The Percentage Calculator helps you perform various percentage calculations quickly and accurately.
Supports four calculation modes: X% of Y, X is what percent of Y, percentage change between two values, and add/subtract a percent from a value. Includes formulas and step-by-step explanations.
Calculator information
📋 How to use this calculator
- Pick the calculation mode: X% of Y, X is what percent of Y, percentage change, or add/subtract a percent.
- For 'X% of Y': enter the percentage and the base value (e.g., 20% of $500).
- For 'X is what percent of Y': enter two values to find their ratio.
- For percentage change: enter the starting and ending values (positive = increase, negative = decrease).
- For add/subtract percent: enter the base value and the percentage, then choose the operation.
- View the result with the formula and steps so you can verify or learn the calculation.
🧮 Four Basic Percentage Modes
Mode 1: X% x Y; Mode 2: (X/Y) x 100%; Mode 3: ((Final-Initial)/Initial) x 100%; Mode 4: Y x (1 +/- X%)
- X = the percentage or comparison value
- Y = the base value or denominator
- Percent (%) = per hundred = value / 100
- Mode 3 (change): positive result = increase, negative = decrease
- Mode 4 (add): e.g., price increase; Mode 4 (subtract): e.g., discount
Percent vs. percentage points: going from 5% to 7% is a 2 percentage point increase, or a 40% relative increase.
💡 Worked example: 25% discount on a $200 shirt
Given:- Initial price = $200
- Discount = 25%
- Mode = Subtract percent
Steps:- Discount amount = 25% x $200 = 0.25 x $200 = $50
- Price after discount = $200 - $50 = $150
- Verify with add/subtract mode: $200 x (1 - 0.25) = $200 x 0.75 = $150
- Cross-check with 'X is what percent of Y' mode: $50 / $200 x 100% = 25%
- Percentage change mode: (($150 - $200) / $200) x 100% = -25%
Result: The price after a 25% discount is $150, a savings of $50 from the original price.
❓ Frequently asked questions
What is the difference between percent (%) and percentage points (pp)?
Percent (%) is a relative ratio, while a percentage point (pp) is the absolute difference between two percentages. Example: a federal funds rate moving from 5% to 6% is a 1 percentage point increase, or 20% relatively (relative to 5%). Media often conflate the two. For comparing tax rates, inflation, or unemployment, percentage points are clearer and less misleading.
How do you compound percentage increases?
Successive percentage increases cannot simply be added. For example, +10% followed by another +10% is not +20% but +21%. Formula: Final = Initial x (1 + r1) x (1 + r2) x ... x (1 + rn). Example: 100 x 1.1 x 1.1 = 121, a total increase of 21%. This concept is fundamental for compound interest, annual inflation, and GDP growth.
Why is a 50% discount stacked with a 20% discount not a 70% discount?
Stacked discounts are applied sequentially, not added together. A '50% + 20%' discount actually leaves the customer paying 0.5 x 0.8 = 0.4 of the original price, a total discount of 60%. Retailers often advertise '50% + 20% off' to make it feel like 70%. Always compute the final price to compare promotions and avoid being misled by labels.
How do you back out sales tax from a total?
If a total already includes a sales tax of, say, 8%, the pre-tax amount = Total / 1.08. Example: a total of $108 -> pre-tax = $108 / 1.08 = $100, sales tax = $8. General formula: Pre-tax = Total / (1 + rate). To add sales tax: Total = Pre-tax x (1 + rate). The same logic applies to marketplace fees, processing fees, or commissions deducted from a gross amount.
How do you check the annual inflation rate?
Annual inflation is calculated as a percentage change in the Consumer Price Index (CPI). Formula: Inflation = ((Current CPI - CPI 12 months ago) / CPI 12 months ago) x 100%. The U.S. Bureau of Labor Statistics (BLS) publishes monthly CPI data. The Federal Reserve's longer-run inflation target is 2% based on the PCE price index, which it considers more representative than CPI.
📚 Sources & references
Last updated: May 11, 2026