How do you calculate what percentage X is of Y?

Divide X by Y, then multiply by 100. For example, to find what percentage 30 is of 120: 30 ÷ 120 × 100 = 25%. Use Card 2 above.

What is the formula for percentage increase?

Percentage increase = ((New Value − Original Value) ÷ |Original Value|) × 100. For example, from 80 to 100: ((100 − 80) ÷ 80) × 100 = 25% increase.

What is the difference between percentage change and percentage difference?

Percentage change measures change from a specific starting point (directional). Percentage difference is symmetric — it compares two values without implying which came first, using the average of the two as the base.

How do I find the original price before a percentage discount?

Use the Reverse Percent formula: Original = Final ÷ (1 − discount%). For example, if a shirt costs $85 after a 15% discount: $85 ÷ (1 − 0.15) = $85 ÷ 0.85 = $100.

20% of 150 is 30. Formula: 150 × (20 ÷ 100) = 30.

How do you calculate percentage difference when one value is zero?

When both values are zero, the percentage difference is 0%. When one value is zero and the other is not, the formula (|A−B| / average) gives a finite result because the average is non-zero. Division by zero only arises when the two values are equal and opposite (e.g. 5 and −5), making their average zero — in that case the difference is undefined and the calculator displays an explanatory message.

Percentage Calculator

All the percentage formulas you need — with answers in plain English.

What is X% of Y?

e.g. What is 20% of 150?

Percentage (X)

Number (Y)

30
20% of 150 is 30

result = (X ÷ 100) × Y

Example: (20 ÷ 100) × 150 = 0.20 × 150 = 30

X is what percent of Y?

e.g. 30 is what % of 120?

Number (X)

Number (Y)

25%
30 is 25% of 120

result = (X ÷ Y) × 100

Example: (30 ÷ 120) × 100 = 0.25 × 100 = 25%

Percentage Increase / Decrease

e.g. From 80 to 100?

Original Value

New Value

+25%
That is a 25% increase from 80 to 100

result = ((new − original) ÷ |original|) × 100

Example: ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25% increase

Percentage Difference

Symmetric — no "before/after"

Value A

Value B

40%
The percentage difference between 40 and 60 is 40%

Note: This is different from percentage change — it's symmetric.

result = |A − B| ÷ ((A + B) ÷ 2) × 100

Example: |40 − 60| ÷ ((40 + 60) ÷ 2) × 100 = 20 ÷ 50 × 100 = 40%

Reverse Percent — Find Original Value

e.g. A shirt costs $85 after 15% discount — what was the original price?

Final Value

Percentage (%)

$100.00
The original value was 100 (before a 15% decrease to 85)


After decrease: original = final ÷ (1 − pct/100)

After increase: original = final ÷ (1 + pct/100)

Example (15% decrease): 85 ÷ (1 − 0.15) = 85 ÷ 0.85 = 100

How to Calculate Percentages

A percentage is a number expressed as a fraction of 100. "Percent" literally means "per hundred." The five most common percentage operations are:

Operation	Formula	Example
X% of Y	(X ÷ 100) × Y	20% of 150 = 30
X is what % of Y?	(X ÷ Y) × 100	30 of 120 = 25%
% Change	((New − Old) ÷ \|Old\|) × 100	80 → 100 = +25%
% Difference	\|A − B\| ÷ avg(A,B) × 100	40 vs 60 = 40%
Reverse % (decrease)	Final ÷ (1 − pct/100)	85 after 15% off → 100

Percentage Change vs Percentage Difference

These two are often confused. Percentage change (Card 3) is directional — it measures how much a value increased or decreased relative to a starting point. Percentage difference (Card 4) is symmetric — it doesn't matter which value is "first," and it uses the average of both values as the denominator.

Frequently Asked Questions

Divide X by Y, then multiply by 100. For example, to find what percentage 30 is of 120: 30 ÷ 120 × 100 = 25%. Use Card 2 above.
Percentage increase = ((New Value − Original Value) ÷ |Original Value|) × 100. For example, from 80 to 100: ((100 − 80) ÷ 80) × 100 = 25% increase.
Percentage change measures change from a specific starting point (directional). Percentage difference is symmetric — it compares two values without implying which came first, using the average of the two as the base.
Use Card 5 (Reverse Percent). Formula: Original = Final ÷ (1 − discount%). For a shirt costing $85 after 15% off: $85 ÷ 0.85 = $100.
20% of 150 is 30. Formula: (20 ÷ 100) × 150 = 0.20 × 150 = 30.
When the denominator is zero (e.g. percentage change from 0, or percentage difference when the two values are equal and opposite so their average is 0), the result is mathematically undefined. The calculator displays an explanatory message instead of an error.