Use this percentage calculator to find a percent of a number, what percent one number is of another, the whole from a part, or a change.
How to use our Percentage Calculator
- Choose a mode in What do you want to find? so the calculator knows which value is unknown.
- Enter the needed numbers only for that mode: Percent (%), Part value, Whole value, or New value.
- For Percent of a number, enter Percent (%) and Whole value.
- For What percent one number is of another, enter Part value and Whole value.
- For Whole from part and percent, enter Part value and Percent (%).
- For Percent change or Percentage point change, enter the old amount in Part value and the later amount in New value.
- Pick Decimal places if you want a shorter or more exact answer, then click Calculate.
- Check Formula with your numbers to make sure the calculator used the values you meant, especially if you are deciding between percent change and percentage point change.
Definitions
Percent (%): A number out of 100. For example, 15% means 15 out of 100, or 0.15 as a decimal.
Part value: The smaller amount or known portion. In change modes, it is the starting or old value.
Whole value: The total or reference amount you compare against.
New value: The later or updated amount used in change calculations.
Decimal equivalent: The percent written as a decimal, such as 25% = 0.25.
Fraction equivalent: The percent written as a fraction of 100 and simplified when practical, such as 25% = 25/100 = 1/4.
Percentage point change: The direct difference between two percentages, such as 12% minus 10% = 2 percentage points.
Common mistakes and quick fixes
Mistake: Typing the total into Part value and the smaller amount into Whole value in What percent one number is of another .
Fix: Put the compared amount in Part value and the reference total in Whole value , then recheck Calculated result .
Mistake: Leaving Percent (%) blank in Percent of a number or Whole from part and percent .
Fix: Enter the rate as a number like 15 for 15 in Percent (%) ; do not leave it empty.
Mistake: Using Percent change when the numbers in Part value and New value are already percentages, such as 10 and 12.
Fix: Switch to Percentage point change if you want the direct difference between two percentage rates, then read Change direction .
Mistake: Using Percentage point change when you really want relative growth from an old amount to a new amount.
Fix: Choose Percent change if you want to know how much larger or smaller New value is compared with Part value .
Mistake: Entering 0 for Whole value in What percent one number is of another or 0 for Percent (%) in Whole from part and percent .
Fix: Use a nonzero Whole value and a percent greater than 0 in Percent (%) so the calculator can divide correctly.
Mistake: Thinking rounded display values changed the math.
Fix: Adjust Decimal places for display only, and use Formula with your numbers plus Decimal equivalent to verify the result.
Limitations & Key Assumptions / Boundary Conditions
- What percent one number is of another is undefined when Whole value is 0, so the calculator shows an error instead of dividing by zero.
- Whole from part and percent needs Percent (%) greater than 0. If the percent is 0, there is no valid whole to solve for.
- Percent change is undefined when the starting amount in Part value is 0, because the formula divides by the original value.
- Negative inputs are allowed, but they can change the meaning of increase and decrease. Read Change direction carefully if you use negative values.
- Percentage point change should be used only when both Part value and New value are already percentages, not plain amounts.
- Decimal places changes only how results are shown on screen. Internal math should stay more precise than the displayed rounding.
Methodology
Core idea
Percent means "per hundred." A standard way to think about percent problems is percent, base, and amount [2].
Formulas used
result = (percent / 100) * whole
percent = (part / whole) * 100
whole = part / (percent / 100)
percent_change = ((new_value - part) / part) * 100
pp_change = new_value - part
How each mode is interpreted
Percent of a number: Use Percent (%) and Whole value to find the part. Example: 15% of 200 is 30.
What percent one number is of another: Divide Part value by Whole value, then multiply by 100. Example: 30 is 15% of 200.
Whole from part and percent: Convert the percent to a decimal first, then divide the known part by that decimal. Example: if 30 is 15% of a whole, the whole is 30 / 0.15 = 200.
Percent change: Subtract the old value from the new value, divide by the old value, then multiply by 100. Positive means increase, negative means decrease.
Percentage point change: Subtract one percentage from the other directly. Example: from 10% to 12% is 2 percentage points, not 20 percentage points.
Mini example
Suppose a price goes from 100 to 120.
percent_change = ((120 - 100) / 100) * 100 = 20%
If an interest rate goes from 10% to 12%, the percentage point change is different.
pp_change = 12 - 10 = 2 percentage points
This is why the calculator separates these two modes: they answer different questions.
Display outputs
Decimal equivalent is shown when a percent input or percent result can be written as a decimal, such as 15% = 0.15. Fraction equivalent is shown when the percent can reasonably be written as a fraction of 100 and simplified.
Error handling and assumptions
The calculator strips commas and spaces before reading numbers. It blocks division by zero in modes that need a nonzero Whole value, nonzero Percent (%), or nonzero starting Part value. Hidden inputs are ignored for the selected mode. Rounding affects only display, not the underlying calculation.