How to Calculate Percentages

A percentage is a way of expressing a number as a fraction of 100. Understanding percentages is essential for everyday calculations — discounts, tax, interest rates, exam scores, and statistics all rely on them.

What is a Percentage?

The word 'percentage' comes from the Latin 'per centum' meaning 'by the hundred'. A percentage tells you how large a part is relative to a whole, expressed out of 100.

ℹ50% means 50 out of 100, or exactly half. 100% means the whole thing. 200% means twice the whole.

Finding a Percentage of a Number

To find X% of a number Y, multiply Y by X and divide by 100.

Result = \frac{X \times Y}{100}

Example: What is 25% of 200?

\frac{25 \times 200}{100} = 50

Write the percentage as a fraction: 25 ÷ 100 = 0.25
Multiply by the number: 0.25 × 200 = 50
Answer: 25% of 200 is 50

Finding What Percentage One Number Is of Another

To find what percentage a part is of the whole, divide the part by the whole and multiply by 100.

P = \frac{Part}{Whole} \times 100

Example: 30 is what percent of 120?

P = \frac{30}{120} \times 100 = 25%

Percentage Increase

Use this when a value has grown and you want to express how much it grew as a percentage of the original.

Percentage Increase = \frac{New - Old}{Old} \times 100

Example: A price rose from $80 to $100. What is the percentage increase?

\frac{100 - 80}{80} \times 100 = \frac{20}{80} \times 100 = 25%

Percentage Decrease

Use this when a value has fallen and you want to express the drop as a percentage of the original.

Percentage Decrease = \frac{Old - New}{Old} \times 100

Example: A salary dropped from $5000 to $4000. What is the percentage decrease?

\frac{5000 - 4000}{5000} \times 100 = 20%

Common Scenarios at a Glance

What to find	Formula	Example
X% of Y	(X / 100) × Y	25% of 200 = 50
A is what % of B	(A / B) × 100	30 of 120 = 25%
% increase	((New − Old) / Old) × 100	80 → 100 = 25% increase
% decrease	((Old − New) / Old) × 100	100 → 80 = 20% decrease
Value after % rise	Original × (1 + P/100)	200 + 10% = 220
Value after % drop	Original × (1 − P/100)	200 − 10% = 180

Quick Mental Math Tips

10% of any number → move the decimal one place left (10% of 350 = 35)
5% = half of 10% (5% of 350 = 17.5)
1% → move decimal two places left (1% of 350 = 3.5)
25% = divide by 4
50% = divide by 2
To find 15%: find 10%, find 5%, add them together

Percentage Calculator — Calculate percentages instantly
Percentage Formula — Full formula with variable definitions

Frequently Asked Questions

What is the easiest way to calculate a percentage?

Multiply the number by the percentage and divide by 100. For example, 30% of 50 = (30 × 50) / 100 = 15. Alternatively, convert the percentage to a decimal (30% = 0.30) and multiply.

How do I calculate percentage increase?

Subtract the old value from the new value, divide by the old value, then multiply by 100. Formula: ((New − Old) / Old) × 100.

How do I calculate percentage decrease?

Subtract the new value from the old value, divide by the old value, then multiply by 100. Formula: ((Old − New) / Old) × 100.

Can a percentage be more than 100?

Yes. A percentage over 100 simply means the value exceeds the original whole. For example, if a quantity doubles, it is a 100% increase — becoming 200% of its original value.

What is the difference between percentage and percentage points?

Percentage points measure the arithmetic difference between two percentages. If interest rises from 2% to 5%, it rose by 3 percentage points — but that is a 150% increase relative to 2%.