What this calculator does
Percentage means per hundred, so a percentage is simply a fraction with 100 on the bottom. Every percentage question reduces to one of three forms: finding a part of a whole, expressing one number as a share of another, or adjusting a number up or down by a proportion.
This calculator answers all three from the same pair of numbers, which removes the step most people find awkward: working out which of the three you actually need. Enter X and Y and read the line that matches your question.
The formula
To take a percentage of a number, divide by 100 and multiply. To express one number as a percentage of another, divide and multiply by 100. To increase or decrease, multiply by one plus or minus the rate: a single step rather than calculating the change and adding it separately.
| Term | Meaning |
|---|---|
| X% of Y | A part of a whole: X × Y ÷ 100. |
| X as a % of Y | A share: X ÷ Y × 100. |
| Increase | Y × (1 + X/100). |
| Decrease | Y × (1 − X/100). |
The inputs explained
| Field | What to enter |
|---|---|
| X | The percentage, or the smaller number when you are asking what share it represents. |
| Y | The base number: the whole, or the number being increased or decreased. |
When to use it
Working out a share
If 37 people out of 240 chose an option, the second line gives the percentage directly. This is the form most survey and test-score questions take.
Applying a rise or a cut
A 3.5% pay rise on a salary, or a 15% cut to a budget. The increase and decrease lines handle both in one step.
Checking a bill or a quote
When someone quotes a percentage, run the numbers yourself. Percentage errors in invoices are common and rarely in your favour.
Reversing a percentage
To find the original from a figure after an increase, divide rather than subtracting the same percentage. Subtracting 20% from a price that already had 20% added does not return you to the start.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Percentages of 200
The full set of answers for a base of 200 at different percentages.
| X | X% of Y | Y increased by X% | Y decreased by X% |
|---|---|---|---|
| 5 | 10.000 | 210.000 | 190.000 |
| 10 | 20.000 | 220.000 | 180.000 |
| 15 | 30.000 | 230.000 | 170.000 |
| 25 | 50.000 | 250.000 | 150.000 |
| 50 | 100.000 | 300.000 | 100.000 |
| 75 | 150.000 | 350.000 | 50.000 |
What 15 is as a percentage of different numbers
Holding X at 15 and varying the base shows how the share shrinks as the whole grows.
| Y | X is what percent of Y | X% of Y | Y increased by X% |
|---|---|---|---|
| 20 | 75.0% | 3.000 | 23.000 |
| 30 | 50.0% | 4.500 | 34.500 |
| 50 | 30.0% | 7.500 | 57.500 |
| 75 | 20.0% | 11.250 | 86.250 |
| 150 | 10.0% | 22.500 | 172.500 |
| 300 | 5.00% | 45.000 | 345.000 |
Questions
How do I calculate a percentage in my head?
Find 10% by moving the decimal point one place left, then build from there. 30% is three times that; 5% is half of it; 15% is 10% plus half of 10%. Most everyday percentages can be assembled from these pieces.
What is the difference between percentage and percentage point?
If a rate rises from 4% to 6%, that is a 2 percentage point rise but a 50% increase. Financial and political reporting frequently conflates the two, and the difference is often large.
How do I reverse a percentage increase?
Divide by one plus the rate. A price of $120 after a 20% increase was originally $120 ÷ 1.2, which is $100: not $120 less 20%, which would give $96.
Can a percentage be over 100?
Yes, whenever the part exceeds the whole. A number that triples has grown by 200%, reaching 300% of its original value. The two phrasings differ and are easy to mix up.
Why do successive percentages not add?
Because each applies to the result of the previous one. A 10% rise followed by another 10% rise gives 21% overall, not 20%, since the second acts on the already-increased amount.
For the change between two values, use the percentage change calculator. For sale prices, see the discount calculator.