Case 1
- What you want to work out
- What is X % of Y
- First value
- 25
- Second value
- 200
50.00
Open with these valuesPercentage Calculator
50.00%
Result: 50.00 %A percentage change always refers to the starting value. Going from 200 to 100 is −50 %, but from 100 to 200 is +100 % — the same difference, two different percentages. Pick the question you actually have; the three modes are not variations of one sum.
The numbers at a glance
Held fixed: What you want to work out What is X % of Y, First value 25.0000.
| Second value | Result |
|---|---|
| 0.0000 | 0.00 |
| 50.0000 | 12.50 |
| 100.0000 | 25.00 |
| 150.0000 | 37.50 |
| 200.0000Your value | 50.00 |
| 250.0000 | 62.50 |
| 300.0000 | 75.00 |
| 350.0000 | 87.50 |
| 400.0000 | 100.00 |
Worked examples
Case 2
- What you want to work out
- X is what percent of Y
- First value
- 30
- Second value
- 120
25.00
Open with these valuesCase 3
- What you want to work out
- Change from X to Y
- First value
- 80
- Second value
- 60
-25.00
Open with these valuesHow it's calculated
of: v₁/100 · v₂ · share: v₁/v₂ · change: Δ/v₁
- StepChoose the question: a percentage of a number, a share, or a change.
- StepEnter the two values in the order the labels ask for.
- ResultRead the result.
What this number means
Percent means out of a hundred, and all three questions on this page are that one idea approached from different sides. Which side you are on decides the arithmetic. The first mode asks how much X % of Y comes to: divide the percentage by 100 and multiply, so the default values give 25/100 × 200 = 50. The second asks what share one number is of another: divide the part by the whole and multiply by 100, so 30 out of 120 is 25 %. The third asks how far something moved: take the difference, divide it by the value you started from, multiply by 100 — from 100 to 130 that is 30/100, an increase of 30 %. The order of the two inputs is not decoration. In the first mode you may swap them freely, because 25 % of 200 and 200 % of 25 both come to 50. In the other two you may not: in share mode the second value is the whole, and in change mode the first value is the starting point. Swap them there and the arithmetic still succeeds — it simply answers a question you did not ask. Both fields accept negative values, so a change from −50 to 20 is a fair thing to enter.
A change always refers to the starting value
Going from 200 to 100 is −50 %, but going from 100 to 200 is +100 %. Same difference, two different percentages.
Percent and percentage points are not the same
A percentage is a share of a whole; a percentage point is the gap between two percentages. A rate going from 4 % to 6 % rises by two percentage points, and that same step is an increase of 50 %.
The three modes are three different questions
A percentage of a number, a share, and a change are not variations of one sum. Decide which question you actually have before entering the values.
Zero as the base has no share
If the reference value is zero the calculator returns 0 instead of an error. A share of nothing, and a change starting from nothing, have no percentage.
Commonly misread
A fall of 50 % is undone by a rise of 50 %.
A fall of 50 % from 100 leaves 50, and getting back to 100 from there is a rise of 100 %. The base changes with the first step, so the two are not mirror images.
A rate going from 4 % to 6 % has risen by 2 %.
It has risen by two percentage points. Measured as a percentage, that same step is an increase of 50 %.
25 % of 200 and 200 % of 25 are different sums.
Both come to 50. Swapping the two values leaves the product unchanged.
Any question with a percent sign belongs in the first mode.
The first mode answers only what X % of Y is. A share or a change entered there returns a well-formed wrong number.
Reference table
| Mode | Reads as | Example |
|---|---|---|
| % of | v₁ % of v₂ | 25 % of 200 = 50 |
| What % | v₁ is what % of v₂ | 30 of 120 = 25 % |
| Change | from v₁ to v₂ | 100 → 130 = +30 % |
Questions
How do I work out X % of Y?
Divide the percentage by 100 and multiply by the number: 25 % of 200 is 25/100 × 200 = 50. The first mode of this calculator does exactly that.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100: 30 out of 120 is 30/120 × 100 = 25 %. That is the second mode.
How do I work out a percentage change?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 100 to 130 that is 30/100 × 100 = 30 %. The change always refers to the starting value, which is why 200 to 100 is −50 % but 100 to 200 is +100 %.
What is the difference between percent and percentage points?
A percentage is a share of a whole; a percentage point is the gap between two percentages. A rate going from 4 % to 6 % rises by two percentage points, and that same step is an increase of 50 %.
Is a fall of 50 % the reverse of a rise of 50 %?
No. A fall of 50 % from 100 leaves 50, and getting back to 100 from there is a rise of 100 %. The base changes with the first step, so the two are not mirror images.
Sources and last check
Information, not professional advice.