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Percentage Calculator

Last Tuesday at 12:00 AM

Our free percentage calculator instantly finds percentages of numbers, percentage differences, increases, decreases, and more. Solve common percentage problems for shopping discounts, taxes, tips, and financial calculations with easy-to-use tools that show step-by-step solutions. Perfect for students, shoppers, business professionals, and anyone needing quick, accurate percentage math without complex formulas. Try our calculator for all your percentage needs - no sign-up required.

Percentage Calculator

Solve any percentage calculation with ease

Enter any two values to calculate the third.

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Master Percentage Calculations: The Complete Guide

Percentages are everywhere in our daily lives—from shopping discounts and tax calculations to data analysis and financial planning. Yet, many people find percentage calculations confusing or intimidating. This comprehensive guide will demystify percentages and provide you with a powerful calculator to solve any percentage problem instantly.

What is a Percentage?

A percentage is a way to express a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred." When we say "25%," we're essentially saying "25 out of 100" or "25/100."
In mathematical notation, a percentage is denoted by the symbol "%". To convert a percentage to a decimal, we divide by 100:
Percentage as decimal=Percentage100\text{Percentage as decimal} = \frac{\text{Percentage}}{100}
For example, 25% as a decimal would be:
25%=25100=0.2525\% = \frac{25}{100} = 0.25

Basic Percentage Formulas

Understanding these fundamental formulas will help you solve any percentage problem:

  1. Finding a percentage of a number:

    P% of X=P100×XP\% \text{ of } X = \frac{P}{100} \times X

  2. Finding what percentage one number is of another:

    What percentage is A of B=AB×100%\text{What percentage is } A \text{ of } B = \frac{A}{B} \times 100\%

  3. Finding the number when a percentage of it is known:

    If P% of X is A, then X=A×100P\text{If } P\% \text{ of } X \text{ is } A, \text{ then } X = \frac{A \times 100}{P}

How to Calculate Percentages (Step-by-Step)

Example 1
Problem:
What is 15% of 80?
Solution:
Step 1: Convert the percentage to a decimal 15%=15100=0.1515\% = \frac{15}{100} = 0.15
Step 2: Multiply by the number 0.15×80=120.15 \times 80 = 12
Therefore: 15% of 80 is 12.
Example 2
Problem:
24 is what percentage of 60?
Solution:
Step 1: Divide the first number by the second 2460=0.4\frac{24}{60} = 0.4
Step 2: Multiply by 100 to get the percentage 0.4×100%=40%0.4 \times 100\% = 40\%
Therefore: 24 is 40% of 60.
Example 3
Problem:
If 30% of a number is 45, what is the number?
Solution:
Step 1: Set up the equation 30% of x=4530\% \text{ of } x = 45 0.3x=450.3x = 45
Step 2: Solve for x x=450.3=150x = \frac{45}{0.3} = 150
Therefore: If 30% of a number is 45, the number is 150.

Percentage Increase and Decrease

Percentage changes are commonly used to describe how values change over time.

Percentage Increase Formula

Percentage Increase=New Value−Original ValueOriginal Value×100%\text{Percentage Increase} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%
Example
Percentage Increase Problem:
If a product's price increases from $80 to $100, what is the percentage increase?
Solution:
Percentage Increase=100−8080×100%=2080×100%=25%\text{Percentage Increase} = \frac{100 - 80}{80} \times 100\% = \frac{20}{80} \times 100\% = 25\%
Therefore, the price increased by 25%.

Percentage Decrease Formula

Percentage Decrease=Original Value−New ValueOriginal Value×100%\text{Percentage Decrease} = \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \times 100\%
Example
Percentage Decrease Problem:
If a product's price decreases from $100 to $75, what is the percentage decrease?
Solution:
Percentage Decrease=100−75100×100%=25100×100%=25%\text{Percentage Decrease} = \frac{100 - 75}{100} \times 100\% = \frac{25}{100} \times 100\% = 25\%
Therefore, the price decreased by 25%.

Percentage Difference

Percentage difference measures the relative difference between two values when neither is necessarily considered the original or new value.

