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Summary
A percentage expresses a number as a fraction of 100. The word itself comes from the Latin per centum, meaning “by the hundred.” Percentages appear everywhere in daily life — discounts, tax rates, exam scores, investment returns, and statistical reports all rely on them. This calculator handles the three most common percentage questions: finding X% of a number, determining what percent one number is of another, and computing the percentage change between two values.
How it works
The calculator solves three distinct problems:
- X% of Y — multiply Y by X/100. This is the classic “what is 15% of 240?” question used for tips, discounts, and tax calculations.
- X is what % of Y — divide X by Y and multiply by 100. This answers questions like “36 out of 150 is what percentage?” commonly seen in test scores and statistics.
- Percentage change — find the difference between two values, divide by the absolute value of the original, and multiply by 100. A positive result means an increase; a negative result means a decrease.
The absolute value of the old value in the denominator ensures correct handling when the starting value is negative (e.g., a loss shrinking from -$100 to -$50 is a 50% change, not negative).
The formulas
Where
Where
Where
Worked examples
What is 15% of 240?
Convert percentage to decimal
= 0.15
Multiply by the base number
= 36
Result
15% of 240 = 36
36 is what percent of 150?
Divide the part by the whole
= 0.24
Multiply by 100 to convert to percentage
= 24%
Result
36 is 24% of 150
Percentage change from 80 to 100
Find the difference
= 20
Divide by the absolute value of the original
= 0.25
Multiply by 100
= 25%
Result
The value increased by 25% (from 80 to 100)
Inputs explained
- Mode selector — choose which of the three percentage problems you want to solve: “X% of Y”, “X is what % of Y”, or ”% change from old to new.”
- Percentage (X) — the rate in percent. For the “X% of Y” mode, this is the percentage you want to find. For the “X is what % of Y” mode, this is the part value.
- Base value (Y) — the number being compared against. In “X% of Y” mode, this is the whole amount. In “X is what % of Y” mode, this is the total.
- Old value / New value — used in percentage change mode. The old value is the starting point; the new value is the ending point. The calculator correctly handles cases where the old value is negative.
Outputs explained
- Result — the calculated answer: either the numeric result of X% of Y, the percentage that X is of Y, or the percentage change between two values.
- Direction (for % change) — indicates whether the change is an increase (positive) or decrease (negative).
- Equivalent fraction — for “X is what % of Y” mode, the result is also shown as a simplified fraction (e.g., 24% = 6/25).
Assumptions & limitations
- Division by zero — if the base value Y is zero, the “X is what % of Y” calculation is undefined. Similarly, if the old value is zero, percentage change is undefined (you cannot measure change from nothing).
- Percentage change is asymmetric — a 50% increase followed by a 50% decrease does not return to the original value. Going from 100 to 150 (+50%) and back to 75 (-50%) leaves you 25% lower. This is a mathematical property, not a calculator limitation.
- Large percentages — percentages above 100% are mathematically valid (e.g., 200% of 50 = 100). The calculator handles these correctly but they can be unintuitive in some contexts.
- Precision — results are rounded to a reasonable number of decimal places. For financial calculations requiring exact precision, consider using a dedicated financial calculator.