Percentage Basics: Part, Rate and Whole

Most percentage questions contain three values: a whole, a percentage rate and the resulting part. If you know any two, you can calculate the third.

What does a percentage mean?

“Percent” means “per hundred.” Therefore, 18% means 18 out of every 100, and it can be written as the decimal 0.18. Converting a percentage to a decimal is usually the first step: divide the percentage by 100.

percentage as a decimal = percentage ÷ 100

Find a percentage of a number

Multiply the whole by the percentage written as a decimal.

part = whole × percentage ÷ 100

Example: 15% of 240 = 240 × 0.15 = 36.

This calculation is useful for taxes, commissions, interest, survey results and many other situations. Always check that the percentage is applied to the correct base value.

Find what percentage one number is of another

Divide the part by the whole, then multiply by 100.

percentage = part ÷ whole × 100

Example: 30 out of 120 = 30 ÷ 120 × 100 = 25%.

The order matters. “30 is what percentage of 120?” is not the same question as “120 is what percentage of 30?” The first answer is 25%; the second is 400%.

Find the whole when the part is known

Divide the known part by the percentage as a decimal.

whole = part ÷ (percentage ÷ 100)

Example: If 42 is 35% of a total, the total is 42 ÷ 0.35 = 120.

Quick reasonableness checks

10% is one tenth, so 10% of 300 must be 30.
50% is one half, so 50% of 80 must be 40.
If the rate is below 100% and the base is positive, the resulting part should normally be smaller than the base.
A percentage above 100% can be valid: 150% of 40 is 60.

Common mistake: Do not treat 15% as the number 15 in multiplication. Use 0.15, or divide by 100 as part of the formula.

Use the percentage calculators