Calculate X% of a number, what percent one value is of another, and the percentage change between an old and a new value.
Example
A 7.5% fee on 2,400 is 180, and 45 correct answers out of 60 is 75%. A price that falls from 120 to 90 changes by −25%, while returning from 90 to 120 is an increase of about 33.33%.
Calculation method
The three modes use three formulas. “What is X% of Y?” multiplies Y by X and divides by 100. “X is what % of Y?” divides X by Y and multiplies by 100. “Percentage change from X to Y” subtracts the old value X from the new value Y, divides by the absolute value of X and multiplies by 100, so a negative starting value still gives a change in the correct direction.
Important notes
Percentage points and percentages are different: a rate that moves from 4% to 5% rises by one percentage point but changes by 25%. Modes that divide need a base other than 0, so Y cannot be 0 in the second mode and X cannot be 0 in change mode. Results are rounded for display, while the calculation keeps full precision.
Match the mode to the question
The three modes answer different questions, so choose the mode before typing. “What is X% of Y?” finds a part of a whole: a 7.5% fee on a purchase of 2,400 is 180. “X is what % of Y?” compares a part with its whole: 45 correct answers out of 60 questions is 75%. “Percentage change from X to Y” compares a starting value with a later value, so X must be the old figure and Y the new one. Swapping the two fields in change mode produces a different percentage, not simply the opposite sign.
Why a rise and a fall do not cancel out
Each percentage change is measured against its own starting value. A price that falls from 120 to 90 changes by −25%, but returning from 90 to 120 is an increase of about 33.33%, because the second change is measured from the smaller base. For the same reason, a value that grows from 80 to 92 rises by 15%, and a value that grows from 50 to 125 changes by 150%: the new value is 2.5 times the original, not 1.5 times. When you compare several changes, anchor each calculation to the value that was current just before that change.
Percentage points, negatives and zero
When a rate moves from 4% to 5%, it rises by one percentage point, yet the relative change is 25%. Enter 4 and 5 in change mode when you need the relative figure, and describe the simple difference as percentage points. If the starting value is negative, the tool divides by its absolute value, so a change from −40 to −10 is shown as 75%: the value moved up by 30, which is 75% of the size of the original. A starting value of zero has no defined percentage change, so the calculator reports an error instead of an infinite result.
Worked examples| Input | Result |
|---|
7.5% × 2400 | 180 |
45 ÷ 60 × 100 | 75% |
80 → 92 | 15% |
120 → 90 | -25% |
90 → 120 | 33.33% |
4 → 5 | 25% |
Frequently asked questions
Why does a 25% rise not undo a 25% fall?
Each percentage change is measured from the value just before that change. When 120 falls to 90, the drop of 30 is 25% of 120. Going back up from 90 to 120 adds the same 30, but 30 is about 33.33% of the smaller base of 90.
Can a percentage be more than 100% or negative?
Yes. A part can be larger than the reference, so 150 of 100 is 150%, and a change from 50 to 125 is +150%. A decrease is shown as a negative change. If the starting value itself is negative, the tool divides by its size, so −40 to −10 shows 75%.
How do I add or remove a percentage such as tax or a markup?
To add a 7.5% fee to 2,400, find 7.5% of 2,400, which is 180, and add it to the original amount. To take out a percentage that is already included in a price, do not subtract the rate from the total; divide by one plus the rate instead, as the VAT Calculator does.