Percentage Calculator

A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin "per centum," meaning "by the hundred." When we say "50 percent" (written as 50%), we mean 50 out of every 100, or simply half.

Percentages are everywhere in daily life:

• Shopping: "30% off sale" means you pay 70% of the original price
• Finance: "5% interest rate" means you earn or pay $5 for every $100
• Statistics: "60% of people prefer..." means 60 out of every 100 people
• Grades: "Scored 85%" means 85 correct answers out of 100 possible points

The power of percentages lies in their ability to standardize comparisons. Whether you're comparing test scores, investment returns, or recipe ingredients, percentages put everything on the same scale of 0 to 100 (and beyond).

There are several common percentage calculations you'll encounter. Here are the key formulas:

1. Finding a Percentage of a Number

To find X% of Y:

To find what percentage X is of Y:

Percentage change measures how much a value has increased or decreased relative to its original value:

Understanding how to convert between these three forms is essential:

Percentage to Decimal

Divide by 100 (or move decimal point 2 places left)

Example: 75% = 75 ÷ 100 = 0.75

Decimal to Percentage

Multiply by 100 (or move decimal point 2 places right)

Example: 0.45 = 0.45 × 100 = 45%

Percentage to Fraction

Put the percentage over 100 and simplify

Example: 25% = 25/100 = 1/4

Fraction to Percentage

Divide the numerator by denominator, then multiply by 100

Example: 3/5 = 0.6 × 100 = 60%

Quick Reference Table

Our percentage calculator handles all common percentage calculations in one place:

Calculate "X% of Y"

1. Enter the percentage value (e.g., 25)
2. Enter the number (e.g., 200)
3. Result shows: 25% of 200 = 50

Calculate "X is what % of Y"

1. Enter the part value (e.g., 30)
2. Enter the whole value (e.g., 150)
3. Result shows: 30 is 20% of 150

Calculate Percentage Change

1. Enter the original value
2. Enter the new value
3. Result shows the percentage increase or decrease

Add/Subtract Percentage

1. Enter the base number
2. Enter the percentage to add or subtract
3. Result shows the final value after adjustment

Understanding percentages is crucial in many real-life situations:

Shopping and Discounts

When an item priced at $80 is "25% off," you calculate the discount as $80 × 0.25 = $20, so you pay $60. Understanding this helps you make informed purchasing decisions and compare deals.

Taxes and Tips

Sales tax, income tax, and restaurant tips are all calculated as percentages. A 15% tip on a $45 meal is $45 × 0.15 = $6.75.

Finance and Investing

Interest rates, investment returns, and inflation are expressed as percentages. If your investment grows from $10,000 to $12,500, that's a 25% return.

Statistics and Data

Survey results, population statistics, and research findings often use percentages to make data understandable and comparable.

Health and Nutrition

Nutritional information shows "% Daily Value" to help you understand how foods contribute to your daily needs.

Academic Grading

Test scores, GPAs, and grade distributions are often expressed as percentages to standardize evaluation.

Even simple percentage calculations can trip people up. Here are common errors to watch out for:

1. Percentage Points vs. Percentage Change

If interest rates rise from 5% to 7%, that's a 2 percentage point increase, but a 40% percentage change (since 2 is 40% of 5). These are very different!

2. Reversing Percentage Changes

A 50% decrease followed by a 50% increase does NOT return to the original value. If $100 decreases by 50% to $50, then increases by 50%, you get $75, not $100.

3. Adding Percentages Incorrectly

You can't simply add successive percentage changes. A 10% increase followed by a 10% increase is NOT a 20% total increase—it's actually 21% (1.1 × 1.1 = 1.21).

4. Confusing "Of" and "More Than"

"150% of X" means 1.5X, while "150% more than X" means X + 1.5X = 2.5X. A huge difference!

5. Forgetting the Base

Always identify what the percentage is "of." 20% off the original price is different from 20% off the sale price.