How to Calculate a Percentage

Q: What is the basic percentage formula?

Percentage = (Part / Whole) x 100. To find the part when you know the percentage: Part = (Percentage / 100) x Whole. To find the whole when you know the part and percentage: Whole = Part / (Percentage / 100).

Q: How do I calculate a percentage in my head?

Start with 10%: move the decimal one place left. Build from there. 20% = double the 10%. 5% = halve the 10%. 15% = 10% + 5%. 25% = divide by 4. These building blocks cover most everyday percentage calculations.

Q: How do I find what percentage one number is of another?

Divide the first number by the second, then multiply by 100. Example: 18 is what percentage of 72? (18 / 72) x 100 = 25%. So 18 is 25% of 72.

Q: How do I increase a number by a percentage?

Multiply the number by (1 + percentage/100). To increase $80 by 15%: $80 x 1.15 = $92. This is equivalent to adding $80 x 0.15 = $12 to $80.

Q: How do I decrease a number by a percentage?

Multiply the number by (1 - percentage/100). To decrease $80 by 15%: $80 x 0.85 = $68. This is equivalent to subtracting $80 x 0.15 = $12 from $80.

Q: What does percent mean literally?

"Percent" comes from the Latin "per centum," meaning "per hundred." A percentage is a ratio expressed as a fraction of 100. So 35% means 35 per hundred, or 35/100, or 0.35 as a decimal.

A percentage is a way of expressing a number as a fraction of 100. Once you understand the core formula, every percentage problem -- tips, discounts, taxes, grades -- becomes straightforward.

The core percentage formula

Every percentage calculation is a variation of one formula. The percent symbol simply means "divided by 100," so any percentage can be converted to a decimal by dividing by 100.

Percentage = (Part / Whole) x 100

Example: You answered 42 out of 50 questions correctly. (42 / 50) x 100 = 84%. Your score is 84%.

To reverse this and find the part from a known percentage: Part = (Percentage / 100) x Whole. So 30% of 200 = (30 / 100) x 200 = 60.

Three versions of the same formula

Percentage = (Part / Whole) x 100. Part = (Percentage / 100) x Whole. Whole = Part / (Percentage / 100). Every percentage problem is one of these three -- you always know two values and need to find the third.

Finding X% of a number

This is the most common percentage question. It shows up for tips, taxes, discounts, and commissions. Convert the percentage to a decimal and multiply.

Part = (Percentage / 100) x Whole

Example: What is 18% of $54? (18 / 100) x 54 = 0.18 x 54 = $9.72.

A quick mental shortcut: to find 10%, move the decimal one place left. To find 20%, double the 10% result. To find 5%, halve the 10% result. To find 15%, add 10% and 5%.

Applied: 15% of $60. 10% = $6.00. 5% = $3.00. 15% = $6.00 + $3.00 = $9.00.

What percentage is X of Y?

This version asks: the part is known, the whole is known, find the percentage. Divide the part by the whole and multiply by 100.

Percentage = (Part / Whole) x 100

Example: You spent $35 out of a $140 budget. What percentage did you spend? (35 / 140) x 100 = 25%. You spent 25% of your budget.

Another example: 27 students passed out of 36. What is the pass rate? (27 / 36) x 100 = 75%.

Percentage change

Percentage change tells you how much a value has grown or shrunk relative to its starting point. A positive result means an increase; a negative result means a decrease.

% Change = ((New Value - Original Value) / Original Value) x 100

Example: Your salary increased from $48,000 to $54,000. ((54,000 - 48,000) / 48,000) x 100 = 12.5% increase.

The original value is always the denominator. This is what makes percentage change directional -- the same two numbers produce different results depending on which came first.