Discount Calculator

What is a Discount Calculator?

A discount calculator, whether a physical device, an app, or a set of formulas, is a powerful tool that empowers you to quickly compute various aspects of a discount. It can calculate the final price after applying a discount, the amount saved, the original price before the discount, or even the discount percentage. This tool simplifies the math involved in discount-related calculations, making it a must-have for shoppers, businesses, or anyone dealing with price reductions.

Such tools are designed to make shopping (and selling) easier, especially when multiple discounts or complicated offers are involved.

What is a Discount?

A discount is a fundamental concept in the world of shopping and business. It's a reduction in the price of an item or service, whether it's a percentage or a fixed amount deducted from the original price. This makes the item more affordable for customers and can attract buyers, encourage purchases, clear inventory, or reward loyal customers.

Discounts are usually expressed as:

• A percentage of the original price (e.g., 20% off), or
• A fixed dollar amount (e.g., $10 off).

For example, a store might reduce a $50 item by 20% or by $10, depending on the discount offered.

How to Calculate Discounted Price and Savings?

To calculate the discounted price and savings, you need to know the original price, discount percentage, or discount amount.

a. Discounted Price

The discounted price (or final price) is the amount you pay after the discount is applied. It depends on whether the discount is a percentage or a fixed amount.

• For a percentage discount:

• Formula:
  Final Price = P × (1 - d/100)

  Where:
• ( P ) = original price
• ( d ) = discount percentage
• Example: A $100 item with a 20% discount:
  Final Price = 100 × (1 - 20/100) = 100 × 0.8 = $80
  
• For a fixed amount discount:

• Formula:
  Final Price = P - D

  Where:
• ( P ) = original price
• ( D ) = fixed discount amount
• Example: A $50 item with a $10 discount:
  Final Price = 50 - 10 = $40

b. Savings

The savings is the amount you don’t pay due to the discount, equal to the discount amount.

• For a percentage discount:
  

  Savings = (d/100) × P

  Where:
  • ( P ) = original price
  • ( d ) = discount percentage
  Example: For the $100 item with 20% off:
  Savings = (20/100) × 100 = 0.2 × 100 = $20
• For a fixed amount discount:
  Savings = D
  Where:
  • ( D ) = fixed discount amount
  
  Example: For the $50 item with $10 off:
  Savings = $10

Types of discount offers

Discounts come in a variety of forms, each with its own unique benefits and calculations. Below are common types with examples and detailed calculations to keep you intrigued and engaged:

• Percentage Discount:
  “20% off all shoes.”
• Fixed Amount Discount:
  “Save $50 on your next purchase in the microwave category.”
• Buy One Get One (BOGO):
  “Buy one, get one free.”
• Buy One Get One at Half Price:
  “50% off for the second product bought.”
• Seasonal Sales:
  “End-of-season clearance: 40% off.”
• Loyalty Discount:
  “10% discount for clients with loyalty card.”
• Early Bird Discount:
  “$50 discount for clients for the first 100 clients.”
• Cashback Offer:
  “5% cashback on a $100 purchase.”
• Coupon Discount:
  “$5 off for on a $20 purchase.”

Find concrete examples and detailed calculations on how to handle each of these discounts:

1. Percentage Discount

A percentage off the original price.

Example: A store offers 30% off a $40 shirt during a sale.

Discount Calculation:

• Formula: Discount Amount: (Discount% /100)×Price
• Original Price ( P ) = $40
• Discount Percentage ( d ) = 30%
• Discount Amount = (30/100) × 40 = 0.3 × 40 = $12
• Final Price = 40 - 12 = $28
• Savings = $12

2. Fixed Amount Discount

A specific dollar amount off.

Example: A $50 book has a $10 off coupon.

Discount calculation:

• Formula: Final Price = Original Price - Discount Amount
• Original Price = $50
• Discount Amount = $10
• Final Price = 50 - 10 = $40
• Savings = $10

3. Buy One Get One Free (BOGO)

Pay for one item, get another free (effectively 50% off two items of equal price).

Example: Two $20 mugs, buy one get one free.

Discount calculation:

• Formula: Discount Amount: (50 /100) × Price
• Original Total for 2 = 20 + 20 = $40
• You Pay = $20 (for one, second is free)
• Savings = 40 - 20 = $20
• Discount Percentage = (20/40) × 100% = 50%

4. Buy One Get One at Half Price

Pay the full price for one and a half times the price for the second.

Example: Two $20 shirts, second at half price.

Discount Calculation:

• First Shirt = $20
• Second Shirt = 20 × 0.5 = $10
• Total Paid = 20 + 10 = $30
• Original Total = 20 + 20 = $40
• Savings = 40 - 30 = $10
• Discount Percentage = (10/40) × 100% = 25%

5. Seasonal Sale

Discounts on items at season’s end.

For example: 30% off $40 summer clothes.

Discount Calculation: Same as percentage discount above: Final Price = $28, Savings = $12.

• Formula: Discount Amount: (Discount% /100)×Price
• Original Price ( P ) = $40
• Discount Percentage ( d ) = 30%
• Discount Amount = (30/100) × 40 = 0.3 × 40 = $12
• Final Price = 40 - 12 = $28
• Savings = $12

6. Loyalty Discount

Discount for loyal customers.

Real-Life Example: 10% off a $100 grocery bill with a loyalty card.

