Percentage Calculator - Change, Points & More
Calculate percentages, find a whole, compare percentage change and difference, measure percentage points, reverse a change, and compound successive rates.
Basic percentage questions
Find a percentage amount, the percentage represented by a part, or the whole behind a known percentage.
Percentage change and comparison
Choose a baseline calculation, a symmetric difference, or a percentage-point comparison between two rates.
Apply or reverse a percentage
Change a starting value by a percentage or recover the original value from a final amount.
Successive percentage changes
Apply up to three signed changes in sequence. Enter a negative rate for a decrease.
Whole and percentage amount
Calculation breakdown
Basic percentage calculation
| Quantity | Value | Meaning |
|---|
Percentage calculator formulas
To find a percentage of a number, multiply the number by the rate divided by 100. To find what percentage one value is of another, divide the part by the whole and multiply by 100. To recover the whole, divide the part by the percentage written as a decimal.
Percentage change vs percentage difference
Percentage change uses the original value as its baseline. Percentage difference treats both values equally and divides their absolute gap by the mean of their absolute magnitudes. Use it when neither value is naturally the starting point.
Percentage points vs percent change
A move from 12% to 15% is an increase of 3 percentage points, but it is a 25% relative increase. The percentage-point mode reports both results so rates are not confused with changes in ordinary values.
Reverse percentage calculations
To recover an original amount, divide the final amount by the change multiplier. After a 15% increase the multiplier is 1.15, while after a 15% decrease it is 0.85.
Successive percentage changes
Sequential percentages compound. Each rate becomes a multiplier and the multipliers are multiplied together. A 10% increase followed by a 10% decrease leaves 99% of the starting value, not 100%.
Negative values and zero baselines
The calculator preserves negative amounts when the formula remains defined. Percentage change requires a nonzero original value; percentage difference requires at least one nonzero comparison value; reverse decreases must stay below 100%.
Percentage formulas at a glance
| Question | Formula |
|---|---|
| What is P% of N? | N x P / 100 |
| X is what percent of Y? | X / Y x 100 |
| X is P% of what? | X / (P / 100) |
| Percentage change | (new - original) / original x 100 |
| Percentage difference | |A - B| / ((|A| + |B|) / 2) x 100 |
| Successive changes | initial x (1 + r1) x (1 + r2) x ... |
Frequently asked questions
Why do equal percentage increases and decreases not cancel?
The decrease is applied to the already changed value. Starting at 100, increasing 10% gives 110, and decreasing that by 10% gives 99.
Can a percentage be over 100%?
Yes. A result can be more than the reference whole, and an increase can exceed 100%. A decrease is capped at 100% because a larger decrease would pass through zero.
When should I use percentage points?
Use percentage points when comparing two values that are already percentages, such as interest rates, conversion rates, or survey shares.
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