Percentage Calculator

The Percentage Calculator handles all common percentage calculations: finding a percentage of a number, finding what percentage one number is of another, calculating percentage change, increase, decrease, difference, marks percentage and exam percentage.

Percentage Calculator

The percentage, part, or original value.

The total, whole, or new value.

What the result means

The result depends on the mode you select. Each mode uses the standard percentage formula appropriate for that calculation.

How to use this calculator

  1. 1Select the type of percentage calculation you need from the dropdown.
  2. 2Enter the two values.
  3. 3Press Calculate to see the result and explanation.

The formula

The calculation uses a standard, verifiable formula. Here it is in its simplest form.

X% of Y = (X / 100) × Y X as % of Y = (X / Y) × 100 Change = ((New − Old) / Old) × 100 Difference = (|A − B| / ((A + B) / 2)) × 100

What each variable means

SymbolNameDescription
XFirst valueThe percentage, part, or original value.
YSecond valueThe total, whole, or new value.

Step-by-step example

Example: What is 20% of 150?

Mode:X% of YX:20Y: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 same percentage can represent very different amounts depending on the base.
  • Percentage change is relative to the original value, not the new value.

Edge cases to be aware of

Unusual situations handled correctly

  • 0% of any number is 0.
  • 100% of a number is the number itself.
  • Division by zero is undefined — enter a non-zero total.
  • Percentage difference uses the average as the base.

Common mistakes

Avoid these errors

  • Calculating percentage change relative to the new value instead of the original.
  • Confusing percentage points with percentage change.
  • Using the wrong base value in calculations.

Assumptions

  • All values are positive numbers.
  • The original value is the reference point for change calculations.

Limitations

  • Percentage values can misrepresent absolute differences when bases differ.
  • Percentage difference is always positive and symmetric.

Key terms to know

Percent+
A unit expressing a value as parts per hundred. The base can change how large the percentage is in absolute terms.
Base value+
The reference value a percentage is calculated against. 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.
Ratio+
A comparison of two quantities. A percentage is a ratio expressed with a denominator of 100.
Proportion+
The relationship of a part to a whole, often written as a fraction or decimal.
Percentage change+
The difference between a new and an original value divided by the original value, then multiplied by 100.
Percentage difference+
The absolute difference between two values divided by their average, multiplied by 100. It is direction-independent.

Real-world scenarios

Shopping discount

An item costing ₹2,000 has a 15% discount.

What it means: The discount is 15% of ₹2,000 = ₹300, so the final price is ₹1,700. A later 15% increase on ₹1,700 gives ₹1,955 — not the original ₹2,000 — because the base changed.

Exam scores

A student scores 37 out of 50.

What it means: The percentage is 37 ÷ 50 × 100 = 74%. The same ratio across a different total, like 74 out of 100, also gives 74% — percentages make comparisons across totals meaningful.

Salary increase

A ₹50,000 salary rises to ₹55,000.

What it means: The increase is 5,000 ÷ 50,000 × 100 = 10%. If the salary later falls 10% from ₹55,000, the new value is ₹49,500 — below where it began.

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 starting value; the percentage-difference method uses the average of the two values as the base.

Discounts and sales

Discounts reduce an original price by a percentage of that price. Stacking markups and markdowns requires careful attention to the base.

Grades and scores

Marks-based percentages compare marks obtained to the maximum possible total, letting you compare assessments of different sizes.

Percentages in finance

In finance, interest and loan changes are percentages of a principal, so even a 1% rate change can significantly change total cost.

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 × 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% 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 a 25% increase.
What is the difference between percentage increase and percentage difference?+
Percentage increase compares a new value to an original value. Percentage difference compares two values symmetrically using the average as the base.

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