Percentage Difference Formula

Percentage Difference=∣V1−V2∣V1+V22×100%\text{Percentage Difference} = \frac{|V_1 - V_2|}{\frac{V_1 + V_2}{2}} \times 100\%
Where ∣V1−V2∣|V_1 - V_2| represents the absolute difference between the two values.
Example
Percentage Difference Problem:
If Town A has a population of 8,000 and Town B has a population of 12,000, what is the percentage difference?
Solution:
Percentage Difference=∣8,000−12,000∣8,000+12,0002×100%=4,00010,000×100%=40%\text{Percentage Difference} = \frac{|8,000 - 12,000|}{\frac{8,000 + 12,000}{2}} \times 100\% = \frac{4,000}{10,000} \times 100\% = 40\%
Therefore, the percentage difference between the populations is 40%.

Common Percentage Applications

  1. Sales and Discounts

    When a store offers a 20% discount on a $50 item:
    • Discount amount = 20% of $50 = 0.2 × $50 = $10
    • Final price = $50 - $10 = $40

  2. Tip Calculation

    To calculate a 15% tip on a $60 restaurant bill:
    • Tip amount = 15% of $60 = 0.15 × $60 = $9

  3. Tax Calculation

    If the sales tax rate is 8.25% on a $120 purchase:
    • Tax amount = 8.25% of $120 = 0.0825 × $120 = $9.90
    • Total cost = $120 + $9.90 = $129.90

  4. Compound Interest

    The formula for compound interest is:
    A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{nt}
    Where:
    • AA is the final amount
    • PP is the principal (initial investment)
    • rr is the annual interest rate (as a decimal)
    • nn is the number of times interest is compounded per year
    • tt is the time in years

  5. Markup and Margin

    Markup and margin are commonly confused but represent different percentage calculations in business:
    • Markup = (Selling Price - Cost) / Cost × 100%
    • Margin = (Selling Price - Cost) / Selling Price × 100%

Why Use Our Percentage Calculator?

Our interactive percentage calculator offers several advantages:
  • Multiple Calculation Types - Solve any percentage problem with our comprehensive tool
  • Instant Results - Get answers immediately without manual calculations
  • User-Friendly Interface - Clear design that's easy to use for anyone
  • Mobile Responsive - Calculate percentages on any device
  • Step-by-Step Solutions - Understand how the results are calculated

How to Use the Percentage Calculator

Our percentage calculator features four main calculation types:

  1. Basic Calculator

    Enter any two values to calculate the third:
    • Percentage value
    • Number value
    • Result value

  2. Common Phrases Calculator

    Solve percentage problems expressed in everyday language:
    • "What is X% of Y?"
    • "X is what % of Y?"
    • "X is Y% of what?"

  3. Percentage Difference Calculator

    Find the percentage difference between two values, useful for comparing relative differences when neither value is considered the "original."

  4. Percentage Change Calculator

    Calculate percentage increases or decreases between two values, ideal for analyzing changes over time.

Conclusion

Percentages are a vital mathematical concept with countless practical applications. With our comprehensive guide and interactive calculator, you can master percentage calculations and solve percentage problems quickly and accurately.
Whether you're calculating discounts, analyzing data, managing finances, or solving academic problems, our powerful percentage calculator makes the process simple and efficient.
Try our calculator above and simplify your percentage calculations today!

Frequently Asked Questions

FAQ
How do I convert a fraction to a percentage?
Answer:
To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100.
For example, to convert 3/4 to a percentage: 34=0.75=0.75×100%=75%\frac{3}{4} = 0.75 = 0.75 \times 100\% = 75\%
FAQ
How do I calculate percentage points?
Answer:
Percentage points represent the arithmetic difference between two percentages. For example, if an approval rating changes from 40% to 45%, it has increased by 5 percentage points (not by 5%).
FAQ
What's the difference between percentage change and percentage points?
Answer:
  • Percentage change is relative to the original value: If something increases from 20% to 25%, the percentage change is (25−20)/20×100%=25%(25-20)/20 \times 100\% = 25\%
  • Percentage points measure the absolute difference: In the same example, the increase is 5 percentage points (25% - 20%)
FAQ
How do I use the percentage calculator for shopping discounts?
Answer:
To calculate the final price after a discount:
  1. Enter the discount percentage and original price in the "What is X% of Y?" section
  2. The calculator will show the discount amount
  3. Subtract this amount from the original price to get the final price
FAQ
Can I calculate tax using the percentage calculator?
Answer:
Yes! Enter the tax rate percentage and the pre-tax amount in the "What is X% of Y?" calculator to find the tax amount. Add this to the pre-tax amount for the total price.
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