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25% of 200 = 50
15% increase 100 → 115
Discount $80 → $64
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Quick Calculators

Choose the calculation type you need and get instant results

Basic Percentage Calculation

What is % of

Find Percentage Value

is what percent of

Percentage Change Calculator

From to

Reverse Percentage Calculator

If % of something is

Add or Subtract Percentage

%

Compound Percentage Calculator

Apply % then % to
Specialized

Specialized Percentage Calculators

Discount Calculator

Calculate final prices after discounts, see how much you save on sales and special offers.

Enter the original price and discount percentage to instantly see your savings and final price. Works for single discounts, sales, and promotional offers. Formula: Final Price = Original × (1 − Discount% ÷ 100).

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Sales Tax Calculator

Add sales tax to prices or calculate tax amounts for any purchase.

Enter the pre-tax amount and your local tax rate to see the tax amount and total. Sales tax rates vary by region — common rates range from 5% to 25%. Formula: Total = Amount × (1 + Tax Rate ÷ 100).

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Tip Calculator

Calculate tip amount and total bill with tip included.

Choose a preset tip percentage or enter a custom amount. Standard restaurant tips are 15–20% in the US. For quick mental math: find 10% by moving the decimal, then double it for 20%.

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Profit Margin Calculator

Calculate profit margin percentage from cost and selling price.

Enter cost and selling price to calculate profit margin. Note: margin ≠ markup. Margin = Profit ÷ Revenue, while Markup = Profit ÷ Cost. A 50% markup equals a 33.3% margin.

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Loan Payment Calculator

Calculate monthly loan payment based on principal, interest rate, and term.

Uses the standard amortization formula to calculate fixed monthly payments. Enter your loan amount, annual interest rate, and repayment term. See your total interest cost over the loan lifetime.

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Compound Interest Calculator

Calculate compound interest with different frequencies.

See how your money grows over time with compound interest — interest that earns interest. Enter principal, annual rate, and time period. Formula: A = P × (1 + r)^t.

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Markup Calculator

Calculate selling price based on cost and desired markup percentage.

Calculate selling price from cost and desired markup percentage. Markup is based on cost price, not selling price. A 100% markup means you double the cost to set the price.

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Commission Calculator

Calculate commission amount based on sales and commission rate.

Enter total sales amount and commission rate to see the commission earned and net amount. Common in real estate (5–6%), sales (3–10%), and affiliate marketing (5–30%).

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VAT Calculator

Add or remove VAT from a price.

Add VAT to a net price or extract VAT from a gross price. Standard VAT rates: EU 17–27%, UK 20%, Canada 5% GST. To remove VAT: Net = Gross ÷ (1 + VAT Rate ÷ 100).

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Inflation Calculator

Calculate the impact of inflation on purchasing power.

See how inflation erodes purchasing power over time. Enter an amount, annual inflation rate, and years to see the future equivalent cost and how much purchasing power you lose.

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Featured Guides

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Shopping

How to Calculate Discounts: Complete Guide

Learn how to calculate discounts, sale prices, and savings with easy formulas and examples....

Read more →
Daily Life

How to Calculate Tips: Restaurant Tipping Guide

Master the art of calculating tips with our comprehensive guide for restaurants, services, and more....

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Finance

How to Calculate Sales Tax

Understanding sales tax calculations for shopping, business, and tax planning....

Read more →
Education

Percentage Increase and Decrease Explained

Learn to calculate percentage changes, growth rates, and understand increases vs decreases....

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Interactive

Master Percentages

10 interactive lessons with practice problems and progress tracking. From basics to advanced calculations.

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Percentage Quiz

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Complete Guide

Complete Guide to Percentage Calculations

What Are Percentages?

Percentages are a way to express numbers as parts of 100. The symbol '%' means 'per hundred', making percentages a universal language for comparing and understanding proportions.

Whether you're calculating shopping discounts, analyzing financial data, or determining grades, percentages simplify complex comparisons and make numbers more understandable.

