Percentage Calculator
Six calculators in one: find a percentage of a number, turn two numbers into a percentage, work back to the total, measure the change or the difference between two numbers, or add and subtract a percentage. Each answer comes with the working.
Fill in both fields and the working appears here.
How to use this calculator
- Pick the tab that matches your question. The six modes cover almost every percentage problem people actually meet.
- Type the two numbers. The answer appears immediately — there is nothing to submit.
- Read the steps under the answer if you need to show the working or check that the calculator understood the question the way you meant it.
- Watch for the increase / decrease badge in the change mode. A negative percentage means the value went down.
Which mode do I want?
- X% of Y — "what is 15% of 200?" for tips, commissions and shares of a total.
- X is what % of Y — "30 out of 200 is what percent?" for test scores and progress.
- X is P% of what — "30 is 15% of what?" to find a total from a known share, like a full price from a deposit.
- Change from X to Y — "sales went from 50 to 75, by how much?" for growth and decline.
- Difference — "how far apart are 10 and 20?" when neither number is the starting point, such as two quotes or two measurements.
- Increase / decrease — "add 15% to 200" for price rises, raises and markdowns.
The formulas
X% of Y = (X ÷ 100) × Y
X is what % of Y = (X ÷ Y) × 100
X is P% of what = X ÷ (P ÷ 100)
change from X to Y = (Y − X) ÷ |X| × 100
difference between X and Y = |X − Y| ÷ ((|X| + |Y|) ÷ 2) × 100
increase Y by X% = Y × (1 + X ÷ 100)
decrease Y by X% = Y × (1 − X ÷ 100)
They are all the same idea wearing different hats: a percentage is a fraction with 100 on the bottom, so you either multiply by it or divide by it depending on which part of the relationship you are missing.
The absolute value bars in the change formula matter only for negative starting values. They make a move from −50 to −25 read as a 50% increase, which is what most people expect.
Worked examples
A 15% share of a total
What is 15% of 200?
- Convert the percentage: 15 ÷ 100 = 0.15
- Multiply: 0.15 × 200 = 30
A test score as a percentage
You scored 47 out of 60. What percentage is that?
- Divide: 47 ÷ 60 = 0.783333…
- Multiply by 100: 78.33%
A price rise, and undoing it
A subscription goes from $12 to $15 a month.
- Difference: 15 − 12 = 3
- Change: 3 ÷ 12 × 100 = +25%
- To get back to $12 from $15 you need a 20% cut, not a 25% one: 3 ÷ 15 × 100 = 20%
Frequently asked questions
Percent means per hundred. Writing 15% is another way of writing the fraction 15/100, or the decimal 0.15.
That is why every percentage calculation starts by dividing by 100: it turns the percentage into a plain multiplier you can use in ordinary arithmetic.
Because the two percentages are taken from different starting points. Going from 100 up by 50% gives 150; taking 50% off 150 gives 75, not 100.
To reverse a rise of X%, you need a fall of X ÷ (100 + X) × 100 percent. Undoing a 50% rise takes a 33.3% fall.
If an interest rate moves from 4% to 5%, that is a rise of one percentage point but a 25% increase in the rate itself.
Use percentage points when you are comparing two percentages, and percent when you are describing how much a value has grown or shrunk.
Percentage change measures against the starting value, so direction matters: 10 to 20 is a 100% increase, but 20 to 10 is a 50% decrease.
Percentage difference measures against the average of the two, so the order does not matter: 10 and 20 are 66.67% apart either way. Use it to compare two values when neither one came first.
You cannot. Percentage change divides by the starting value, and dividing by zero is undefined — going from 0 to anything is an infinitely large increase in percentage terms.
In that situation, report the absolute change instead: sales went up by 40 units, rather than by some percentage.
The calculator measures change against the size of the starting value, ignoring its sign. Going from −50 to −25 is reported as a 50% increase, because the value rose by 25 on a base of 50.
This is the usual convention, but it is worth stating explicitly whenever you publish a figure, since some sources handle negatives differently.
Start from 10%, which is the number with the decimal point moved one place left. 5% is half of that, 20% is double, and 15% is 10% plus 5%.
Also useful: X% of Y always equals Y% of X. Working out 4% of 75 is awkward, but 75% of 4 is obviously 3.