Percentage Calculator
"Percentage" means four different sums, and picking the wrong one is the usual mistake. Choose the question, and the working is shown underneath the answer.
Runs on your device — nothing is sent anywhereA percentage change from zero has no answer, and nothing is a percentage of zero. The calculator says so rather than showing infinity.
How it works
No account, no sending anything anywhere, and the sum is shown.
Pick the question
Four buttons, because these are four different sums. Most wrong answers come from doing one of them when you meant another.
Type the two numbers
The answer appears as you type. Decimals and negatives are both fine.
Check the working
The arithmetic is written out underneath, so you can see how the answer was reached instead of taking it on trust.
What people work out
A discount, a tip, a tax
"20% of 85" is the first question, and the one people mean most often when they say percentage.
A test score or a survey result
"37 out of 45 is what percent" turns a raw count into something comparable.
A price rise or a drop in numbers
Percentage change is the second question, and the one where dividing by the wrong number is easy and common.
A price with tax added or a raise applied
"350 plus 21%" is a different sum from "21% of 350", and the calculator keeps them apart.
Four questions that all get called "percentage"
Per cent means "per hundred". A percentage is a fraction with 100 on the bottom, so 15% is 15/100, which is 0.15. Everything else follows from that, and every mistake comes from losing track of what the percentage is of.
1. What is A% of B
Turn the percentage into a decimal and multiply. 15% of 200 is 0.15 × 200 = 30.
Worth knowing: this is symmetrical. 15% of 200 and 200% of 15 are both 30, which makes some sums easier in your head — 4% of 75 is awkward, 75% of 4 is obviously 3.
2. A is what percent of B
Divide and multiply by a hundred. 30 out of 200 is 30 ÷ 200 = 0.15, so 15%.
The trap is which way round. "37 out of 45" divides 37 by 45; doing it the other way gives 121%, which is the kind of answer worth noticing.
3. Percentage change from A to B
Subtract, then divide by the old value. From 200 to 250 is 50 ÷ 200 = 25% up. From 250 to 200 is −50 ÷ 250 = 20% down.
Notice those are different numbers for the same pair. That is not an error — a rise of 25% and a fall of 20% take you between the same two places, because the number you are dividing by changed. This is why "prices rose 25% then fell 25%" does not get you back where you started.
4. A plus or minus B%
Work out the percentage, then add or subtract it. 350 plus 21% is 350 + 73.50 = 423.50.
The fast way is a multiplier: adding 21% is × 1.21, taking 20% off is × 0.80. Useful when several apply in a row.
The mistake everybody makes
Percentages are not reversible, and this costs people money.
| Starting from | Do this | You get |
|---|---|---|
| 100 | Add 20% | 120 |
| 120 | Take off 20% | 96, not 100 |
| 100 | Take off 20%, then add 20% | 96 again |
| 100 | Add 10%, then another 10% | 121, not 120 |
The reason is always the same: the second percentage is taken from a different number than the first. To undo "+20%" you divide by 1.2, which is taking off 16.67%.
Percentages and percentage points
If an interest rate goes from 4% to 6%, that is a rise of two percentage points — and a rise of 50 per cent. Both are correct and they describe the same event. News reports mix them up constantly, usually in whichever direction sounds more dramatic.
The rule: percentage points for the difference between two percentages, per cent for the relative change.
Where the arithmetic goes strange
Nothing is a percentage of zero. Asking what percent 5 is of 0 has no answer, because there is no whole to compare against.
A change from zero is not a percentage either. Going from 0 sales to 10 is not a 1000% increase or any other number; every increase from nothing is infinite. The honest phrasing is "up by 10", which is why this calculator says so rather than printing a number.
Percentages can exceed 100. 250 out of 200 is 125%, and there is nothing wrong with that — it only means the part is bigger than the thing it is being compared to.
Common questions
How do I work out a percentage of a number?
Divide the percentage by 100 and multiply. 15% of 200 is 0.15 × 200 = 30. The first button here does exactly that and shows both steps.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 37 out of 45 is 37 ÷ 45 × 100 = 82.2%. Getting the division the wrong way round is the usual slip.
How do I calculate percentage increase or decrease?
Subtract the old value from the new, divide by the old value, and multiply by 100. Dividing by the new value instead is the most common error in this sum.
Why does adding 20% then taking off 20% not return the original?
Because the second percentage is taken from a bigger number. 100 + 20% is 120; 20% of 120 is 24, so you land on 96. To undo a 20% rise you divide by 1.2, which is taking off 16.67%.
What is the difference between per cent and percentage points?
A rate moving from 4% to 6% has risen two percentage points, and also risen 50 per cent. Percentage points describe the gap between two percentages; per cent describes the relative change.
Can a percentage be more than 100?
Yes. 250 out of 200 is 125%. It simply means the part is larger than what it is being compared with — normal for growth figures and for anything measured against a target.
Why does it refuse a change from zero?
Because there is no answer. A percentage change divides by the starting value, and dividing by zero is undefined — every increase from nothing is infinite. "Up by 10" is the honest description.
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