Percentage Calculator

The Percentage Calculator allows you to easily perform percentage calculations for a variety of everyday situations. Calculate the percentage of a number, find percentage increases or decreases, determine percentage changes, and more.

Whether you're calculating a tip, a discount, tax, or analyzing data trends, this tool simplifies percentage math and helps you get accurate results quickly.

Percentage Calculator

Understanding Percentages

A percentage is a number expressed as a fraction of 100. The term comes from the Latin "per centum," meaning "by the hundred." Percentages provide a standardized way to express proportions and make comparisons between numbers.

Basic Percentage Concepts

Percentage (%): A number expressed as a fraction of 100. For example, 20% means 20 out of 100, or 0.2 as a decimal.
Percentage of a number: To find X% of Y, multiply Y by (X/100). For example, 15% of 80 is 80 × (15/100) = 12.
Converting decimals to percentages: Multiply the decimal by 100 and add a % symbol. For example, 0.45 = 45%.
Converting fractions to percentages: Divide the numerator by the denominator, then multiply by 100. For example, 3/4 = 0.75 = 75%.

Common Percentage Formulas

Finding the percentage: (Part ÷ Whole) × 100 = Percentage
Finding the part: (Percentage × Whole) ÷ 100 = Part
Finding the whole: (Part × 100) ÷ Percentage = Whole

Percentage change measures how much a value has increased or decreased relative to its original value, expressed as a percentage. This is frequently used in finance, economics, statistics, and everyday life.

Percentage Change Formula

Percentage Change = ((New Value - Original Value) ÷ Original Value) × 100

A positive result indicates a percentage increase
A negative result indicates a percentage decrease

Example: Salary Change

If your salary increases from $50,000 to $57,500, the percentage change is:

Percentage Change = ((57,500 - 50,000) ÷ 50,000) × 100
Percentage Change = (7,500 ÷ 50,000) × 100
Percentage Change = 0.15 × 100
Percentage Change = 15%

Your salary has increased by 15%.

Example: Price Reduction

If the price of a product drops from $80 to $60, the percentage change is:

Percentage Change = ((60 - 80) ÷ 80) × 100
Percentage Change = (-20 ÷ 80) × 100
Percentage Change = -0.25 × 100
Percentage Change = -25%

The price has decreased by 25%.

Percentage increase and decrease calculations help you find a new value after applying a percentage change to an original value.

Percentage Increase Formula

New Value = Original Value × (1 + (Percentage ÷ 100))

Example: To increase $200 by 15%

New Value = $200 × (1 + (15 ÷ 100))
New Value = $200 × (1 + 0.15)
New Value = $200 × 1.15
New Value = $230

Percentage Decrease Formula

New Value = Original Value × (1 - (Percentage ÷ 100))

Example: To decrease $80 by 25%

New Value = $80 × (1 - (25 ÷ 100))
New Value = $80 × (1 - 0.25)
New Value = $80 × 0.75
New Value = $60

Important Note: Percentage increases and decreases are not symmetric! A 50% increase followed by a 50% decrease does not return to the original value. This is why understanding percentage calculations is so important.

Percentages are used in countless real-world situations. Here are some common applications:

Discounts and Sales

When a store offers a 30% discount on a $50 item:
Discount amount = $50 × (30 ÷ 100) = $15
Sale price = $50 - $15 = $35

Interest Rates

If you invest $1,000 at 5% annual interest:
Interest earned in one year = $1,000 × (5 ÷ 100) = $50
New balance = $1,000 + $50 = $1,050

Tips and Gratuities

For a 15% tip on a $60 restaurant bill:
Tip amount = $60 × (15 ÷ 100) = $9
Total bill with tip = $60 + $9 = $69

Taxes

For a purchase with 8% sales tax on a $200 item:
Tax amount = $200 × (8 ÷ 100) = $16
Total price = $200 + $16 = $216

Business and Statistics

Profit margins and revenue growth
Market share and customer demographics
Probability and statistical analysis
Efficacy rates in healthcare and medical studies
Concentration of solutions in chemistry and manufacturing

Here are some helpful tips and shortcuts for working with percentages:

Mental Math Shortcuts: To find 10% of a number, move the decimal point one place to the left. For 5%, halve the 10% value. For 1%, divide the 10% value by 10.
Doubling/Halving Rule: If a value increases by a certain percentage and then decreases by the same percentage, it will not return to the original value. To return to the original after an X% increase, you need a decrease of X/(1+X/100)%.
Percentage Points vs. Percentages: A change from 10% to 15% is an increase of 5 percentage points but a 50% increase in the percentage itself. Be clear about which you're calculating.
Consecutive Percentage Changes: For consecutive percentage changes, multiply the factors rather than adding the percentages. For example, a 10% increase followed by another 10% increase is equivalent to a single increase of 21% (1.1 × 1.1 = 1.21), not 20%.
Working with Tax-Inclusive Prices: To find the pre-tax amount when you know the total price and tax rate, divide the total by (1 + tax rate/100). For example, for a $108 item with 8% tax included, the pre-tax price is $108 ÷ 1.08 = $100.

When in doubt, use the calculator above to ensure accurate percentage calculations. Slight errors in percentage calculations can have significant impacts, especially when working with large values.

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Frequently Asked Questions

How do I calculate a percentage of a number?

Multiply the number by the percentage divided by 100. For example, 15% of 80 is 80 × 0.15 = 12. To find what percent X is of Y, divide X by Y and multiply by 100: 12 is 15% of 80 because 12 ÷ 80 × 100 = 15.

How do I calculate percentage increase or decrease?

Subtract the old value from the new value, divide by the old value, then multiply by 100: (new − old) ÷ old × 100. Going from 50 to 65 is a 30% increase; going from 65 to 50 is about a 23% decrease. Note the two directions give different percentages because the starting base differs.

What is the difference between percentage change and percentage points?

Percentage points measure the simple arithmetic difference between two percentages, while percentage change is relative. If an interest rate rises from 4% to 6%, that is an increase of 2 percentage points, but a 50% increase relative to the original rate.

How do I convert a fraction to a percentage?

Divide the numerator by the denominator and multiply by 100. For example, 3/8 = 0.375, so 3/8 is 37.5%. To go the other way, divide the percentage by 100 and simplify: 62.5% = 62.5/100 = 5/8.

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Frequently Asked Questions

How do I calculate a percentage of a number?

How do I calculate percentage increase or decrease?

What is the difference between percentage change and percentage points?

How do I convert a fraction to a percentage?