Percentage Calculator

Calculate percentages, percentage change, and reverse percentages.

What is this percentage (%)

Of this number (X)

Result

20% of 350 is 70

How It Works

A percentage represents a portion of a whole expressed as a fraction of 100. This calculator performs the five most common percentage operations instantly using high-precision decimal arithmetic without cumulative rounding errors.

Switch between modes to calculate a straightforward percentage of a quantity, determine what proportion one number represents of another, find a base value from a known percentage, or evaluate relative percentage increase and decrease.

Formula & Calculation

Percentage of a Number

Y = X × (P / 100)

X=Base number

P=Percentage rate

Y=Resulting value

Converts rate P into a decimal fraction by dividing by 100, then multiplies by the base number X.

Percentage Proportion (X is what % of Y)

P = (X / Y) × 100

X=Part / numerator

Y=Whole / denominator

P=Percentage result

Y cannot equal zero, as division by zero is mathematically undefined.

Percentage Change (Increase / Decrease)

Change % = ((New − Old) / |Old|) × 100

Old=Initial value (A)

New=Final value (B)

Using the absolute value of Old in the denominator ensures proper directional sign when starting from negative baselines.

Reverse Percentage (X is P% of what?)

Base = X / (P / 100)

X=Known portion value

P=Percentage rate

Base=Total starting value

P cannot equal 0% for non-zero X values.

Step-by-Step Example

Example 1: Finding 20% of $350

Suppose an item costs $350 and is discounted by 20%:

Step 1: Convert rate to decimal: 20 / 100 = 0.20→ 0.20

Step 2: Multiply base by rate: 350 × 0.20 = 70→ $70.00 savings

Step 3: Subtract discount from base: 350 − 70 = 280→ $280.00 final price

20% of $350 is $70. The discounted final price is $280.

Example 2: Percentage Increase from $50 to $65

Find the growth percentage when revenue rises from $50 to $65:

Step 1: Find absolute difference: 65 − 50 = 15→ $15 growth

Step 2: Divide by baseline: 15 / 50 = 0.30→ 0.30 ratio

Step 3: Convert to percentage: 0.30 × 100 = 30%→ +30.00%

Revenue increased by 30.00% over the baseline.

Assumptions & Edge Cases

Zero Denominator Rule: When calculating "X is what % of Y", the denominator Y cannot equal zero because division by zero is mathematically undefined. An inline warning explains the condition.
Zero Percentage in Reverse Calculation: Finding a total base when the given percentage is 0% is rejected inline because a non-zero portion cannot originate from a 0% share.
Negative Number Handling: Negative inputs are supported across all modes. For percentage change, dividing by |Old| ensures positive growth represents an increase even across negative baselines.

Frequently Asked Questions

How do I calculate a percentage in my head?

To find 10% of any number, move the decimal point one place to the left (10% of 250 is 25). To find 20%, double the 10% amount (25 × 2 = 50). To find 5%, halve the 10% amount (25 / 2 = 12.5).

What is the difference between percentage and percentage points?

A percentage is a relative ratio, while a percentage point is the simple arithmetic difference between two percentage figures. If an interest rate climbs from 5% to 6%, it rose by 1 percentage point, which is a 20% relative increase.

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