Percentage Basics

  • 100% represents the whole or complete amount
  • 50% is half, 25% is a quarter, 75% is three quarters
  • Percentages can exceed 100% when showing increases
  • 0% means nothing, empty, or zero amount

Percentages in Daily Life

Percentages are everywhere - from price tags in stores to economic news reports. Understanding how to work with percentages helps you make better decisions.

Shopping and Retail

Calculate exact discounts, compare deals, determine final prices with tax, and understand the true value of loyalty programs and cashback offers.

Finance and Investing

Track interest rates, calculate investment returns, understand compound interest, and analyze financial growth over time.

Statistics and Data

Interpret surveys, understand market trends, analyze data changes, and present information in an understandable format.

Percentage Conversion Table

Quick reference for converting between percentages, decimals, and fractions:

Percentage Decimal Fraction
1%0.011/100
5%0.051/20
10%0.101/10
12.5%0.1251/8
20%0.201/5
25%0.251/4
33.33%0.33331/3
50%0.501/2
66.67%0.66672/3
75%0.753/4
100%1.001/1

Step-by-Step Guides

How to Calculate Discounts

  1. Identify the original price of the item
  2. Find the discount percentage
  3. Multiply the price by the discount percentage
  4. Subtract the discount from the original price
Example

$100 shirt with 30% off: Discount = $100 × 0.30 = $30. Final price = $100 - $30 = $70

How to Calculate Tips

  1. Take the total bill amount
  2. Decide on the tip percentage
  3. Multiply the bill by the tip percentage
Example

$50 bill with 15% tip: $50 × 0.15 = $7.50 tip

Step-by-Step

How to Calculate Percentages: Complete Tutorial

Whether you are a student, professional, or everyday shopper, understanding percentages is essential. Here is everything you need to know.

How to Find a Percentage of a Number

Finding a percentage of a number is one of the most common calculations people need. The formula is straightforward: multiply the number by the percentage and divide by 100. For example, to find 15% of 200, calculate (15 × 200) ÷ 100 = 30. This is useful when calculating tips at restaurants, figuring out sales tax on purchases, or determining how much you save during a sale.

Formula: X% of Y = (X × Y) ÷ 100

Real-world example: A store offers 30% off a $85 jacket. The discount is (30 × 85) ÷ 100 = $25.50, so you pay $85 − $25.50 = $59.50. Our discount calculator above automates this instantly.

How to Calculate Percentage Change

Percentage change tells you how much a value has increased or decreased relative to its starting point. This is critical for tracking investment returns, salary changes, price inflation, and business growth metrics. The formula divides the difference between the new and old values by the old value, then multiplies by 100.

Formula: Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100

Real-world example: Your rent increased from $1,200 to $1,380 per month. The percentage increase is ((1380 − 1200) ÷ 1200) × 100 = 15%. Understanding this helps you budget and negotiate.

How to Find the Original Value (Reverse Percentage)

Sometimes you know the result after a percentage was applied and need to find the original number. For instance, if a discounted price is $72 after a 20% discount, what was the original price? Since $72 represents 80% of the original (100% minus 20%), divide by 0.80 to get $90. This reverse calculation is invaluable for tax-inclusive pricing, post-discount shopping, and financial analysis.

Formula: Original = Result ÷ (1 ± Percentage ÷ 100)

How Compound Percentages Work

Compound percentages occur when multiple percentage changes are applied sequentially. A common misconception is that a 20% increase followed by a 20% decrease returns to the original value — it does not. Starting with $100: a 20% increase gives $120, then a 20% decrease of $120 gives $96, not $100. This concept is fundamental in compound interest calculations, multi-year investment returns, and successive price changes.

In finance, compound interest uses this principle: your interest earns interest. A $1,000 investment at 5% annual compound interest grows to $1,050 after year one, then $1,102.50 after year two (5% of $1,050, not 5% of $1,000). Over 10 years, it becomes $1,628.89 — significantly more than the $1,500 from simple interest.

