Amounts, percentage shares, and percentage change
Percent of, whole, increase and decrease return an amount. Ratio and percentage change return a percentage. The result includes the calculation with your numbers, and change is labelled as an increase, decrease or no change.
For a price reduction, the Discount Calculator also calculates the sale price and tax.
For coursework, the Grade Calculator combines scores using points or category weights.
To calculate with exact fractional parts, use the Fraction Calculator to add, subtract, multiply, or divide fractions.
The formula
A percentage share is Part ÷ Whole × 100. Percentage change is (New − Original) ÷ |Original| × 100. To find the whole, use Part ÷ Percentage × 100. To add or subtract a percentage, multiply the starting value by (1 + Percentage ÷ 100) or (1 − Percentage ÷ 100).
What is 15% of 240?
Divide 15 by 100 to get 0.15, then multiply by 240. The answer is 36. If this is a 15% discount on an item priced at 240, subtract 36 from 240 to get a sale price of 204.
How to use this calculator
- Choose the question you want to answer.
- Enter the two numbers requested by that mode. Use a positive percentage for increase or decrease.
- The answer and working update as you type. Calculate updates immediately; Reset restores the example values.
Choose the percentage question
Finding a percentage of a number gives you a portion of a total: a discount, a tip, or the amount represented by a rate. Finding what percentage one number is of another describes their relative size.
Percentage change compares a new value with an original value. Going from 80 to 100 is a 25% increase, but going from 100 to 80 is a 20% decrease. The original value determines the denominator.
Find the whole reverses the part calculation: if 30 is 20% of a total, that total is 30 ÷ 20 × 100 = 150. For a price change, increase or decrease applies a known rate directly. Increasing 50 by 12.5% gives 56.25; decreasing 50 by 12.5% gives 43.75.
Percentages and percentage points
A rate moving from 10% to 15% rises by 5 percentage points. Its relative increase is 50%, because the difference of 5 is half of the original 10. Specify which measure you mean when comparing rates.
Successive percentage changes multiply rather than add. A 20% increase followed by a 20% decrease leaves 96% of the starting amount.
Assumptions & limitations
What this calculation assumes
- Numbers use a period as the decimal separator.
- For negative starting values, percentage change uses the absolute value of the original as the denominator.
What to keep in mind
- A ratio with a zero whole, a change from zero, and finding a whole from zero percent are undefined.
- Negative starting values can make percentage comparisons misleading; consider the absolute difference as well.
- Results are rounded for display. Very small and very large results use scientific notation.
Common questions
How do I calculate a discount?
Choose Decrease by %, enter the original price as the starting value and the discount rate as the percentage. The result is the discounted price. For example, 20% off 100 gives 80.
Can a percentage be greater than 100?
Yes. A percentage over 100 means the part is larger than the reference whole. For example, 150 is 150% of 100.
Why can’t I calculate a percentage change from zero?
Percentage change divides by the original value. Division by zero is undefined, so use the absolute increase instead.
How do I find the whole from a known part?
Choose Find the whole, enter the known part and the percentage it represents. If 30 is 20% of a number, enter 30 and 20 to get 150.
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