Percentage Calculator

How to Use This Percentage Calculator

Our free percentage calculator handles the three most common percentage problems you'll encounter in everyday life, academics, and business. Select the calculation type using the tabs at the top, enter your numbers, and get instant results.

Steps:

1. Choose your calculation type: "% of a Number," "What % is X of Y?," or "% Change"
2. Enter the required values in the input fields
3. Your result appears automatically below the inputs
4. Switch tabs to perform a different type of percentage calculation

What Is a Percentage?

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." The percent symbol (%) is used to denote this ratio.

Percentages are everywhere in daily life — from store discounts and restaurant tips to interest rates on loans and credit cards, exam scores, and statistical data. Understanding how to calculate and interpret percentages is an essential mathematical skill.

For example, 50% means 50 out of 100, or one-half. 25% means one-quarter, and 10% means one-tenth. Any fraction can be converted to a percentage by multiplying by 100.

Percentage Formulas

Here are the three core formulas used in this calculator:

1. Percentage of a Number

Result = (Percentage ÷ 100) × Number

Example: What is 15% of 200?
Result = (15 ÷ 100) × 200 = 0.15 × 200 = 30

2. What Percent is X of Y?

Percentage = (X ÷ Y) × 100

Example: 30 is what percent of 150?
Percentage = (30 ÷ 150) × 100 = 0.2 × 100 = 20%

3. Percentage Change (Increase or Decrease)

Change = ((New Value − Old Value) ÷ |Old Value|) × 100

A positive result means an increase; a negative result means a decrease.
Example: From 80 to 100
Change = ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = +25% (25% increase)

Real-World Applications

Percentages are used across many fields. Here are some common scenarios:

Common Percentage Mistakes

Being aware of these pitfalls will help you avoid errors:

• Confusing percentage increase with percentage of. A 50% increase on $100 gives $150 (not $50). The new value is the original plus the increase.
• Double-counting discounts. Two successive 20% discounts are not 40% off. They equal 36% off (0.8 × 0.8 = 0.64, so you pay 64% of the original price).
• Using the wrong base for percentage change.If a stock drops from $100 to $80, that's a 20% decrease. If it then rises from $80 to $100, that's a 25% increase — not the same percentage, because the base changed.
• Mixing up percentage and percentage points. An interest rate rising from 5% to 7% is a 2 percentage point increase, but a 40% increase in the rate itself ((7−5)÷5 = 0.4).

Percentage vs. Fraction vs. Decimal

These three forms are interchangeable. Knowing how to convert between them is essential:

To convert: Percentage to decimal → divide by 100. Decimal to percentage → multiply by 100. Fraction to percentage → divide numerator by denominator, then multiply by 100.

Frequently Asked Questions

How do I calculate a percentage without a calculator?

For common percentages, use mental math tricks: 10% = move the decimal point one place left. 5% = half of 10%. 20% = double 10%. 25% = divide by 4. 50% = divide by 2. For example, 15% of $80: find 10% ($8) + 5% ($4) = $12.

What is the difference between percentage and percentile?

A percentage expresses a fraction of 100 (e.g., 75% correct answers). A percentileindicates a position in a ranked dataset (e.g., scoring in the 90th percentile means you scored higher than 90% of test-takers). They measure different things.

How do I calculate percentage increase or decrease?

Subtract the old value from the new value, divide by the old value (using the absolute value), and multiply by 100. If the result is positive, it's an increase; if negative, it's a decrease. Formula: ((New − Old) ÷ |Old|) × 100.

Can a percentage be greater than 100%?

Yes. A percentage over 100% means the value exceeds the whole. For example, a 200% increase means the final value is three times the original. Sales can grow by 150%, and you can be 110% sure about something (figuratively).

How do I calculate a percentage of a percentage?

Multiply the two percentages as decimals, then convert back. For example, 50% of 30% = 0.50 × 0.30 = 0.15, which is 15%. This is common when calculating compound interest or stacked discounts.

What is the formula for calculating GPA from percentages?

GPA scales vary by school. A common US scale: A (90–100%) = 4.0, B (80–89%) = 3.0, C (70–79%) = 2.0, D (60–69%) = 1.0, F (below 60%) = 0.0. Weighted GPA adds extra points for honors or AP courses.