Percentage Calculator

Math

Calculate percentages, find the original base, compute percentage difference, percentage change (increase/decrease), and add/subtract percentages with step-by-step math.

15% of 240

Formula & Mathematical Steps

(15 / 100) × 240 = 36

To find 15% of 240, convert 15% to a decimal (0.15) and multiply by 240.

How This Calculator Works

How percentages, base quantities, relative differences, and percentage changes work in mathematics and business

📐 The Fundamental Percentage Formula

P = \frac{\text{Part}}{\text{Whole}} \times 100\% \quad \Longleftrightarrow \quad \text{Part} = \frac{P}{100} \times \text{Whole}

P (Percentage Rate): The number of units per 100 (e.g. 25% = 25/100 = 0.25).

Part (Value X): The portion or subset of the base quantity.

Whole / Base (Value Y): The total reference quantity corresponding to 100%.

Percentage Difference: Compares two quantities relative to their average: |X - Y| / ((X + Y)/2) × 100%. Used when neither number is the "original".

Key Mathematical Rules & Properties

What is P% of X?

Multiply X by the decimal equivalent of the percentage: Part = (P / 100) × X.

X is What % of Y?

Divide the part X by the whole Y and multiply by 100%: P = (X / Y) × 100%.

X is P% of What Number?

Divide the part X by the decimal percentage: Whole = X / (P / 100).

Percentage Change vs Difference

Percentage Change = ((New - Old) / |Old|) × 100%. Percentage Difference = (|X - Y| / ((X + Y) / 2)) × 100%.

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Worked Example

Find the percentage change when an investment grows from $80 to $120

Calculate the absolute difference: $120 − $80 = +$40
Divide difference by initial value: 40 / 80 = 0.50
Multiply by 100% to find percentage change: 0.50 × 100% = +50% increase

Final Answer: +50% Increase

Frequently Asked Questions

What is the difference between percentage change and percentage difference?

Use Percentage Change when there is an "old" value and a "new" value (e.g., price increase over time). Use Percentage Difference when comparing two values of equal standing where neither is the initial reference (e.g., comparing the height of two trees).

How do I add sales tax or a tip to a bill?

Multiply the pre-tax bill by (1 + tax_rate / 100). For example, adding 8% sales tax to $50 gives $50 × 1.08 = $54.

How do I find the original price before a discount was applied?

If an item is discounted by D%, the sale price represents (100 - D)%. Divide the sale price by (1 - D/100) to find the original price.

Understanding your calculation

Method, example and limitations

How the calculation works

A percentage is a value per hundred. P percent of X equals P × X / 100; percentage change uses the original value as its denominator.

Example to check

15% of 240 is 36. An increase from 80 to 100 is 25%, while the reverse decrease is 20%.

Before using the result

Percentage change from a zero starting value is undefined. Percentage points describe the difference between percentages and are different from relative percentage changes.

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