Percentage calculator

How to work with percentages

A percent (%) is one hundredth of a whole. 100% is the whole, 50% is half, 1% is a hundredth. Percentages are useful for comparing proportions independently of size – “15% of $170” and “15% of a million” express the same ratio.

What is X% of a number

Divide the percentage by 100 and multiply by the base:

X% of Y = (X ÷ 100) × Y

Example: 15% of 200 = 0.15 × 200 = 30.

What percentage one number is of another

Divide the part by the whole and multiply by 100:

part ÷ whole × 100 = %

Example: 30 out of 200 = 30 ÷ 200 × 100 = 15%.

Percentage change (increase and decrease)

Divide the difference by the original value and multiply by 100:

(new − original) ÷ original × 100 = change in %

Example: from 200 to 250 is an increase of (250 − 200) ÷ 200 × 100 = +25%. Note: a 25% increase followed by a 25% decrease does not return to the original value – percentages are always computed from the current base.

Percent vs. percentage points

When an interest rate rises from 2% to 3%, that is an increase of 1 percentage point, but 50 percent (relatively). Percentage points compare the difference between two percentages; percent compares the relative change.