About the Percentage Calculator
A percentage is just a fraction with 100 on the bottom. The word comes from the Latin per centum, meaning "by the hundred", and that is the whole idea: rather than comparing 37 out of New York's 8.5 million residents to 12 out of a village of 400, we rescale both to the same denominator and compare them fairly.
That rescaling is why percentages turn up everywhere — interest rates, exam marks, sales tax, battery levels, opinion polls. It is also why they cause so much confusion. Three genuinely different questions all get called "working out a percentage", and mixing them up produces answers that are not slightly wrong but completely wrong.
This calculator keeps the three separate:
- What is X% of Y? You know the rate and the total, and you want the amount.
A 15% tip on a $200 bill.
- X is what percent of Y? You know two amounts and want the rate between
them. You scored 30 out of 150.
- What is the percentage change from X to Y? Something moved, and you want
the size of the move relative to where it started. Traffic went from 80 to 100 visits.
Pick the question you are actually asking, and the arithmetic takes care of itself.
How to Use the Percentage Calculator
Start by choosing one of the three modes at the top. The fields change to match, so you only ever see the two numbers that question needs.
For What is X% of Y?, put the rate in the first box and the total in the second. For 15% of 200, that is 15 and 200.
For X is what percent of Y?, the first box is the part you have and the second is the total it came out of. For a score of 30 out of 150, that is 30 and 150. The order matters here — swapping the boxes answers a different question and gives 500% instead of 20%.
For percentage change, the first box is where you started and the second is where you ended. The calculator works out the direction for you, so a fall comes back as a negative percentage rather than something you have to interpret.
Press Calculate. Along with the answer you get the working, line by line, so you can check the method rather than just trusting the number. Reset clears everything, and Copy result puts the answer on your clipboard.
Decimals are fine in every field. Negative numbers are accepted too, which matters for things like temperature changes and accounts that move between profit and loss.
How Percentages Are Calculated
Every percentage question is the same single relationship, rearranged:
part = rate x whole
Three quantities, and knowing any two gives you the third. The reason it feels like three different calculations is that in each case a different one is missing.
When you want a percentage of a number, the rate and the whole are known. Convert the rate from a percentage into a decimal by dividing by 100 — 15% becomes 0.15 — then multiply. The division by 100 is the only step people skip, and skipping it makes the answer a hundred times too big.
When you want to know what percentage one number is of another, the part and the whole are known and the rate is missing. Divide the part by the whole to get a decimal, then multiply by 100 to express that decimal as a percentage.
Percentage change is the second case with an extra step in front. First work out how much the value actually moved by subtracting the start from the end. That difference becomes the part, and the starting value becomes the whole. The starting value is the baseline, which is the detail that makes percentage change behave in ways people find surprising.
Percentage Formula
The three forms, written out:
Percentage of a number: result = (rate / 100) x whole
Part as a percentage: rate = (part / whole) x 100
Percentage change: change = ((end - start) / |start|) x 100The vertical bars around start mean absolute value — the size of the number with its sign removed. This matters when the baseline is negative. If a business moves from a loss of 50 to a loss of 25, dividing by −50 would report a 50% decrease, when the situation has plainly improved. Dividing by the absolute value reports a 50% increase, which matches the direction of travel.
Step-by-Step Example
A jacket is listed at 80. Next week it is 100. What happened, in percentage terms?
Step 1 — find the absolute change. Subtract the starting value from the ending value: 100 − 80 = 20. The price rose by 20.
Step 2 — divide by the starting value. 20 / 80 = 0.25. The rise is a quarter of what you started with.
Step 3 — convert to a percentage. 0.25 x 100 = 25. The price rose 25%.
Now run it backwards. The jacket goes from 100 back down to 80. The absolute change is −20, but this time you divide by 100 rather than 80: −20 / 100 = −0.2, which is −20%.
The same 20 units of movement is a 25% rise in one direction and a 20% fall in the other. Nothing has gone wrong — the two percentages are measured against different baselines, and that is exactly what percentage change means.
Understanding Your Result
The large figure is your answer. Below it, the working shows each step so you can see where the number came from.
In the first two modes the result is a plain amount or a plain rate, and there is not much to interpret. Percentage change needs slightly more care.
A positive result is growth; a negative result is a fall. The size is relative to the starting value, not to any absolute scale, so a 300% increase on a base of 2 is a move to 8 — dramatic as a percentage, small in absolute terms. Whenever the baseline is small, quote the absolute numbers alongside the percentage or you will mislead your reader, usually without meaning to.
Watch out for percentage points. If an interest rate moves from 4% to 6%, it has risen by 2 percentage points, but that is a 50% increase in the rate itself. Both statements are true and they describe the same event. Newspapers mix them up constantly.
When Should You Use This Calculator?
Reach for it when the numbers are awkward enough that mental arithmetic is a risk, or when you want the working recorded.
In shopping, to check a discount, split a bill, or work out a tip. In school and university, to convert a raw mark into a percentage or to see how far a grade has moved. In work, for margins, commission, target attainment and month-on-month movement. In personal finance, for savings rates, budget shares, and whether a price rise outpaced your income.
It is equally useful in reverse — as a check on someone else's number. If a report claims a 40% improvement, the change mode will tell you in seconds whether the underlying figures support it.
Common Mistakes
Forgetting to divide by 100. Treating 15% as 15 rather than 0.15 makes every answer a hundred times too large. It is the single most common slip.
Swapping the part and the whole. 30 out of 150 is 20%; 150 out of 30 is 500%. The calculator cannot tell which you meant, so read the field labels.
Using the wrong baseline for change. Percentage change is always measured against where you started, never against where you ended and never against the average of the two. Dividing by the end value is a genuinely different calculation and gives a genuinely different answer.
Assuming percentages reverse. A 50% fall needs a 100% rise to get back to where you were. This trips up investors, dieters and anyone tracking a recovery.
Adding percentages of different totals. A 10% rise followed by a 10% fall does not return you to the start — it leaves you 1% down, because the fall is taken from the larger, post-rise figure. Percentages only add up when they are percentages of the same whole.
Confusing percentage change with percentage difference. Change has a clear before and after. Difference compares two values neither of which is the baseline, and divides by their average instead. If the two numbers have no natural order, change is the wrong tool.