Free Tool · 5 Modes · Step-by-Step

Percentage Calculator

Five modes in one tool — percent of a number, percent increase, percent decrease, percent change, and percent difference.

Find a portion of a total. Example: what is 15% of 250?

What this percentage calculator does

This tool answers five of the most common percentage questions in one place. It can find a percentage of a number (what is 15% of 250?), work out what percentage one number is of another (60 is what percent of 240?), calculate percentage increase, percentage decrease, and percentage change between two values, and compute the percentage difference between two numbers when neither is a natural reference point. Each mode shows the result with the full worked steps, so you can see exactly how the answer was produced — useful for checking homework and for understanding the underlying arithmetic rather than just getting a number.

Formulas used in each mode

All five modes reduce to variations on the same underlying relationship:

Percent of a number
\[ \text{Result} = \frac{p}{100} \times n \]
X is what percent of Y
\[ \text{Percentage} = \frac{X}{Y} \times 100 \]
Percentage change (increase or decrease)
\[ \text{Change \%} = \frac{Y - X}{X} \times 100 \]
Percentage difference
\[ \text{Difference \%} = \frac{|X - Y|}{\dfrac{X + Y}{2}} \times 100 \]

Variable definitions

  • p — the percentage rate you supply (for example, 15 for 15%).
  • n — the number you are taking a percentage of.
  • X — the original (or first) value; the base for percentage change.
  • Y — the new (or second) value.
  • |X − Y| — the absolute difference, always positive.

Worked examples

Example 1: What is 15% of 250?

  1. Formula: Result = (p ÷ 100) × n.
  2. Substitute: (15 ÷ 100) × 250 = 0.15 × 250.
  3. Multiply: 0.15 × 250 = 37.5.
  4. Result: 37.5 — 15% of 250 is 37.5.

Example 2: 60 is what percent of 240?

  1. Formula: Percentage = (X ÷ Y) × 100.
  2. Substitute: (60 ÷ 240) × 100.
  3. Divide: 0.25 × 100 = 25.
  4. Result: 25% — 60 is 25% of 240.

Example 3: Percentage increase from 80 to 100

  1. Formula: Change % = ((Y − X) ÷ X) × 100.
  2. Substitute: ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100.
  3. Divide: 0.25 × 100 = 25.
  4. Result: 25% increase.

Example 4: Percentage change from 100 to 75

  1. Formula: Change % = ((Y − X) ÷ X) × 100.
  2. Substitute: ((75 − 100) ÷ 100) × 100 = (−25 ÷ 100) × 100.
  3. Compute: −0.25 × 100 = −25.
  4. Result: −25% — a 25% decrease. The negative sign confirms the direction.

Example 5: Percentage difference between 40 and 60

  1. Formula: |X − Y| ÷ ((X + Y) ÷ 2) × 100.
  2. Numerator: |40 − 60| = 20.
  3. Denominator: (40 + 60) ÷ 2 = 50.
  4. Combine: (20 ÷ 50) × 100 = 40.
  5. Result: 40% difference. Notice this is symmetric — reversing the inputs gives the same 40%, unlike percentage change.

When to use which mode

  • Percent of a number — calculating a discount, a tax, a mark weight, or any portion of a total.
  • X is what percent of Y — working out your marks as a percentage of the total, or what fraction one quantity is of another.
  • Percentage increase — price rises, population growth, salary increments.
  • Percentage decrease — discounts, depreciation, reduction in error rate.
  • Percentage change — the general case; works for increases and decreases and reports the sign automatically.
  • Percentage difference — comparing two measurements with no established reference, such as two experimental results.

Common mistakes to avoid

  • Confusing percentage points with percentage. Going from 20% to 25% is an increase of 5 percentage points but a 25% relative increase. State which one you mean.
  • Using the new value as the base for change. Percentage change always divides by the original value. Dividing by the new value gives a different, incorrect number.
  • Assuming percentage difference is the same as percentage change. It is not. Change uses one value as the reference; difference uses the average. The two answers can differ substantially.
  • Forgetting the sign. A negative percentage change is meaningful — it means the value went down. Do not drop the minus sign.
  • Percentage change from zero. Undefined, because it requires division by zero. If a value starts at zero, describe the change in absolute terms instead.
  • Stacking percentages incorrectly. A 10% increase followed by a 10% decrease does not return to the original value. They act on different bases.

FAQ

What is the difference between percentage change and percentage difference?

Percentage change uses the starting value as the base: (new − old) ÷ old × 100. Percentage difference uses the average of the two values as the base: |a − b| ÷ ((a + b) ÷ 2) × 100. Use change when one value is clearly the original; use difference when neither is a reference point.

How do I calculate a percentage increase?

Subtract the original from the new value, divide by the original, then multiply by 100. For example, 80 to 100 is (100 − 80) ÷ 80 × 100 = 25 percent increase.

Can the percentage change be negative?

Yes. A negative result means a decrease. For instance, 100 to 75 gives −25 percent, which is a 25 percent decrease. The mode labels the sign explicitly so there is no ambiguity.

What if the original value is zero?

Percentage change from zero is undefined because you cannot divide by zero. This calculator will show an error message if you try. Percentage of a number and percentage difference still work if only one of the values is zero, as long as the base of the division is non-zero.

How is percentage difference different from percentage error?

Percentage error compares an experimental value to a known or accepted value using the accepted value as the base. Percentage difference compares two measured values with no established reference, using their average as the base.

How do I increase a number by a percentage without the calculator?

Multiply the number by (1 + percent ÷ 100). To increase 250 by 15 percent, compute 250 × 1.15 = 287.5. To decrease, multiply by (1 − percent ÷ 100).

Related tools

Related Hira Academy resources

Percentages appear throughout the BISE Punjab board syllabus — from profit and loss in Class 9 mathematics to concentration calculations in Class 10 chemistry. Revise the basics with our free Class 9 notes and Class 10 notes.

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