Percentage Calculator

Calculate percentages quickly and easily with our free percentage calculator. Find percentage increase, decrease, or calculate what percent one number is of another.

Understanding Percentage Calculations

The Percentage Calculator is a versatile tool for all types of percentage calculations. Whether you need to calculate discounts, find percentage changes, or determine simple percentages, this calculator makes it easy and fast.

What is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The word “percentage” comes from the Latin “per centum,” meaning “out of one hundred.” The symbol % represents percentage.

Basic percentage formula:

• Percentage = (Part / Whole) × 100

For example:

• 25 out of 100 = 25%
• 50 out of 200 = 25%
• 15 out of 60 = 25%

Common Percentage Calculations

This calculator helps you with:

• Finding Percentages - What is X% of Y? (e.g., 20% of 150 = 30)
• Percentage Increase/Decrease - Calculate the percentage change between two numbers
• Proportion as Percentage - X is what percent of Y? (e.g., 30 of 150 = 20%)
• Discount Calculation - Find final price after percentage discount

Why Percentages are Useful

Percentages make it easier to:

• Compare quantities of different sizes
• Understand proportions quickly
• Calculate taxes and discounts accurately
• Analyze changes in values over time

Sales Tax Calculator - Tax Rates in the US and UK

Tax systems vary significantly between countries and even within regions. Understanding how to calculate sales tax is essential for accurate budgeting and financial planning.

US Sales Tax System

The United States has a complex sales tax system with rates varying by state, county, and city:

• No Sales Tax States: Alaska, Delaware, Montana, New Hampshire, Oregon
• Low Sales Tax: Colorado (2.9%), Alabama (4%), Hawaii (4%)
• Average Sales Tax: California (7.25%), Texas (6.25%), Florida (6%)
• High Sales Tax: Tennessee (7%), Louisiana (4.45% state + local)

Note: Most states allow local jurisdictions to add additional sales tax, so combined rates can exceed 10% in some areas.

UK VAT System

The United Kingdom uses a Value Added Tax (VAT) system:

• Standard Rate (20%) - Most goods and services
• Reduced Rate (5%) - Energy-saving materials, children’s car seats
• Zero Rate (0%) - Most food, children’s clothes, books, newspapers

Practical Tax Examples

Adding sales tax (US example - 8% rate):

• Base price: $100
• Sales tax 8%: $8
• Total price: $108

Calculating base price from total (UK VAT 20%):

• Price including VAT: $120
• Base price: $120 ÷ 1.20 = $100
• VAT amount: $20

Adding UK VAT to a base price:

• Base price: £50
• VAT 20%: £10
• Total price: £60

Tax Table by Product Category (US/UK)

Product/Service	US Sales Tax	UK VAT
Electronics	Varies by state	20%
Clothing	Varies (exempt in some states)	0% (children), 20% (adults)
Food - groceries	Exempt in most states	0%
Food - restaurants	Taxable in most states	20%
Books	Varies by state	0%
Healthcare	Exempt	0%
Digital services	Varies by state	20%

Business Tax Considerations

Businesses must collect sales tax from customers and remit it to tax authorities. In the US, this varies by state. In the UK, businesses registered for VAT must charge VAT and file quarterly returns.

Discount Calculator - Sales and Special Offers

Discounts are a major part of retail shopping, especially during Black Friday, Cyber Monday, and seasonal sales.

How to Calculate Final Price with Discount

Formula:

• Final price = Original price × (1 - Discount/100)

Example:

• Original price: $80
• Discount: 25%
• Final price: $80 × (1 - 0.25) = $80 × 0.75 = $60
• Savings: $20

Calculate Original Price from Discounted Price

If you see a product for $60 with a 25% discount, the original price was:

• Original price = $60 ÷ (1 - 0.25) = $60 ÷ 0.75 = $80

Compound Discounts (Multiple Discounts)

When there are multiple discounts, they don’t add up directly. They apply consecutively:

Example:

• Original price: $100
• First discount 20%: $100 × 0.80 = $80
• Second discount 10% on $80: $80 × 0.90 = $72
• Total effective discount: 28% (not 30%)

Common Discount Events in US/UK

• Black Friday: 20-70% off (November)
• Cyber Monday: 15-50% off online
• Boxing Day (UK): 30-70% off (December 26)
• Prime Day: 15-40% off on Amazon
• Back to School: 15-30% off (August-September)
• January Sales: 40-70% off

Real-World Use Cases

Online and In-Store Shopping

Percentages are essential when comparing deals:

