Percentage Calculator
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Calculate a percentage of a number, percentage change, and percentage increase or decrease instantly in one tool.
What is X% of Y?
X is what percent of Y?
Percentage change from X to Y
The four questions this page answers
Most percentage problems people actually have are one of these, and each has its own box above:
| Question | Example | Answer | Method |
|---|---|---|---|
| What is P% of X? | 20% of 250 | 50 | X × P ÷ 100 |
| X is what percent of Y? | 15 of 60 | 25% | X ÷ Y × 100 |
| Percentage change from A to B | 80 → 100 | +25% | (B − A) ÷ A × 100 |
| Value after a change | 250 +20% | 300 | X × (1 + P ÷ 100) |
The third and fourth rows are where most mistakes happen, because the direction and the base matter: a change from 80 to 100 is an increase of 25%, but a change from 100 to 80 is a decrease of 20%. Same gap of 20, different percentages, because the base is not the same.
How to use it
- Decide which of the four questions above you are actually asking - that choice fixes which box to use.
- Type the two numbers and read the result; each box calculates as you type.
- Check the direction: an increase and a decrease between the same two numbers give different percentages.
Percentage points versus percent
A rate moving from 4% to 5% has risen by one percentage point and by 25 percent. Both statements are true, and confusing them is one of the most common ways numbers get misread in news, medicine and finance.
Use percentage points when you are describing the difference between two percentages that are themselves rates: an interest rate, a tax rate, a support share in a poll. Use percent when you are describing the relative size of that change. A headline saying "risk up 25%" and a paper saying "risk up 1 percentage point" can describe the same finding.
The traps worth knowing
- Percentages do not add. A price cut of 20% followed by another cut of 20% is not a 40% cut: 0.8 × 0.8 = 0.64, so the final price is 36% below the original.
- Losses need bigger gains to recover. A 50% loss needs a 100% gain to get back to even, and an 80% loss needs 400%. This is why drawdowns matter so much in investing.
- Compound growth is not linear. 10% a year for three years is 1.331 times the starting value, not 1.3 - small differences that matter over decades.
- Watch the base. "Up 50%" on what? Of the original, of last year, of the competitor? A percentage without a stated base is not a fact yet.
- Rounding compounds. Rounding each step and then multiplying gives a different answer from multiplying first and rounding once.
Mental shortcuts that are accurate enough
You rarely need a calculator for a rough figure if you break the percentage into pieces you can do in your head:
- 10% is a decimal shift. 10% of 84 is 8.4 - move the point one place left.
- Build from 10%. 15% = 10% + half of 10%; 30% = 3 × 10%; 5% is half of 10%.
- Flip the question. 8% of 50 equals 50% of 8, which is 4. Multiplication is commutative, and one direction is often far easier.
- 1% is two shifts. Useful for tips and quick estimates: 1% of 240 is 2.4, so 18% is 18 × 2.4 = 43.2.
Where percentages mislead
Three patterns are worth recognising on sight. Small bases inflate percentages: going from 2 to 3 is a 50% increase that means almost nothing. Survivorship hides the denominator: "90% of our users report..." says nothing without knowing who was asked and who dropped out. And averaging percentages is usually wrong: the average of 10% and 20% is not 15% unless the two groups are the same size, which is why weighted averages exist.
Related tools: the compound interest calculator applies percentages repeatedly over time, the GPA calculator is the weighted-average case where the weights are credit hours, and the final grade calculator answers the reverse question - what score you still need.
FAQ
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 20% of 250 is 250 times 20 divided by 100, which is 50.
How do I calculate percentage change?
Subtract the original from the new value, divide by the original, and multiply by 100. Going from 80 to 100 is plus 25%; going from 100 to 80 is minus 20%, because the base is different in each direction.
What is the difference between percentage points and percent?
Percentage points measure the gap between two rates that are already percentages: 4% to 5% is one percentage point. Percent measures the relative change: the same move is a 25% increase. Both are correct; they answer different questions.
Why is a 20% discount twice not a 40% discount?
Because the second discount applies to the already-reduced price. Two 20% cuts multiply out to 0.8 times 0.8, which is 0.64, so the final price is 36% below the original.
How much gain do I need to recover a loss?
A 50% loss needs a 100% gain, a 75% loss needs a 300% gain, and an 80% loss needs a 400% gain. Percentage losses and percentage gains are not symmetric.