Percentage Calculator

How to Calculate Percentages

Percentages are one of the most commonly used mathematical concepts in everyday life, from calculating discounts and tax to understanding statistics and financial growth. This calculator covers the four most common percentage problems.

The Basic Percentage Formulas

• What is X% of Y? Multiply Y by X/100.
  Result = Y × (X / 100)
• X is what % of Y? Divide X by Y and multiply by 100.
  Percentage = (X / Y) × 100
• X is Y% of what? Divide X by Y/100.
  Base = X / (Y / 100)
• Percentage change: Subtract the old value from the new value, divide by the absolute value of the old value, and multiply by 100.
  % Change = ((New - Old) / |Old|) × 100

Common Percentage Calculations

Some everyday uses of percentages include: calculating sales tax (e.g., 8.25% of $49.99), figuring out discounts (e.g., 30% off $120), determining tips (e.g., 20% of a $75 restaurant bill), computing grade percentages (e.g., 45 out of 50 questions), and understanding investment returns (e.g., a stock rising from $50 to $65).

Percentage Increase vs. Decrease

A percentage increase of 50% means the new value is 150% of the original. A percentage decrease of 50% means the new value is 50% of the original. Note that a 50% increase followed by a 50% decrease does not return you to the original number. For example, $100 increased by 50% becomes $150. That $150 decreased by 50% is only $75, not $100. This asymmetry is important in finance and statistics.

Percentage Points vs. Percentages

A common source of confusion is the difference between "percentage points" and "percentages." If an interest rate increases from 5% to 7%, it has increased by 2 percentage points but by 40% in relative terms (2/5 = 0.40). News reports and financial data often mix these terms, so pay attention to which one is being used.