# 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.

النسخة التفاعلية: https://www.calcopenly.com/ar/everyday/discount-and-markup-calculator
الموضوع: حاسبات الحياة اليومية

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.

## المدخلات

- **أريد حساب** (الخيارات: 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)**

## النتائج

- Final price — النتيجة الرئيسية
- Amount off
- Effective discount
- Profit per item
- Margin
- Markup

## الصيغة

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

## أمثلة محلولة

### 250 with 20% then 10% off

- أريد حساب: Price after discounts
- Original price: 250
- Discounts (%): 20, 10
- **Final price: 180.00**
- **Amount off: 70.00**
- **Effective discount: 28%**
- مصدر التحقق: ⁨Python decimal: 250 × 0.8 × 0.9 = 180; 1 − 0.72 = 28%⁩

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

- أريد حساب: Price after discounts
- Original price: 100
- Discounts (%): 50, 50
- **Final price: 25.00**
- **Effective discount: 75%**
- مصدر التحقق: ⁨Python decimal: 100 × 0.5 × 0.5 = 25⁩

### No discount

- أريد حساب: Price after discounts
- Original price: 250
- Discounts (%): 0
- **Final price: 250.00**
- **Effective discount: 0%**
- مصدر التحقق: ⁨Definition: 0% off leaves the price unchanged⁩

### Cost 80 with 25% markup

- أريد حساب: Price from cost and markup
- Cost: 80
- Markup (on cost): 25%
- **Final price: 100.00**
- **Margin: 20%**
- **Profit per item: 20.00**
- مصدر التحقق: ⁨Python decimal: 80 × 1.25 = 100; 20/100 = 20% margin⁩

### Cost 60 with 40% margin

- أريد حساب: Price from cost and margin
- Cost: 60
- Margin (on price): 40%
- **Final price: 100.00**
- **Markup: 66.6667%**
- **Profit per item: 40.00**
- مصدر التحقق: ⁨Python decimal: 60 / 0.6 = 100; 40/60 = 66.67% markup⁩

### Cost 70 sold at a 30% margin

- أريد حساب: Price from cost and margin
- Cost: 70
- Margin (on price): 30%
- **Final price: 100.00**
- **Markup: 42.9%**
- مصدر التحقق: ⁨AccountingTools worked example: sells for 100, costs 70 → 30% margin, 42.9% markup⁩

## الأسئلة

### 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.

### ما مدى دقة «⁨Discount, markup and margin calculator⁩»؟

تعتمد الدقة على مدخلاتك وافتراضات الطريقة. يستخدم الحساب العشري 50 رقمًا معنويًا، لكن التقديرات والأساليب العددية وبيانات المصدر قد تكون أقل دقة؛ تقريب القيم المعروضة لا يزيل هذه الحدود. أمثلة محلولة جرى التحقق منها بمصادر مستقلة: 7. مثلًا، يجري التحقق من «⁨250 with 20% then 10% off⁩» بالرجوع إلى ⁨Python decimal: 250 × 0.8 × 0.9 = 180; 1 − 0.72 = 28%⁩.

### ما مصدر هذه الطريقة؟

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

## المصادر

- [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/)