Percentage Formula: How to Calculate

This calculator works out the percentage one number is of another, or the percentage change between two numbers. You enter the two values, and it returns the percentage and the percentage difference. The core formula is percentage = (part / whole) × 100.

Formula

The basic percentage formula is:

Percentage = (Part / Whole) × 100

• Part – the portion or amount you are comparing (same unit as the whole).
• Whole – the total or reference amount (same unit as the part).
• Percentage – the ratio expressed as a number out of 100.

For percentage change between two values, use:

Percentage change = ((New value – Original value) / Original value) × 100

A positive result means an increase; a negative result means a decrease. The unit cancels out, so the percentage is dimensionless.

Worked Example

Using the default values from the calculator: Part = 25, Whole = 200.

1. Divide the part by the whole: 25 ÷ 200 = 0.125
2. Multiply by 100 to get the percentage: 0.125 × 100 = 12.5%
3. So 25 is 12.5% of 200.

For the percentage change from 25 to 200:

1. Subtract the original from the new: 200 – 25 = 175
2. Divide by the original: 175 ÷ 25 = 7
3. Multiply by 100: 7 × 100 = 700%

The calculator shows 12.50% and 700.00%, matching these steps.

When to Use This Formula

Use the basic percentage formula whenever you need to express a part of a whole as a fraction of 100. Common situations include:

• Calculating a test score: 18 correct out of 20 questions → (18/20) × 100 = 90%.
• Finding what percent of a budget was spent: $450 spent out of $1,200 → (450/1200) × 100 = 37.5%.
• Converting a fraction or decimal to a percentage: 0.75 → 75%.

Use the percentage change formula when comparing an old value to a new one, such as price increases, population growth, or performance improvements over time.

How to Read the Result

The percentage result tells you the proportion of the whole that the part represents. For example, if you score 90% on a test, you got 90 out of every 100 possible points. The percentage change result tells you the relative increase or decrease. A 50% increase means the new value is 1.5 times the original; a 50% decrease means the new value is half the original.

Be careful with percentage change when the original value is zero or negative. If the original is zero, the formula divides by zero and is undefined. If the original is negative, the result can be misleading (e.g., going from -10 to -5 gives +50%, but the magnitude actually decreased).

Common Mistakes and Unit Mix-ups

• Mixing units: The part and whole must be in the same unit. If one is in dollars and the other in cents, convert first.
• Forgetting to multiply by 100: The ratio 0.25 is not 0.25%; it is 25%.
• Confusing percentage points with percent: A rise from 10% to 15% is a 5 percentage point increase, but a 50% increase relative to the original 10%.
• Using the wrong base for change: Percentage change always uses the original value as the denominator, not the new value.
• Rounding too early: Round only the final answer, not intermediate steps, to avoid accumulated error.

Limitations of the Formula

The basic percentage formula assumes a linear relationship and a meaningful whole. It does not work well when the whole is zero or negative. For percentage change, the formula is symmetric only in the sense that a change from A to B is not the negative of a change from B to A. For example, going from 100 to 150 is a 50% increase, but going from 150 back to 100 is a 33.33% decrease. This asymmetry is normal but can confuse.

Also, percentages can be misleading when the base is very small. A 100% increase from 1 to 2 is numerically tiny, but the percentage sounds large. Always consider the actual values.

Frequently Asked Questions

How do I calculate a percentage of a number?

To find what X% of Y is, multiply Y by X/100. For example, 20% of 150 = 150 × 0.20 = 30. This is the reverse of the basic formula: here you know the percentage and the whole, and you solve for the part.

What is the difference between percentage and percentage points?

A percentage is a ratio out of 100. A percentage point is the arithmetic difference between two percentages. If interest rates go from 4% to 5%, that is a 1 percentage point increase, but a 25% increase relative to the original 4%.

How do I calculate percentage increase or decrease?

Use the formula: ((New – Original) / Original) × 100. For example, if a price goes from $80 to $100, the increase is ((100-80)/80) × 100 = 25%. If it drops from $100 to $80, the decrease is ((80-100)/100) × 100 = -20%.

Can a percentage be greater than 100?

Yes. If the part is larger than the whole, the percentage exceeds 100. For example, if you have 150 apples and the whole is 100 apples, you have 150% of the original amount. This often happens in growth contexts.

What if the whole is zero?

The formula is undefined because division by zero is not possible. In practical terms, you cannot express a part as a percentage of zero. If you encounter this, you need a different measure, such as the actual difference or a ratio to a non-zero baseline.

How do I convert a percentage to a decimal or fraction?

To convert a percentage to a decimal, divide by 100 (e.g., 45% = 0.45). To convert to a fraction, write it over 100 and simplify (e.g., 45% = 45/100 = 9/20). This is useful when applying percentages in calculations.

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in a | Part | - | 25 | 0
in b | Whole | - | 200 | 0
out pct | Percentage | % | (a / b) * 100 | 2
out change | Percentage change from a to b | % | ((b - a) / a) * 100 | 2