Discount calculation for this case:

• Formula: Discount Amount: (Discount% /100)×Price
• Original Price ( P ) = $100
• Discount Percentage ( d ) = 10%
• Discount Amount = (10/100) × 100 = $10
• Final Price = 100 - 10 = $90
• Savings = $10

7. Early Bird Discount

Discount for early purchases.

Real example: Conference fee is $200 if paid early, $250 regular.

Discount Calculation:

• Percentage Discount = (Original Price-Discounted Price) / Original Price × 100
• Savings = Original Price-Discounted Price = 250 - 200 = $50
• Discount Percentage = (50/250) × 100% = 20%

8. Volume Discount

Discount for buying in bulk.

Example: 10 items at $5 each without discount, or $4 each if you buy 10 with discount.

Discount calculation:

• Formula: Percentage Discount = (Original Price-Discounted Price) / Original Price × 100
• Original Total = 10 × 5 = $50
• Discounted Total = 10 × 4 = $40
• Savings = 50 - 40 = $10
• Discount Percentage = (10/50) × 100% = 20%

9. Cashback Offer

Money returned after purchase, similar to a discount.

For example: 5% cashback on a $100 purchase.

Calculation:

• Formula: Discount Amount = Original Price × (Discount% / 100)
• Cashback = $100 × (5/100) = $5
• Net Cost = 100 - 5 = $95
• Savings = $5 (equivalent to a 5% discount).

10. Coupon Discount

Discount via a coupon code. Especially popular for retail stores both physically and online.

For example: $5 off a $20 purchase.

Discount calculation:

• Formula: Final Price = Original Price - Discount Amount
• Original Price = $20
• Discount Amount = $5
• Final Price = 20 - 5 = $15
• Savings = $5
• Discount Percentage = (5/20) × 100% = 25%

How to Calculate the Dollar Amount from the Percentage Discount?

Formula:

Discount Amount = Original Price× (Discount% / 100 )

Example:
Original price = $120, Discount = 25%
Discount amount = $120 × 0.25 = $30

How to Calculate the Final Price Given a Discount?

Formula:

Final Price = Original Price−(Original Price×Discount %/100)

Example:
Original price = $200, Discount = 40%
Final price = $200 – ($200 × 0.40) = $200 – $80 = $120

How to Calculate the Price Before Discount?

Formula:

Original Price = Discounted Price/(1−Discount %/100)

Example:
Discounted price = $70, Discount = 30%
Original price = $70 / (1 – 0.30) = $70 / 0.70 = $100

How to Calculate the Percentage Discount Given the Initial and Discounted Price?

Formula:

Percentage Discount=(Original Price−Discounted Price)/Original Price×100

Example:
Original price = $245, Discounted price = $225
Percentage discount = ($245 – $225) / $245 × 100 = $20 / $245 × 100 ≈ 8.16%

How to Calculate a 10% Discount?

To calculate a 10% discount from a price, follow these steps: 

1. Find the original price: Identify the original price of the item.
2. Calculate 10% of the price: Multiply the original price by 0.10 (or 10%).
3. Subtract the discount: Subtract the discount amount from the original price.

Formulas:

• Discount = Original Price x 0.10
• Discounted Price = Original Price - Discount

Example:

If the original price is 100, then we have

• Discount = 100 x 0.10 =10
• Discounted Price = 100 - 10 = 90

How to Take 20% Off a Price?

Let’s see again the steps to calculate the discount amount and the final price:

1. Find the original price: Identify the original price of the item.
2. Calculate 20% of the price: Multiply the original price by 0.20 (or 20%).
3. Subtract the discount: Subtract the discount amount from the original price.

Formulas:

• Discount = Original Price x 0.20
• Discounted Price = Original Price - Discount

Example:

Consider the original price is 400 for a product

• Discount = 400 x 0.20 = 80
• Discounted Price = 400 - 80 = 320

How to Calculate 30 Percent Off?

Same as above, we will use the three steps to calculate the required values:

1. Find the original price: Identify the original price of the item.
2. Calculate 30% of the price: Multiply the original price by 0.30 (or 30%).
3. Subtract the discount: Subtract the discount amount from the original price.
   

Formulas:

• Discount = Original Price x 0.30
• Discounted Price = Original Price – Discount

Example:

Let's take a service with the original price is $100.

• Discount = $100 x 0.30 = $30
• Discounted Price = $100 - $30 = $70

Therefore, a service with a cost of $100 with a 30% off, then the final price will be $70, and a discount of $30.

You might like Percent off calculator

Summary of key formulas

Here is your cheatsheet with the formulas to help you handle discounts:

• Discount Amount: (Discount% /100)×Price
• Final Price: Price ×(1−Discount%/100)
• Original Price: Discounted price/(1−Discount%/100)
• Discount Percentage: [(Price−Final price)/Percent discount]×100%

These formulas and examples provide a comprehensive guide to understanding and calculating discounts, making a discount calculator a handy tool for applying them efficiently!

Also remember:

• Know your original price and discount type.
• Use the formulas above to find savings, final price, or percentage discount.
• Real-life discounts come in many forms- always check the math before you buy.

Related calculators:

• Percentage calculator – for most types of percentage calculator needs.
• Percentage decrease calculator if you want to compute the decrease between two numbers or a percent.
• Percent change calculator – how much a value has increased or decreased over a specific period of time.