Percentage Calculator
Calculate percentages, percentage change, and what percent one number is of another.
Percentages are one of the most fundamental concepts in everyday math, used in finance, shopping, taxes, science, and statistics. This calculator covers the five most common percentage operations: finding X% of a value, determining what percentage one number is of another, calculating percentage change between two values, increasing a value by a percentage, and decreasing a value by a percentage. Each result shows the formula so you understand exactly how the answer was reached.
From calculating VAT and discounts to tracking portfolio growth and exam scores, percentage calculations are unavoidable in daily life. Understanding the difference between percentage points and relative percent change prevents many common misunderstandings in finance and media reporting.
Frequently Asked Questions
How do I calculate X% of Y?
Multiply Y by X/100. For example, 25% of 200 = 200 × 0.25 = 50. Used for tips, taxes, discounts, and commissions.
How do I find what percentage X is of Y?
Divide X by Y and multiply by 100. 50 is what % of 200? → (50 / 200) × 100 = 25%. Useful for test scores, market share, completion rates.
How is percentage change calculated?
% Change = ((New − Old) / Old) × 100. Sales from 100 to 150: ((150 − 100) / 100) × 100 = +50%. A negative result means a decrease.
What is the difference between percentage points and percent?
Percentage points = arithmetic difference between two percentages. Interest from 3% to 5% = 2 percentage points, but a 66.7% increase in relative terms. This distinction matters in finance and statistics.
How do I calculate compound percentage growth?
For compound growth over multiple periods: Final = Initial × (1 + rate)^n. Example: $1,000 growing at 5% per year for 3 years: $1,000 × 1.05³ = $1,157.63. This differs from simple percentage growth (1,000 × 1.15 = $1,150).
What does a 200% increase mean?
A 200% increase means the value tripled (original + 200% of original = 3× original). Example: $100 increases by 200% → $100 + $200 = $300. Note: a 100% increase doubles the value; a 200% increase triples it. "Increased by 200%" ≠ "increased to 200%".
What is a basis point (bp)?
A basis point is 0.01 percentage point, or 1/100th of 1%. Used in finance for interest rates and bond yields: 25 basis points = 0.25%. Example: if the ECB raises rates by 50bp from 3.5%, the new rate is 4.0%. Using basis points avoids ambiguity between "percent" and "percentage points".
What is percentage error?
Percentage error = |Measured − Actual| / Actual × 100. It measures how far a measured value is from the true value. Example: estimated 95 km, actual 100 km → error = |95 − 100| / 100 × 100 = 5%. Used in science, engineering, and forecasting accuracy.
How do I convert a percentage to a decimal and fraction?
Decimal: divide by 100. 75% → 0.75. Fraction: write as X/100 and simplify. 75% → 75/100 = 3/4. To go back: decimal × 100 = %. Common: 25% = 1/4, 50% = 1/2, 33.3% ≈ 1/3, 20% = 1/5, 10% = 1/10.
What is relative vs absolute change?
Absolute change = New − Old (in original units). Relative change = (New − Old) / Old × 100 (in percent). Example: salary from €2,000 to €2,200. Absolute change: +€200. Relative change: +10%. Both are useful — absolute shows impact in real terms; relative allows fair comparison between different-sized values.