

### 250 with 20% then 10% off

- Tôi muốn tính: Price after discounts
- Original price: 250
- Discounts (%): 20, 10
- **Final price: 180.00**
- **Amount off: 70.00**
- **Effective discount: 28%**
- Nguồn đối chiếu: Python decimal: 250 × 0.8 × 0.9 = 180; 1 − 0.72 = 28%

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

- Tôi muốn tính: Price after discounts
- Original price: 100
- Discounts (%): 50, 50
- **Final price: 25.00**
- **Effective discount: 75%**
- Nguồn đối chiếu: Python decimal: 100 × 0.5 × 0.5 = 25

### No discount

- Tôi muốn tính: Price after discounts
- Original price: 250
- Discounts (%): 0
- **Final price: 250.00**
- **Effective discount: 0%**
- Nguồn đối chiếu: Definition: 0% off leaves the price unchanged

### Cost 80 with 25% markup

- Tôi muốn tính: Price from cost and markup
- Cost: 80
- Markup (on cost): 25%
- **Final price: 100.00**
- **Margin: 20%**
- **Profit per item: 20.00**
- Nguồn đối chiếu: Python decimal: 80 × 1.25 = 100; 20/100 = 20% margin

### Cost 60 with 40% margin

- Tôi muốn tính: Price from cost and margin
- Cost: 60
- Margin (on price): 40%
- **Final price: 100.00**
- **Markup: 66.6667%**
- **Profit per item: 40.00**
- Nguồn đối chiếu: Python decimal: 60 / 0.6 = 100; 40/60 = 66.67% markup

### Cost 70 sold at a 30% margin

- Tôi muốn tính: Price from cost and margin
- Cost: 70
- Margin (on price): 30%
- **Final price: 100.00**
- **Markup: 42.9%**
- Nguồn đối chiếu: AccountingTools worked example: sells for 100, costs 70 → 30% margin, 42.9% markup

## Câu hỏi

### 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.

### “Discount, markup and margin calculator” chính xác đến mức nào?

Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 7. Ví dụ, “250 with 20% then 10% off” được kiểm tra bằng Python decimal: 250 × 0.8 × 0.9 = 180; 1 − 0.72 = 28%.

### Phương pháp này lấy từ đâu?

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

## Nguồn

- [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/)