Profit Margin vs. Markup: Understanding the Difference

Profit margin and markup are both expressed as percentages but calculated differently. Margin is profit divided by selling price, while markup is profit divided by cost. If you buy a product for $60 and sell it for $100, your profit is $40. The margin is $40/$100 = 40%, but the markup is $40/$60 = 66.7%. Business owners must understand this distinction for correct pricing strategies, financial reporting, and competitive analysis.

Mental Math Tricks for Quick Percentage Calculations

You do not always need a calculator. Here are proven mental math shortcuts that professionals use daily:

  • Finding 10%: Move the decimal point one place left. 10% of $85 = $8.50.
  • Finding 5%: Find 10% and halve it. 5% of $85 = $4.25.
  • Finding 25%: Divide by 4. 25% of $85 = $21.25.
  • Finding 1%: Move the decimal two places left. 1% of $85 = $0.85. Then multiply for any percentage.
  • The commutative trick: X% of Y = Y% of X. So 8% of 50 = 50% of 8 = 4. Choose whichever is easier to calculate.
FAQ

Frequently Asked Questions

To calculate a percentage of a number, multiply the number by the percentage and divide by 100. For example, to find 20% of 150: multiply 150 × 20 = 3,000, then divide by 100 = 30. Alternatively, convert the percentage to a decimal (20% = 0.20) and multiply: 150 × 0.20 = 30. This method works for any percentage calculation, whether you're calculating discounts, tips, taxes, or any other percentage-based value.

The percentage increase formula is: ((New Value - Original Value) ÷ Original Value) × 100. For example, if a price increases from $50 to $75, the calculation is: ((75 - 50) ÷ 50) × 100 = (25 ÷ 50) × 100 = 0.5 × 100 = 50% increase. This formula is essential for calculating price changes, salary raises, growth rates, and investment returns. Always subtract the original from the new value first, then divide by the original value.

To calculate percentage decrease: 1) Find the difference between original and new value (Original - New). 2) Divide the difference by the original value. 3) Multiply by 100 to get the percentage. Example: Price drops from $80 to $60. Step 1: 80 - 60 = 20. Step 2: 20 ÷ 80 = 0.25. Step 3: 0.25 × 100 = 25% decrease. This method is perfect for calculating discounts, depreciation, weight loss, or any reduction in value.

To find what percent X is of Y, use the formula: (X ÷ Y) × 100. For instance, to find what percent 25 is of 200: (25 ÷ 200) × 100 = 0.125 × 100 = 12.5%. This calculation is useful for determining test scores (85 out of 100 = 85%), completion rates, market share, or any scenario where you need to express one value as a percentage of another. Always divide the partial value by the total value.

To calculate discount percentage: 1) Subtract the sale price from the original price to find the discount amount. 2) Divide the discount amount by the original price. 3) Multiply by 100. Example: Original price $120, sale price $90. Discount amount: $120 - $90 = $30. Discount percentage: ($30 ÷ $120) × 100 = 25% off. This helps you compare deals, understand savings, and make informed shopping decisions.

Reverse percentage calculation finds the original value when you know the final value and percentage. Formula: Original Value = Final Value ÷ (1 + Percentage/100) for increases, or Original Value = Final Value ÷ (1 - Percentage/100) for decreases. Example: If a price after 20% tax is $120, the original price is: $120 ÷ 1.20 = $100. This is crucial for calculating pre-tax amounts, original prices before discounts, or base salaries before raises.

To add a percentage to a number: 1) Convert the percentage to decimal (divide by 100). 2) Multiply the original number by (1 + decimal). Or use: Original × (1 + Percentage/100). Example: Add 15% to $200. Method 1: 15% = 0.15, so $200 × 1.15 = $230. Method 2: $200 × (1 + 15/100) = $200 × 1.15 = $230. This is used for calculating prices with tax, salary increases, markup pricing, and growth projections.

To calculate percentage difference between two numbers: 1) Find the absolute difference (larger - smaller). 2) Find the average of the two numbers. 3) Divide the difference by the average. 4) Multiply by 100. Formula: |A - B| ÷ ((A + B)/2) × 100. Example: Compare 80 and 100. Difference: 20. Average: 90. Percentage difference: 20 ÷ 90 × 100 = 22.22%. This method is ideal for comparing values without a clear 'before' and 'after' relationship.