• Discount codes and coupon percentages
• Cashback rewards (1-5% typical)
• Credit card rewards points
• Amazon Subscribe & Save discounts (5-15%)

Business Invoices and Freelancing

Freelancers and contractors need to calculate:

• Service fees (typically 15-20% on platforms like Upwork)
• Payment processing fees (2.9% + $0.30 for Stripe)
• Early payment discounts (2/10 net 30 terms)

Example invoice calculation:

• Service fee: $500
• Platform commission 20%: $100
• Processing fee 2.9%: $14.50
• Net received: $385.50

Salary Increases and Raises

If you receive a 5% raise and your current salary is $60,000:

• Raise amount: $60,000 × 0.05 = $3,000
• New salary: $63,000

Investment Returns

Calculate investment performance:

• Initial investment: $10,000
• Final value: $12,500
• Return: (($12,500 - $10,000) / $10,000) × 100 = 25%

Restaurant Tips

In the US, tipping 15-20% is customary:

• Restaurant bill: $75
• Tip 18%: $13.50
• Total: $88.50

Mortgage and Loan Interest

Understanding percentage rates on loans:

• Loan amount: $200,000
• Annual interest rate: 4.5%
• Annual interest: $200,000 × 0.045 = $9,000

Frequently Asked Questions About Percentages

How do I calculate sales tax on a purchase?

Multiply the base price by the tax rate. For example:

• Base price: $50
• Sales tax 8%: $50 × 0.08 = $4
• Total: $54

How do I remove sales tax from a total price?

Divide the total price by (1 + tax rate). For 8% tax:

• Total price: $108
• Base price: $108 ÷ 1.08 = $100

What’s the difference between a discount and a tax?

• Discount: reduces the price (subtract)
• Tax: increases the price (add)

How do I calculate compound discounts?

Apply each discount sequentially, don’t add them:

• 20% + 10% ≠ 30%
• Actual result: $100 → $80 → $72 = 28% total discount

Which is better: 30% off or Buy 2 Get 1 Free?

It depends on how many items you need:

• Buy 2 Get 1 Free = 33.3% effective discount (better than 30%)
• But only if you need 3 items

How do I calculate percentage change between two values?

Use this formula:

• % Change = ((New Value - Old Value) / Old Value) × 100

Example:

• Old price: $80, New price: $100
• Change: (($100 - $80) / $80) × 100 = 25% increase

What common mistakes should I avoid when calculating percentages?

1. Adding discounts directly (20% + 10% ≠ 30%)
2. Confusing increase with total value (10% increase on $100 is $10, not $110)
3. Calculating percentages from the wrong base
4. Forgetting to include tax in final prices

How do I calculate how much I saved with a discount?

Subtract the final price from the original price:

• Original price: $150
• Discounted price: $105
• Savings: $150 - $105 = $45
• Savings percentage: ($45/$150) × 100 = 30%

How do I calculate tip percentage quickly?

For a 20% tip, move the decimal point one place left and double it:

• Bill: $50
• 10% = $5
• 20% = $5 × 2 = $10

Tips and Tricks for Quick Calculations

Mental Math Shortcuts for Common Percentages

• 10%: Divide by 10 ($100 → $10)
• 5%: Calculate 10% and divide by 2
• 20%: Calculate 10% and multiply by 2
• 25%: Divide by 4 ($100 → $25)
• 50%: Divide by 2 ($100 → $50)
• 1%: Divide by 100 ($100 → $1)

Calculating 15% (Tips)

1. Calculate 10% (move decimal one place)
2. Calculate 5% (half of 10%)
3. Add them together

Example with $40:

• 10% of $40 = $4
• 5% of $40 = $2
• 15% = $4 + $2 = $6

Verifying Discounts in Stores

If a product has a 30% discount:

1. Calculate 30% of the price
2. Subtract from original price
3. Or multiply price by 0.70 (faster)

When to Use Each Type of Calculation

• Percentage of a number: Calculate tax, discounts, tips
• What percentage is X of Y: Compare values, calculate shares
• Percentage change: Analyze growth, inflation, price variations
• Reverse percentage: Remove tax, find original price before discount

Conclusion

The percentage calculator is an essential tool for everyday life, from calculating sales tax to finding the best Black Friday deals. Mastering percentage calculations helps you:

• Better manage personal finances
• Understand paychecks and taxes
• Take advantage of discounts intelligently
• Make informed purchasing decisions

Use our free calculator above for all your percentage calculation needs!