Percentage Calculator

About Percentage Calculator

This percentage calculator solves three common percentage problems: finding a percentage of a value, determining what percentage one number is of another, and calculating percentage change (increase or decrease). Each calculation uses standard mathematical formulas with step-by-step breakdowns.

It is useful for discounts and markups, tax calculations, score changes, growth rates, financial analysis, statistical comparisons, grade calculations, and everyday percentage problems.

Percentage Fundamentals

Percentage means "per hundred" and represents a fraction with denominator 100:

Percentage Basics:

Definition:
  X% = X/100 = X hundredths

Conversions:
  Percentage to Decimal: Divide by 100
    25% = 25/100 = 0.25

  Decimal to Percentage: Multiply by 100
    0.75 = 0.75 × 100 = 75%

  Percentage to Fraction: Simplify
    50% = 50/100 = 1/2
    20% = 20/100 = 1/5

Common Percentage Equivalents:
  1%    = 0.01   = 1/100
  5%    = 0.05   = 1/20
  10%   = 0.10   = 1/10
  20%   = 0.20   = 1/5
  25%   = 0.25   = 1/4
  33.33%= 0.3333 = 1/3
  50%   = 0.50   = 1/2
  66.67%= 0.6667 = 2/3
  75%   = 0.75   = 3/4
  100%  = 1.00   = 1
  150%  = 1.50   = 3/2
  200%  = 2.00   = 2

Percentage Formulas

Calculation Examples

Type 1: What is X% of Y?

Example 1: What is 15% of 200?
  Step 1: Convert percentage to decimal
    15% = 15/100 = 0.15
  Step 2: Multiply
    200 × 0.15 = 30
  Answer: 30

Example 2: What is 7.5% of 450?
  Step 1: 7.5% = 0.075
  Step 2: 450 × 0.075 = 33.75
  Answer: 33.75

Type 2: X is what percent of Y?

Example 1: 45 is what percent of 180?
  Step 1: Divide
    45 / 180 = 0.25
  Step 2: Convert to percentage
    0.25 × 100 = 25%
  Answer: 25%

Example 2: 17 is what percent of 85?
  Step 1: 17 / 85 = 0.2
  Step 2: 0.2 × 100 = 20%
  Answer: 20%

Type 3: Percentage Change from A to B

Example 1: From 40 to 60
  Step 1: Find difference
    60 - 40 = 20
  Step 2: Divide by original
    20 / 40 = 0.5
  Step 3: Convert to percentage
    0.5 × 100 = 50%
  Answer: +50% (increase)

Example 2: From 100 to 80
  Step 1: 80 - 100 = -20
  Step 2: -20 / 100 = -0.2
  Step 3: -0.2 × 100 = -20%
  Answer: -20% (decrease)

Example 3: From 250 to 375
  Step 1: 375 - 250 = 125
  Step 2: 125 / 250 = 0.5
  Step 3: 0.5 × 100 = 50%
  Answer: +50% (increase)

Real-World Applications

Code Examples by Language

JavaScript:
  // Percentage of value
  function percentageOf(percent, value) {
    return value * (percent / 100);
  }

  // What percent
  function whatPercent(part, whole) {
    return (part / whole) * 100;
  }

  // Percentage change
  function percentChange(old, new) {
    return ((new - old) / old) * 100;
  }

Python:
  def percentage_of(percent, value):
      return value * (percent / 100)

  def what_percent(part, whole):
      return (part / whole) * 100

  def percent_change(old, new):
      return ((new - old) / old) * 100

PHP:
  function percentageOf($percent, $value) {
      return $value * ($percent / 100);
  }

  function whatPercent($part, $whole) {
      return ($part / $whole) * 100;
  }

  function percentChange($old, $new) {
      return (($new - $old) / $old) * 100;
  }

Java:
  public static double percentageOf(double percent, double value) {
      return value * (percent / 100);
  }

  public static double whatPercent(double part, double whole) {
      return (part / whole) * 100;
  }

  public static double percentChange(double old, double new) {
      return ((new - old) / old) * 100;
  }

Excel/Google Sheets:
  ' Percentage of value
  =B1*A1/100    or   =B1*(A1%)

  ' What percent
  =A1/B1*100

  ' Percentage change
  =(B1-A1)/A1*100

  ' Format cells as Percentage (%)

Percentage Tricks

Mental Math Shortcuts:

1. 10% of any number: Move decimal one place left
   10% of 250 = 25
   10% of 47.5 = 4.75

2. 5% = Half of 10%
   5% of 80 = (10% of 80) / 2 = 8 / 2 = 4

3. 15% = 10% + 5%
   15% of 200 = 20 + 10 = 30

4. 20% = Double 10%
   20% of 75 = 7.5 × 2 = 15

5. 25% = Divide by 4
   25% of 100 = 100/4 = 25

6. 50% = Half
   50% of 87 = 87/2 = 43.5

7. 75% = 50% + 25% = Half + Quarter
   75% of 80 = 40 + 20 = 60

8. 100% = The number itself
   100% of 42 = 42

9. Reversibility: X% of Y = Y% of X
   4% of 25 = 25% of 4 = 1
   8% of 50 = 50% of 8 = 4

10. Percentage increase followed by decrease:
    +10% then -10% ≠ Original
    100 → 110 → 99 (net -1%)

Common Mistakes

Mistake 1: Adding percentages incorrectly
  Wrong: +20% then +30% = +50%
  Correct: 100 → 120 → 156 = +56% total
  (Percentages compound, not add)

Mistake 2: Reversing percentage change
  Wrong: If A is 25% more than B, then B is 25% less than A
  Correct: A = 125, B = 100
           B is (125-100)/125 = 20% less than A

Mistake 3: Percentage of percentage
  Wrong: 50% of 50% = 100%
  Correct: 50% of 50% = 25% (0.5 × 0.5 = 0.25)

Mistake 4: Division by zero in percentage change
  Cannot calculate: From 0 to 100
  Result would be infinite (division by zero)

Mistake 5: Confusing percentage points with percent
  From 10% to 15%:
  - 5 percentage points increase
  - 50% percent increase
  (These are different measurements)

Best Practices

• Check for zero denominators: Percentage calculations involving division require non-zero denominators.
• Distinguish absolute vs relative: Understand when to use percentage points (absolute) vs percent change (relative).
• Round appropriately: For currency, round to 2 decimal places; for statistics, use appropriate significant figures.
• Verify reasonableness: Quick mental estimate helps catch calculation errors.
• Document base values: Always specify what the percentage is relative to for clarity.

Limitations

• Cannot compute change from zero: Percentage change requires non-zero starting value.
• Floating-point precision: JavaScript Number type may introduce small rounding errors for very precise calculations.
• Single-step calculations: Does not handle multi-step percentage problems (e.g., successive discounts).
• No context awareness: Cannot determine if result makes sense in real-world context.