About Percentage Calculator
This percentage calculator with steps answers five questions: what is X% of Y, X is what percent of Y, the percentage change from X to Y, X increased by Y%, and X decreased by Y%. Under each answer it writes a sentence in plain words and the working, such as (25 ÷ 100) × 200 = 50. For example, 5% of 200 is 10, 47 is 69.12% of 68, and going from 120 to 96 is a decrease of 20%. Results are rounded to two decimal places and large numbers get thousands separators. Negative numbers and decimals are accepted. The only inputs it refuses are a Value Y of zero when asking what percent X is of Y, and a starting value of zero for percentage change.
Percentage formulas for each of the five modes
The formula the tool uses for each option in What do you want to work out?, with a real result.
| Mode | Formula | Example | Answer |
|---|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | X = 25, Y = 200 | 50 |
| X is what percent of Y? | (X ÷ Y) × 100 | X = 18, Y = 24 | 75% |
| Percentage change from X to Y | ((Y − X) ÷ |X|) × 100 | X = 1,200, Y = 1,350 | Increase of 12.5% |
| Increase X by Y% | X + (X × Y ÷ 100) | X = 80, Y = 15 | 92 |
| Decrease X by Y% | X − (X × Y ÷ 100) | X = 1,200, Y = 12.5 | 1,050 |
|X| means the size of X without its sign, which keeps the direction of the change correct when the starting value is negative.
What is 5 percent of common numbers
Results from What is X% of Y? with Value X set to 5. For 10%, double each answer; for 2.5%, halve it.
| Number | 5% of it | Number | 5% of it |
|---|---|---|---|
| 10 | 0.5 | 200 | 10 |
| 20 | 1 | 250 | 12.5 |
| 25 | 1.25 | 300 | 15 |
| 30 | 1.5 | 400 | 20 |
| 40 | 2 | 500 | 25 |
| 50 | 2.5 | 1,000 | 50 |
| 60 | 3 | 1,500 | 75 |
| 75 | 3.75 | 2,000 | 100 |
| 80 | 4 | 5,000 | 250 |
| 100 | 5 | 10,000 | 500 |
| 120 | 6 | 20,000 | 1,000 |
| 150 | 7.5 | 50,000 | 2,500 |
5% is the same as one twentieth, so dividing any number by 20 gives the same answers.
Common percentages of 200, from 1% to 150%
| Percent | Of 200 | Percent | Of 200 |
|---|---|---|---|
| 1% | 2 | 25% | 50 |
| 2% | 4 | 30% | 60 |
| 3% | 6 | 33% | 66 |
| 5% | 10 | 40% | 80 |
| 7.5% | 15 | 50% | 100 |
| 10% | 20 | 60% | 120 |
| 12.5% | 25 | 75% | 150 |
| 15% | 30 | 90% | 180 |
| 20% | 40 | 150% | 300 |
A percent above 100 gives a result larger than the number you started with: 150% of 200 is 300.
Worked examples with the working line
Test score as a percent
Mode: X is what percent of Y? Value X 47, Value Y 68
Answer 69.12. In words: 47 is 69.12% of 68. Working: (47 ÷ 68) × 100 = 69.12%
Pay rise
Mode: Percentage change from X to Y. Value X 42000, Value Y 45500
Answer 8.33. In words: Increase of 8.33%. Working: ((45,500 − 42,000) ÷ 42,000) × 100 = 8.33%
Sales tax on a purchase
Mode: What is X% of Y? Value X 8.25, Value Y 64
Answer 5.28. In words: 8.25% of 64 is 5.28. Working: (8.25 ÷ 100) × 64 = 5.28
Switch to Increase X by Y% with Value X 64 and Value Y 8.25 to get the total including tax, 69.28.
Price after a reduction
Mode: Decrease X by Y%. Value X 49.99, Value Y 20
Answer 39.99. In words: 49.99 decreased by 20% is 39.99. Working: 49.99 − (49.99 × 20%) = 39.99
A fall in monthly sales
Mode: Percentage change from X to Y. Value X 120, Value Y 96
Answer -20. In words: Decrease of 20%. Working: ((96 − 120) ÷ 120) × 100 = -20%
The 24 unit drop is divided by the starting value of 120, not by 100, which is why it is 20% and not 24%.
Finding the whole when you know the part and the percent
Mode: X is what percent of Y? Value X 10 (the part), Value Y 5 (the percent)
Answer 200. Working: (10 ÷ 5) × 100 = 200%
There is no separate mode for 10 is 5% of what, but this one does the same arithmetic: part ÷ percent × 100. Read the Answer as the whole and ignore the percent sign and the In words sentence.
Percent increase vs percent decrease between the same two numbers
Going up and coming back down are different percentages, because the starting value changes. All figures are from Percentage change from X to Y.
| Two numbers | Change going up | Change coming back down |
|---|---|---|
| 80 and 100 | Increase of 25% | Decrease of 20% |
| 50 and 75 | Increase of 50% | Decrease of 33.33% |
| 100 and 150 | Increase of 50% | Decrease of 33.33% |
| 1 and 2 | Increase of 100% | Decrease of 50% |
| 50 and 200 | Increase of 300% | Decrease of 75% |
A value can rise by more than 100%, but a positive value cannot fall by more than 100% without going below zero.
Percent vs percentage points, and other common mix-ups
Percentage points measure the gap between two percentages; percent change measures it relative to where you started. An interest rate moving from 10% to 12% has gone up by 2 percentage points, and by 20 percent, since ((12 − 10) ÷ 10) × 100 = 20%. News reports and loan documents use both, so check which one is meant.
Percentage change is not percentage difference. Change has a direction and a starting value. Percentage difference compares two numbers with no before and after by dividing their gap by their average. This tool calculates change only.
A percent off is not reversed by the same percent on. 120 decreased by 20% is 96, but getting from 96 back to 120 takes an increase of 25%. In general, to undo an increase of p%, divide by 1 + p ÷ 100 instead of subtracting p%.
X% of Y always equals Y% of X. 8% of 50 is awkward in your head, but 50% of 8 is plainly 4. It is a handy check on any answer from the first mode.
How to get your result
- 1
Open What do you want to work out? and choose one of the five modes.
- 2
Enter Value X. In What is X% of Y? it is the percent; in the other four modes it is the part or the starting number.
- 3
Enter Value Y. It is the whole or the new number in the first three modes, and the percent to apply in Increase X by Y% and Decrease X by Y%.
- 4
Read Answer, which has a copy button, and check In words to confirm the numbers went in the right way round.
- 5
Copy the Working line if you need to show how the answer was reached.