What the result explains
What This Calculator Provides
Use the three independent panels to find a percentage of an amount, determine what percentage one number is of another, or measure relative change from an original value to a new value. Each panel calculates as soon as its own two inputs are complete. Negative values are allowed where they are mathematically meaningful, but division by zero is not. The page also explains why a change measured in percentage points is different from a relative percentage change.
- X percent of Y
- X as a percentage of Y
- percentage increase, decrease, or no change
How to Use This Calculator
- Enter the known valuesUse the labeled fields and units shown in the calculator. Correct any validation message before continuing.
- Review the resultRead the main answer together with its breakdown, formula, rounding, and assumptions.
- Copy and verifyCopy the result when available, then check important decisions against the relevant record, institution, or professional.
Method
Formula and Calculation Method
What is X% of Y?
result = (X ÷ 100) × Y
Convert the percentage to a decimal, then multiply by the base amount.
X is what percent of Y?
percentage = (X ÷ Y) × 100
Y is the reference whole and cannot be zero.
Percentage change
change = ((new − original) ÷ original) × 100
The original value is the comparison base and cannot be zero. A negative answer is a decrease.
Worked from input to answer
Worked Examples
Find a percentage of an amount
- 20% = 20 ÷ 100 = 0.2
- 0.2 × 150 = 30
Result: 20% of 150 = 30.
Find what percentage a part represents
- Part = 15 and whole = 60
- 15 ÷ 60 × 100 = 25
Result: 15 is 25% of 60.
Find a percentage increase
- Original = 80; new = 100
- Increase = 100 − 80 = 20
- 20 ÷ 80 × 100 = 25%
Result: The relative increase is 25%.
Where Percentages Actually Turn Up
Most percentage questions arrive wearing a costume. A sale price is a percentage problem — the discount calculator does it with the retail arithmetic attached — and so is a restaurant bill, which the tip calculator also splits per person.
Interest is a percentage stretched over time, which is why the loan calculator exists as a separate page, and payroll deductions are percentages of gross pay handled by the paycheck calculator.
Percentage versus percentage points
If an interest rate moves from 5% to 7%, it rises by 2 percentage points. Relative to the original 5%, the increase is (7 − 5) ÷ 5 × 100 = 40%. Percentage points compare two percentages directly; percent change compares the difference with the original value.
Choosing the correct base
The denominator controls the meaning. “15 is what percent of 60?” uses 60 as the whole. Percentage change uses the original value as the base, which is why an increase from 80 to 100 is 25%, while the reverse decrease from 100 to 80 is 20%.
Division by zero
A part cannot be expressed as a percentage of a zero whole, and relative change from an original value of zero is undefined. The calculator reports that condition rather than showing infinity.
Practical Uses
- Calculating a grade or completion rate
- Comparing prices, revenue, or traffic over time
- Finding tax, commission, or allocation amounts
- Checking discounts and tips
- Distinguishing relative change from percentage-point change
Assumptions
- The chosen whole or original value is the intended comparison base.
- Results are mathematical values before any domain-specific rounding rule.
- A zero denominator is treated as undefined.
Important Limitations
- Percent change can be misleading when the original value is very small.
- A percentage alone does not communicate the size of the underlying values.
- Domain rules may require different rounding or weighting.
Help & support
Frequently Asked Questions
Quick answers to common questions about the Percentage calculator.
What is 20% of 150?
Convert 20% to 0.2 and multiply by 150. The result is 30.
How do I calculate percentage increase?
Subtract the original from the new value, divide by the original, then multiply by 100.
What is the difference between percent and percentage points?
Percentage points are the direct difference between two percentages. Percent change compares that difference with the original percentage.
Can a percentage change be negative?
Yes. A negative change indicates the new value is below the original value.
Why is percentage change from zero undefined?
The formula divides by the original value, and division by zero has no finite result.