Percentage Calculator — Of, Change, and Reverse
Free percentage calculator online — find what X% of Y is, percentage increase or decrease, and reverse percentages instantly. No signup, works on any device.
Four Questions, Four Different Formulas
Nearly every percentage problem is one of four, and picking the wrong one is far more common than getting the arithmetic wrong. Identify the question first and the calculation is trivial.
| The question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 15% of 240 = 36 |
| X is what percent of Y? | X ÷ Y × 100 | 36 out of 240 = 15% |
| What is the change from X to Y? | (Y − X) ÷ X × 100 | 240 to 300 = 25% increase |
| Y is X% of what number? | Y ÷ (X ÷ 100) | 36 is 15% of 240 |
The third row hides the detail that causes most errors: the divisor is always the original value, not the new one and not the average of the two. Change is always measured relative to where you started.
Percent and Percentage Points Are Different Units
This is the distinction that turns correct numbers into wrong statements, and it appears constantly in news reports, interest rates and survey results.
Suppose an interest rate moves from 4% to 6%. Two true statements:
The rise is 2 percentage points (6 − 4) The rise is 50 percent ((6 − 4) ÷ 4 × 100)
Both describe the same event and they are wildly different numbers. Saying "rates rose 2%" when they moved from 4% to 6% is simply wrong — that would mean a rise to 4.08%.
The rule is straightforward once stated. When the underlying quantity is itself a percentage, the difference between two values is measured in percentage points. The relative change between them is measured in percent. Any time you see a percentage change applied to a percentage, check which one is meant, because the difference is often a factor of ten or more.
| From | To | Percentage points | Percent change |
|---|---|---|---|
| 2% | 3% | 1 point | 50% |
| 4% | 6% | 2 points | 50% |
| 40% | 42% | 2 points | 5% |
| 50% | 25% | −25 points | −50% |
Rows two and three make the point sharply. The same two-point movement is a 50% change at the bottom of the scale and a 5% change nearer the middle, because percent change depends entirely on the starting value.
Working Backwards to the Original Number
Reverse percentage problems come up whenever you know a figure that already includes something and need the amount before it.
Original = Final ÷ (1 + increase ÷ 100) Original = Final ÷ (1 − decrease ÷ 100)
A price of 90 after a 25% reduction was 90 ÷ 0.75 = 120. A total of 480 after a 20% increase started at 480 ÷ 1.2 = 400.
The error to avoid is applying the percentage to the final figure instead of dividing. Adding 25% back to 90 gives 112.50, not 120, because the 25% was calculated on the larger original number rather than on the reduced one. Reversing a percentage is always a division, never the opposite operation applied to the result.
Percentage of Marks, and Weighted Scores
Converting marks to a percentage is the first formula in the table: marks obtained divided by marks available, multiplied by 100. So 68 out of 80 is 85%.
Where it gets misapplied is across several assessments of different sizes. Averaging the percentages only works when every assessment carried the same weight. A student scoring 90% on a paper worth 20 marks and 60% on one worth 80 marks has not averaged 75%.
Total obtained = 18 + 48 = 66 Total available = 20 + 80 = 100 Overall = 66%
Add the raw marks and divide once at the end. Averaging the two percentages gives 75%, which is nine points too generous and would change a grade.
Where Percentages Mislead
- A percentage with no base is meaningless. "Up 300%" from two incidents to eight is true and unremarkable. Always ask what the starting number was.
- Percentages of small samples are unstable. One person changing their mind in a group of eight moves the result by 12.5 points. Report the count alongside the percentage.
- Averaging percentages hides the weights. This is the same trap as the marks example, and it appears in survey results, regional figures and departmental performance.
- Percentages above 100 are legitimate for growth — tripling something is a 200% increase — but impossible for a share of a whole. A figure above 100% in a proportion is a signal that the denominator is wrong.
For percentage-off shopping calculations including stacked offers, the discount calculator covers those specifically. For converting a grade point average into a percentage, use the GPA to percentage converter, which depends on the scale rather than on plain percentage arithmetic.