Percentage Calculator

Solve every common percentage question in one place — percent of a number, the three phrasing variations, percentage difference between two values, and percentage increase or decrease. Every result includes a step-by-step working so you can see how the answer was reached.

Percentage Calculator

Enter a percentage and a number to get the result.

Percentage in Common Phrases

The three ways percentage questions are usually worded.

What is X% of Y?

X is what % of Y?

X is Y% of what?

Percentage Difference Calculator

Compare two values and get the percentage difference between them.

Percentage Change Calculator

Increase or decrease a base value by a percentage.

What is a percentage?

A percentage is a way of writing a number as a portion of one hundred. The word comes from the Latin per centum, "by the hundred." When you say 25%, you are saying "25 out of every 100." That makes percentages a shared language for comparing things that would otherwise be hard to line up — discounts at different shops, or how full one glass is versus another of a different size. Any time you take a part, divide by the whole, and multiply by 100, you have converted a plain ratio into a percentage.

Every percentage question, walked through

Every question this page can answer is one of six patterns below. Each card shows the formula, a picture and a worked value you can verify with the tools above.

What is X% of Y? — take a slice of a whole

The most common question. Convert the percentage to a decimal by dividing by 100, then multiply by the number. This is what the main tool at the top of the page does.

Result = (X / 100) × Y
Xpercentage (e.g. 15)·Ythe number you're taking a share of
15% of 240
= 0.15 × 240
= 36
Example
Given
X = 15
Y = 240
Substitute
(15 / 100) × 240 = 0.15 × 240
Answer
36

X is what % of Y? — turn a ratio into a percent

When you know a part and a whole and want the share as a percent, divide part by whole and multiply by 100. The result answers questions like "what percent of my score did I get right?"

Percent = (X / Y) × 100
Xthe part·Ythe whole (Y ≠ 0)
15 out of 60
= (15 / 60) × 100
= 25%
Example
Given
X = 15
Y = 60
Substitute
(15 / 60) × 100 = 0.25 × 100
Answer
25%

X is Y% of what? — recover the original whole

The reverse-percentage question. You know a part and the percentage it represents, and want the whole. Divide the part by the percentage as a decimal — or equivalently, multiply by 100 and divide by the percent.

Whole = X ÷ (Y / 100)
= (X / Y) × 100
Xthe known part·Ythe percentage (Y ≠ 0)
30 is 25% of ?
= 30 / 0.25
= 120
Example
Given
X = 30
Y = 25
Substitute
30 / 0.25
Answer
120

Percentage difference — comparing two equal values

Use this when neither value is more of a "reference" than the other — two sensor readings, two survey results. Because they're on equal footing, divide by their average (not by one of them).

% diff = |V₁ − V₂| ÷ ((|V₁| + |V₂|) ÷ 2) × 100
V₁, V₂the two values being compared
40 vs 60
|40−60| / 50 × 100
= 40%
Example
Given
V₁ = 40
V₂ = 60
Substitute
|40 − 60| / ((40 + 60) / 2) × 100 = 20 / 50 × 100
Answer
40%

Percentage change — before and after

Use this when one value clearly came first (a price, a population, a score) and another came after. The original value is the reference, so you divide by it — not by an average. Positive means an increase, negative means a decrease.

% change = (New − Original) ÷ |Original| × 100
Originalstarting value (≠ 0)·Newvalue after the change
200 → 170
(170 − 200) / 200 × 100
= −15%
Example
Given
Original = 200
New = 170
Substitute
(170 − 200) / 200 × 100 = −30 / 200 × 100
Answer
−15% (a 15% decrease)

Compound percentages — why 15% + 15% ≠ 30%

Successive percentage changes multiply, they don't add. Two 15% discounts on $100 give $100 × 0.85 × 0.85 = $72.25 — the second discount is applied to the already-reduced price, so it's worth less in dollar terms than the first.

Final = Base × (1 ± p₁) × (1 ± p₂) × …
pᵢeach rate as a decimal (0.15 for 15%)
$100 − 15% − 15%
100 × 0.85 × 0.85
= $72.25
Example
Given
Base = 100
two 15% discounts
Substitute
100 × 0.85 × 0.85
Answer
$72.25 (not $70)

Features of this calculator

  • Find X% of a number with the main percentage tool
  • Three phrasing variations — "what is X% of Y", "X is what % of Y", and reverse "X is Y% of what?"
  • Percentage difference between two values, using the average as the denominator
  • Percentage change (increase or decrease) — same math used for tips, taxes, discounts, and markups
  • Every result shows collapsible step-by-step working plus copy and download-as-image actions

Frequently asked questions

+How do I calculate a percentage increase?

Subtract the original value from the new value, divide by the original value, then multiply by 100. For example, going from 80 to 100 is (100 − 80) / 80 × 100 = 25% increase. The Percentage Change tool on this page does this automatically.

+What's the difference between percentage change and percentage difference?

Percentage change compares a new value to an original value where one clearly came first (prices, populations over time) and divides by the original. Percentage difference compares two values on equal footing (two survey results, two sensor readings) and divides by their average. They give different numbers for the same pair of values.

+How do I work backwards from a percentage to the original value?

Use the "X is Y% of what?" tool. Divide the known part by the percentage (as a decimal) — for example, if 30 is 25% of the whole, the whole is 30 ÷ 0.25 = 120. This is the reverse-percentage calculation.

+How do I calculate a discount, tip, tax, or markup?

All four are the same math. Multiply the base price by the rate as a decimal to get the amount, then add it (tax, tip, markup) or subtract it (discount) from the base. Example: a 15% tip on a $40 bill is 0.15 × 40 = $6, so the total is $46. Use the "What is X% of Y?" or Percentage Change tool.

+Why do 15% off followed by 15% off not equal 30% off?

Percentages compound multiplicatively, not additively. Two successive 15% discounts on $100 give $100 × 0.85 × 0.85 = $72.25, not $70 — the second discount is applied to the already-reduced price, so it's worth less in dollar terms than the first.

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