Percentage Calculator
Solve percentage, ratio, and change calculations with step-by-step math breakdowns and visual aids.
Formula & Steps
Formula: Result = Y × (X / 100)
Steps: 200 × (15 / 100) = 200 × 0.15 = 30
Formula & Steps
Formula: Result = (X / Y) × 100%
Steps: (50 / 200) × 100 = 0.25 × 100 = 25%
Formula & Steps
Formula: Result = ((Y - X) / X) × 100%
Steps: ((150 - 120) / 120) × 100 = (30 / 120) × 100 = 25%
Formula & Steps
Add: Y + (Y × X / 100) = 100 + 10 = 110
Subtract: Y - (Y × X / 100) = 100 - 10 = 90
Everyday Percentage Problems
This calculator covers the four questions people ask most: "What is X% of Y?" (multiply Y by X/100), "X is what percent of Y?" (divide X by Y, times 100), "What is the percentage change from X to Y?" (the difference divided by the original value), and "Add or subtract a percentage from a number" (useful for tip calculations, tax, and discounts). Every result updates instantly and is computed locally.
Built and maintained by Meet Shah · Last updated
What this tool is used for
- Solving the three common percentage questions in one place.
- Working out an increase or a decrease and the resulting value.
- Finding what percentage one number is of another.
- Reverse-solving an original value from a percentage result.
- Checking a percentage figure someone else produced.
How it works in practice
A worked example
A price went up and then came back down by what looks like the same amount, and the number on the invoice does not agree.
15% of 200 50 is what percent of 200 200 → 250 250 → 200
15% of 200 = 30 50 is 25.00% of 200 200 → 250 change = +25.00% 250 → 200 change = −20.00%
Each of the three modes answers a different question and the last two are the pair people conflate. Going from 200 to 250 adds fifty to a base of two hundred, which is a quarter of it. Coming back down subtracts the same fifty from a base of two hundred and fifty, which is only a fifth. The amount is identical both times and the percentage is not, because a percentage is always a ratio to whatever you started from — and the starting point moved.
The edge case that catches people
So a rise and a fall of the same percentage never cancel, and a rise and a fall of different percentages sometimes do. Up twenty-five and down twenty brings you exactly back; up twenty-five and down twenty-five leaves you below where you began, because the second base is larger than the first. This is why a discount stacked on a discount is not their sum, why a stock that halves needs to double to recover, and why anyone quoting a percentage without naming the base has told you almost nothing.
When not to use this tool
Watch for the other ambiguity, which this tool cannot resolve for you: a rate moving from four percent to five percent has risen by one percentage point and by twenty-five percent, and both statements are true of the same change. Reporting the second where the first was meant is one of the easiest ways to mislead without saying anything false. And repeated growth is not additive — three consecutive ten percent rises come to thirty-three percent and not thirty — so anything spanning several periods wants a compound calculation rather than this one.
Frequently Asked Questions
- What are the four calculations?
- X% of Y, X as a percentage of Y, the percentage change from one value to another, and adding or subtracting a percentage from a value. Between them they cover almost every everyday percentage question.
- Why is percentage change asymmetric?
- Because the base is the starting value. Going from 100 to 150 is a 50% rise, but 150 back to 100 is a 33.3% fall — the same absolute move against a bigger base. This is the single most common percentage error.
- Why is change from zero undefined?
- Because the formula divides by the initial value. Any increase from zero is infinite in percentage terms, so the tool reports it as undefined rather than showing a number that would be meaningless.
- Why does adding then removing 10% not return the original?
- Because the second percentage applies to the new, larger value. 100 plus 10% is 110; 110 minus 10% is 99. To reverse an increase you divide by 1.1, which is why a discount and a markup of the same rate never cancel.
- What is the difference between percent and percentage points?
- A rate moving from 5% to 6% is a rise of one percentage point but a 20% increase. Reporting the second as "up 20%" without saying which is meant is a standard way of making a small change sound large.
- How are results rounded?
- To four decimal places, with trailing zeros trimmed. That keeps a recurring result such as one third readable while preserving enough precision that chained calculations do not drift.
Common errors and gotchas
- Confusing percentage and percentage point, which describe different things.
- Reversing an increase by subtracting the same percentage, which under-recovers every time.
- Using the wrong base, which changes both the number and its meaning.
- Chaining percentages additively when they compound.
- Computing a change from zero, which is undefined.