Percentage Calculator
The universal solver for all three fundamental percentage problems: finding a percent of a number, calculating proportional ratios, and determining the original total from a known percentage.
Calculate Percentages
Visual Representation
How to Calculate a Percentage
A percentage represents a dimensionless ratio or fraction of 100. To find a percentage, divide the given part by the total whole and multiply by 100.
The Three Fundamental Percentage Problems
Every standard percentage question in mathematics is an algebraic rearrangement of three interconnected variables: the Percentage (P), the Part, and the Whole (Base).
Example: "What is 25% of 200?"
Example: "50 is what % of 200?"
Example: "50 is 25% of what?"
Mathematical Formula Reference
The core relationship between percentage, numerator, and denominator is derived from the proportional equivalence ratio:
Cross-multiplying this proportion yields the three essential algebraic forms:
- Solving for Part: Part = (Percentage × Whole) ÷ 100 = (Percentage × 0.01) × Whole
- Solving for Percentage (P): Percentage = (Part ÷ Whole) × 100
- Solving for Whole: Whole = (Part × 100) ÷ Percentage = Part ÷ (Percentage ÷ 100)
Sibling Calculators in the Percentage Ecosystem
Depending on your specific mathematical objective, different specialized tools calculate variations of percentage metrics:
Step-by-Step Worked Examples Table
| Problem Description | Applied Formula | Calculation Steps | Final Result |
|---|---|---|---|
| Find 18% of $450 | Part = (P ÷ 100) × Whole | (18 ÷ 100) × 450 = 0.18 × 450 | 81 |
| What % is 42 of 168? | P = (Part ÷ Whole) × 100 | (42 ÷ 168) × 100 = 0.25 × 100 | 25% |
| 72 is 60% of what number? | Whole = Part ÷ (P ÷ 100) | 72 ÷ (60 ÷ 100) = 72 ÷ 0.60 | 120 |
| Calculate a 20% tip on $65 | Tip = 0.20 × Bill | 0.20 × 65 = 13.00 | $13.00 (Total: $78.00) |
Sequential & Compounded Percentages Explained
A common mathematical fallacy is assuming that sequential percentage adjustments can simply be added together. Because each consecutive change modifies the underlying base value, percentages must be multiplied using decimal multipliers:
2. +50% Increase: 100 × (1 + 0.50) = 150
3. -50% Decrease: 150 × (1 - 0.50) = 75
Net Result: 75 (A net loss of 25%, not 0%)
Common Pitfalls to Avoid
An increase from 10% to 15% is a 5 percentage point increase, but a 50% relative increase: ((15 - 10) ÷ 10) × 100 = 50%.
Always verify what value represents 100%. Dividing the whole by the part will produce the reciprocal ratio rather than the percentage.