Discount Calculator

Contents

• What means Discount Calculator?
• What is a discount?
• How to calculate the discounted price and savings?
• What types of discount offers exist?
• What is the Percentage discount formula?
• Types of discounts with examples
• How do you calculate the dollar amount from the percentage?
• How to calculate the final price given a discount
• How to calculate the price before the discount
• What is the percentage discount if you know the initial and discounted price?

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

• Description: A percentage off the original price.
• Real-Life Example: A store offers 30% off a $40 shirt during a sale.
• 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

• Description: A specific dollar amount off.
• Real-Life Example: A $50 book has a $10 off coupon.
• 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)

• Description: Pay for one item, get another free (effectively 50% off two items of equal price).
• Real-Life Example: Two $20 mugs, buy one get one free.
• 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

• Description: Pay the full price for one and a half times the price for the second.
• Real-Life Example: Two $20 shirts, second at half price.
• 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

• Description: Discounts on items at season’s end.
• Real-Life Example: 30% off $40 summer clothes.
• 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

• Description: Discount for loyal customers.
• Real-Life Example: 10% off a $100 grocery bill with a loyalty card.
• Calculation:
• 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

• Description: Discount for early purchases.
• Real-Life Example: Conference fee is $200 if paid early, $250 regular.
• 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

• Description: Discount for buying in bulk.
• Real-Life Example: 10 items at $5 each without discount, or $4 each if you buy 10 with 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

• Description: Money returned after purchase, similar to a discount.
• Real-Life 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

• Description: Discount via a coupon code.
• Real-Life Example: $5 off a $20 purchase.
• 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%

Percentage Discount Formula

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

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%

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.