Part of Math Calculators

Percentage Calculator

The Percentage Calculator handles every common percentage calculation in one place. The two most-used modes answer the questions people search for most: finding a percentage of a number (for example, what is 20% of 150?) and finding what percentage one number is of another (for example, 30 is what percentage of 150?). It also covers percentage change, applying an increase or decrease, finding the original value, percentage difference, and marks percentage.

Percentage Calculator

%

The percentage to apply.

The number you want a percentage of.

What the result means

Every mode returns one of two kinds of result. In 'X% of Y' the answer is a number — the portion of Y that X% represents. In every other mode the answer is a percentage, and the label says exactly what it measures (PERCENTAGE, PERCENTAGE INCREASE, PERCENTAGE DIFFERENCE, SCORE PERCENTAGE, and so on). The 'Calculation details' section shows the formula and the step-by-step working so you can trace where the number came from.

How to use this calculator

  1. 1Choose the type of percentage calculation from the dropdown. The fields change to match the mode.
  2. 2Enter the values shown — percentages, originals, finals, or marks — with the units and directions that apply.
  3. 3Press Calculate to see the result, the formula, and a short step-by-step breakdown.
  4. 4Read the label next to the result to see what number measures: a plain number for X% of Y, or a percentage for every other mode.

The formula

Each mode uses one standard formula. The two you will use most often are:

X% of Y = (X / 100) × Y X as a % of Y = (X / Y) × 100 Change = ((New − Old) / Old) × 100 Apply change: Original × (1 ± P / 100) Find original: Final ÷ (1 ± P / 100) Difference = (|A − B| / ((A + B) / 2)) × 100 Marks % = (Obtained / Total) × 100

What each variable means

SymbolNameDescription
XPercentage or partIn 'X% of Y', X is the percentage. In 'X is what % of Y', X is the part.
YNumber or wholeThe value the percentage is applied to or compared against.
Old / NewOriginal & new valuesUsed for percentage change. Change is always relative to Old.
PPercentage changeThe rate applied to an original value, or applied to reach a final value.
A / BTwo compared valuesPercentage difference uses the average of A and B as its base.
Obtained / TotalMarksMarks scored divided by total marks, then multiplied by 100.

Step-by-step example

Example: What is 20% of 150?

Mode:X% of YPercentage:20Number:150
  1. 120% of 150 = (20 ÷ 100) × 150
  2. 2= 0.20 × 150
  3. 3= 30

Result

30

What changes the result

  • Percentages are always relative to a base value — the 100% reference.
  • The same percentage can represent very different amounts depending on the base.
  • Percentage change uses the original value as the base, never the new value.
  • Applying a percentage and then reversing it with the same percentage does not return to the starting value, because the base changes.

Edge cases to be aware of

Unusual situations handled correctly

  • 0% of any number is 0, and 100% of a number is the number itself.
  • Percentages can be greater than 100% — for example, 150% of 80 = 120. That simply means the result is 1.5 times the reference value.
  • Decimal percentages work normally: 12.5% of 80 = 10, and 2.5% of 200 = 5.
  • Division by zero is undefined — the total (whole), original value, and total marks must be non-zero in their modes. The calculator shows “Undefined” for these inputs.
  • A 100% decrease leaves a final value of 0, so the original value cannot be recovered by reversing the calculation.
  • Percentage difference is undefined when both values are 0.
  • Equal non-zero values produce 100% in the ‘X is what % of Y’ mode — for example, 20 is 100% of 20.
  • Negative values are accepted where meaningful (for example, a negative difference), but the result is shown with its true sign in the absolute-change field.

Common mistakes

Avoid these errors

  • Confusing ‘what is 20% of 150?’ with ‘20 is what percentage of 150?’. The first asks for 20% of a number (20 ÷ 100 × 150 = 30); the second asks what percentage 20 is of 150 (20 ÷ 150 × 100 = 13.33%).
  • Forgetting to divide the percentage by 100 first, so 20% is used as 20 instead of 0.20.
  • Using the wrong reference value — percentage change always divides by the original value, never the new value.
  • Confusing percentage points (the arithmetic gap between two percentages) with percentage change (a relative measure).
  • Assuming a percentage must be between 0% and 100%. Percentages above 100% are valid: 150% of 80 = 120.
  • Treating percentage difference as a signed value — it is always non-negative and symmetric.
  • For 'find original value', dividing by (1 + P/100) after a decrease instead of (1 − P/100).

Assumptions

  • Percentages are entered as plain numbers: 20 means 20%, so 20 ÷ 100 = 0.20.
  • The original value is the 100% reference for percentage change and for finding an original value.
  • Percentage difference uses the average of the two values as its base and is direction-independent.

Limitations

  • Percentages can misrepresent absolute differences when the bases differ greatly.
  • Percentage change and percentage difference measure different things and are not interchangeable.
  • Results are estimates of the relationship between the values you entered; they do not account for rounding conventions used by specific institutions.

Key terms to know

Percent+
A unit expressing a value as parts per hundred. 20% means 20 out of every 100. The base can change how large the percentage is in absolute terms.
Base value+
The reference value a percentage is calculated against — the 100% mark. Changing the base changes the absolute amount a percentage represents.
Percentage point+
The arithmetic difference between two percentages. Going from 10% to 15% is a 5 percentage point increase, but a 50% relative increase.
Percentage change+
The difference between a new and an original value divided by the original value, then multiplied by 100. It is signed and compares over time or between states.
Percentage difference+
The absolute difference between two values divided by their average, multiplied by 100. It is symmetric and direction-independent.
Percentage increase / decrease+
Applying a percentage rate to an original value to reach a final value. An increase multiplies by (1 + P/100); a decrease multiplies by (1 − P/100).
Ratio+
A comparison of two quantities. A percentage is a ratio expressed with a denominator of 100.

