Percentage Calculator
Every common percentage question in one place — of, change, and reverse.
Last updated
Your details
Result
- 25.00% of 200.00
- 50.00
- 200.00% of 25.00
- 50.00
Percentages are commutative — these are always equal
Let's work it out…
Result = (X ÷ 100) × Y
Result = (25 ÷ 100) × 200
Result = 0.25 × 200
Result = 50.00
Formula — written step by step
What is 25% of 200?
Result = (X ÷ 100) × Y
Result = (25 ÷ 100) × 200
Result = 0.25 × 200
Result = 50
X is the percentage and Y the whole. A percentage is a fraction with 100 underneath, which is why dividing by 100 is always the first move.
25 is what percent of 200?
Result = (X ÷ Y) × 100
Result = (25 ÷ 200) × 100
Result = 0.125 × 100
Result = 12.5%
X is the part and Y the whole. Divide first to get a fraction, then multiply by 100 to read it as a percentage.
From 25 up to 200 — by what percent?
Change = ((Y − X) ÷ X) × 100
Change = ((200 − 25) ÷ 25) × 100
Change = (175 ÷ 25) × 100
Change = 7 × 100
Change = 700%
X is where you started and Y where you ended. The division is by the starting value, which is why a rise and the fall that undoes it are never the same percentage.
Increase 25 by 200%…
New = X × (1 + Y ÷ 100)
New = 25 × (1 + 200 ÷ 100)
New = 25 × 3
New = 75
X is the value and Y the percentage to add or remove. Adding 100% doubles a number; the decrease line uses the same formula with a minus.
25 is 200% of what number?
Whole = (X × 100) ÷ Y
Whole = (25 × 100) ÷ 200
Whole = 2500 ÷ 200
Whole = 12.5
X is the part you know and Y the percentage it represents. This is the "of" calculation rearranged to solve for the whole instead of the part.
The formula for each shape
-
What is X% of Y?
Result = (X ÷ 100) × Y
Needs the percentage and the whole
-
X is what percent of Y?
Result = (X ÷ Y) × 100
Needs the part and the whole
-
Change from X to Y
Change = ((Y − X) ÷ X) × 100
Needs the starting and ending values
-
Increase or decrease X by Y%
New = X × (1 ± Y ÷ 100)
Needs the value and the percentage
-
X is Y% of what number?
Whole = (X × 100) ÷ Y
Needs the part and the percentage
A worked example
What is 15% of 80?
- Percentage
- 15%
- Whole
- 80
- Result = (X ÷ 100) × Y
- Result = (15 ÷ 100) × 80
- Result = 0.15 × 80
Result = 12
This is the same as 80% of 15, which is easier to do in your head. Multiplication is commutative, so you can always flip the awkward one.
A price rises from 40 to 50 — by what percent?
- Started at
- 40
- Ended at
- 50
- Change = ((Y − X) ÷ X) × 100
- Change = ((50 − 40) ÷ 40) × 100
- Change = (10 ÷ 40) × 100
- Change = 0.25 × 100
Change = 25% increase
The division is by the starting value, not the ending one. Falling back from 50 to 40 is a 20% decrease, not 25% — which is why a 25% rise never cancels a 25% fall.
How to use this calculator
- Pick which of the five questions you are asking from the top menu.
- Enter your two numbers as X and Y. The menu wording tells you which is which for the mode you chose.
- The answer updates as you type.
- For "increase or decrease", both the increased and the decreased figure are shown at once, along with the amount added or removed.
The three questions people actually ask
Almost every percentage problem is one of three shapes: finding a part from a percentage ("what is 15% of 80"), finding a percentage from two numbers ("12 is what percent of 80"), or finding the whole from a part and a percentage ("12 is 15% of what").
They are the same equation rearranged: part = percent ÷ 100 × whole. Identify which term is missing and the arithmetic follows.
Percentage points are not percentages
If an interest rate rises from 4% to 5%, that is a one percentage point increase but a 25% increase in the rate itself. News reports blur these constantly, and the difference is enormous when the base is small.
Similarly, a 50% fall followed by a 50% rise does not return you to the start — it leaves you 25% down, because the rise is calculated on the smaller number.
Percentages worth knowing by heart
| Percentage | Decimal | Fraction |
|---|---|---|
| 5% | 0.05 | 1/20 |
| 10% | 0.1 | 1/10 |
| 12.5% | 0.125 | 1/8 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33.3% | 0.333… | 1/3 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
Recognising a percentage as a simple fraction turns most mental arithmetic into a division: 25% off is a quarter off, and 12.5% is an eighth.
Frequently asked questions
Why is 15% of 80 the same as 80% of 15?
Both compute 0.15 × 80 = 12. Multiplication is commutative, which makes some mental arithmetic much easier — 4% of 75 is awkward, but 75% of 4 is obviously 3.
How do I work out a reverse percentage?
Divide rather than multiply. If a price of 120 includes 20% tax, the pre-tax figure is 120 ÷ 1.2 = 100, not 120 minus 20%, which gives 96. Subtracting the percentage from the total is the single most common error in this arithmetic, and it always understates the original.
What is the difference between percentage change and percentage difference?
Percentage change has a direction and uses the original value as its denominator, so going from 40 to 50 is a 25% rise while 50 to 40 is a 20% fall. Percentage difference is symmetric and compares both against their average, giving the same answer either way round.
Why does a 50% loss need a 100% gain to recover?
Because each percentage is taken on a different base. Losing half of 100 leaves 50, and getting back to 100 from 50 means doubling — a 100% gain. This asymmetry is why a sequence of equal percentage rises and falls always ends below where it started.