What are percentages?
A percentage is one hundredth of a number, denoted by the symbol %. For example, 25% means 25 hundredths, or 0.25. Percentage calculation is one of the most commonly used mathematical operations in everyday life — from discounts to taxes.
How to calculate percentages?
What is X% of Y: Result = Y × (X / 100). For example, 15% of 200 = 200 × 0.15 = 30.
X is what percent of Y: Percentage = (X / Y) × 100. For example, 30 is 15% of 200.
Percentage change: Change = ((New - Old) / Old) × 100. For example, the change from 200 to 250 is +25%.
What is the percentage formula?
The basic percentage formula is: Percentage = (Part / Whole) × 100. This formula lets you find what fraction one number is of another. The inverse formula: Part = Whole × (Percentage / 100) — lets you find a specific percentage of a number.
What are some percentage calculation examples?
Discount: An item costs $50, discount is 20%. Discount amount = 50 × 0.20 = $10. Final price = $40.
Salary change: Salary increased from $1,500 to $1,800. Change = ((1800 – 1500) / 1500) × 100 = 20%.
Exam result: You answered 42 out of 50 questions correctly. Percentage = (42 / 50) × 100 = 84%.
How do you find the original value from a percentage?
Reverse percentage finds the original amount when you know the final result and the percentage applied. The formula is: Original = Final ÷ (1 ± rate). Example: a product is discounted 20% and now costs $64 — the original price was $64 ÷ 0.80 = $80. If a salary increased 15% to $2,300, the original salary was $2,300 ÷ 1.15 = $2,000. This is the inverse of percentage change and is useful for recovering pre-discount or pre-tax prices.
What is the difference between a percentage point and a percent?
A percentage point (pp) is the arithmetic difference between two percentages. Example: if a loan interest rate rises from 3% to 5%, that is a 2 percentage point increase — but a 66.7% increase in relative terms. Politicians and media often say "rates rose 2%" when they mean "rose by 2 percentage points." Knowing the distinction helps you read financial news and economic reports accurately.
How do you add or subtract a percentage from a number?
To add X% to a number, multiply by (1 + X/100). To subtract X%, multiply by (1 − X/100). Adding 20% VAT to 500 → 500 × 1.20 = 600. Applying a 20% discount to 500 → 500 × 0.80 = 400. Adding a 15% tip to a $40 bill → 40 × 1.15 = $46. The multiplier method is faster than computing the percentage amount separately and then adding — one step instead of two. For quick discount calculations, see our discount calculator.