Real-world scenarios

20% of 150

What is 20% of 150?

What it means: Use the 'X% of Y' mode: (20 ÷ 100) × 150 = 0.20 × 150 = 30. So 20% of 150 is 30.

30 is what percentage of 150

A score of 30 out of 150.

What it means: Use 'X is what % of Y': (30 ÷ 150) × 100 = 0.20 × 100 = 20%. So 30 is 20% of 150.

100 to 125 — percentage increase

A value grows from 100 to 125.

What it means: Use 'Percentage change': (125 − 100) ÷ 100 × 100 = 25 ÷ 100 × 100 = 25%. That is a 25% increase, with an absolute change of 25.

200 to 150 — percentage decrease

A value falls from 200 to 150.

What it means: Use 'Percentage change': (150 − 200) ÷ 200 × 100 = −50 ÷ 200 × 100 = −25%. That is a 25% decrease, with an absolute change of −50.

500 increased by 20%

Add 20% to 500.

What it means: Use 'Apply a percentage increase': 500 × (1 + 20 ÷ 100) = 500 × 1.20 = 600. The increase adds 100, so the final value is 600.

120 after a 20% increase — the original value

A price rose 20% and is now 120.

What it means: Use 'Find the original value': 120 ÷ (1 + 20 ÷ 100) = 120 ÷ 1.20 = 100. The original value was 100.

435 out of 500 marks

Marks obtained are 435 out of 500.

What it means: Use 'Percentage of marks': (435 ÷ 500) × 100 = 0.87 × 100 = 87%. So the score is 87%.

Markup then discount

An item is marked up 50% and then discounted 50%.

What it means: Starting at 100, a 50% markup gives 150, then a 50% discount gives 75. The two moves do not cancel because the percentage applies to a different base each time.

Percentage change calculator

Percentage change is relative to the original value and is signed. The percentage-difference method uses the average of two values and is symmetric.

Discount calculator

A discount is a percentage decrease applied to an original price. See how a sale price and the amount saved are derived from the same base.

Grade and attendance calculators

Marks-based percentages compare marks obtained to the maximum total. Grade and attendance calculators use the same percentage idea for scores and class attendance.

Attendance percentage

Attendance is calculated as classes attended divided by total classes, then multiplied by 100 — the same 'X is what % of Y' relationship.

Fraction and ratio calculators

Fractions, ratios and percentages are all ways to express the same relationship between two quantities. Convert between them for cleaner comparisons.

GST calculator

GST is applied as a percentage of a base price. The GST and total price calculations use the same percentage-of-a-number logic.

Frequently asked questions

How do I calculate a percentage of a number?+
Multiply the number by the percentage divided by 100. For example, 20% of 150 = 150 × (20 ÷ 100) = 150 × 0.20 = 30.
What is the difference between percentage and percentage points?+
A percentage is a relative measure. Percentage points measure the absolute difference between two percentages. Going from 10% to 15% is a 5 percentage point increase but a 50% relative increase.
How is percentage change calculated?+
Subtract the original value from the new value, divide by the original value, and multiply by 100. For example, 100 to 125 is (125 − 100) ÷ 100 × 100 = 25%, an increase.
How do I add or subtract a percentage from a number?+
Use the 'apply a percentage increase / decrease' mode: multiply the original value by (1 + P/100) to increase, or (1 − P/100) to decrease. For example, 500 increased by 20% = 500 × 1.20 = 600.
How do I find the original value before a percentage change?+
Divide the final value by (1 + P/100) if it was increased, or (1 − P/100) if it was decreased. For example, 120 after a 20% increase = 120 ÷ 1.20 = 100.
What is the difference between percentage change and percentage difference?+
Percentage change compares a new value to an original value and is signed (positive for increase, negative for decrease). Percentage difference compares two values symmetrically using their average as the base and is always non-negative.
How do I calculate my marks percentage?+
Divide the marks obtained by the total marks and multiply by 100. For example, 435 ÷ 500 × 100 = 87%.
How do I find what percentage one number is of another?+
Divide the part by the whole and multiply by 100. For example, 30 is what percentage of 150? 30 ÷ 150 × 100 = 20%. Use the 'X is what % of Y' mode.
Can a percentage be greater than 100%?+
Yes. A percentage above 100% simply means the result is more than the reference value. For example, 150% of 80 = 120, because 1.5 × 80 = 120.
How do I calculate a percentage of a total?+
Divide the part by the total and multiply by 100. For example, 25 items out of a total of 100 is 25 ÷ 100 × 100 = 25%. This is the same relationship as the 'X is what % of Y' mode.
Can I use decimal percentages?+
Yes — percentages such as 2.5%, 12.5% and 37.5% work normally. For example, 12.5% of 80 = 10.
What happens when the reference value is zero?+
Dividing by zero is undefined, so the calculator shows “Undefined” when the whole, original value, or total is zero. Enter a non-zero reference value to get a result.
Why is percentage change undefined when the original value is 0?+
Percentage change divides by the original value. If it is 0, the division has no defined result, so the calculator shows an explanation instead of a misleading number.

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Attendance Calculator

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GST Calculator

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