Compound percentage applies multiple percentage changes sequentially. Formula: Final = Initial × (1 + %1/100) × (1 + %2/100)... Example: $100 increased by 10% then 20%. Step 1: $100 × 1.10 = $110. Step 2: $110 × 1.20 = $132. Total increase is 32%, not 30%! This is crucial for understanding compound interest, multi-year growth rates, sequential price changes, and investment returns. Each percentage is applied to the result of the previous calculation.

To calculate tip percentage quickly: 1) For 20% tip: Divide bill by 5. 2) For 15% tip: Divide bill by 10, then add half of that. 3) For 10% tip: Divide bill by 10. Example on $80 bill: 20% = $80 ÷ 5 = $16. 15% = $8 + $4 = $12. 10% = $8. Mental math trick: Move decimal one place left for 10%, double it for 20%. These shortcuts help you calculate tips instantly without a calculator.

To calculate sales tax: 1) Multiply the purchase amount by the tax rate (as a decimal). 2) Add the tax to the original amount for the total. Formula: Tax = Price × (Tax Rate/100), Total = Price + Tax. Example: $50 item with 8.5% tax. Tax amount: $50 × 0.085 = $4.25. Total price: $50 + $4.25 = $54.25. To find tax rate from total: Tax Rate = ((Total - Subtotal) ÷ Subtotal) × 100.

Percentage error measures the accuracy of a measurement or estimate. Formula: |Actual Value - Expected Value| ÷ |Expected Value| × 100. Example: You estimate 250 people will attend an event, but 280 actually come. Error: |280 - 250| ÷ 250 × 100 = 30 ÷ 250 × 100 = 12% error. The absolute value ensures error is always positive. This is essential in science, forecasting, quality control, and any field requiring precision measurement.

To calculate percentage of total in Excel: 1) Divide the part by the total using formula =Part/Total. 2) Format as percentage (Ctrl+Shift+%). Example: If cell A1 contains 25 and B1 contains 200, enter =A1/B1 in C1, which gives 0.125 or 12.5%. For running totals: =A2/SUM($A$2:$A$10). The dollar signs create absolute references. Excel automatically multiplies by 100 when you apply percentage formatting. Use for budgets, sales analysis, and data reports.

Markup and margin are different: Markup = ((Selling Price - Cost) ÷ Cost) × 100. Margin = ((Selling Price - Cost) ÷ Selling Price) × 100. Example: Cost $50, Selling Price $75. Markup: (($75 - $50) ÷ $50) × 100 = 50% markup. Margin: (($75 - $50) ÷ $75) × 100 = 33.33% margin. Markup is based on cost (how much you add), margin is based on selling price (your profit percentage). Retailers use markup for pricing, while investors focus on margin.

To calculate percentage change over time, use: ((End Value - Start Value) ÷ Start Value) × 100 ÷ Number of Time Periods = Average % Change per Period. For compound annual growth rate (CAGR): ((End Value ÷ Start Value)^(1/Years) - 1) × 100. Example: Investment grows from $1,000 to $1,500 over 3 years. Simple: 50% ÷ 3 = 16.67% per year average. CAGR: ((1,500 ÷ 1,000)^(1/3) - 1) × 100 = 14.47% annual compound growth.

Pro Tips

Pro Tips for Percentage Calculations

1

Convert Percentages to Decimals

For easier calculations, convert percentages to decimals by dividing by 100. For example, 25% becomes 0.25, making multiplication simpler and reducing errors.

2

Use the 10% Rule

To quickly estimate percentages, find 10% first (move decimal one place left), then multiply. For 30%, calculate 10% and multiply by 3.

3

Remember Common Percentages

Memorize common percentage equivalents: 50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10. This speeds up mental calculations significantly.

4

Double-Check with Reverse Calculation

Verify your results by working backwards. If you calculated 20% of 150 as 30, check: is 30 ÷ 150 = 0.20? This catches errors quickly.

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