How to Calculate Percentages: Of, What Percent and Change

“Is 15% off a good deal?” “My rent went up 8%.” “I scored 45 out of 180.” All three are percentage questions, but each needs a different calculation. The Percentage Calculator has a mode for each, and knowing which one you need is most of the work.

1. A percent of a number

Multiply the number by the percentage divided by 100. 15% of 240 is 240 × 0.15 = 36. Use this for tips, taxes, discounts and commissions.

2. What percent one number is of another

Divide the part by the whole and multiply by 100. 45 out of 180 is 45 ÷ 180 = 0.25, which is 25%. The order matters: the whole always goes underneath.

3. Percentage change

Subtract the old value from the new one, divide by the old value, and multiply by 100. Going from 80 to 100 is a rise of 20 ÷ 80 = 25%. Going back from 100 to 80 is a fall of 20 ÷ 100 = 20%. The same 20-point gap gives different percentages because each change is measured against its own starting point.

Using the calculator

1. Choose the mode: “of”, “what percent” or “change”.
2. Enter the two values. In “change” mode, X is the old value and Y the new one.
3. Read the sentence it returns, such as “an increase of 25% (from 80 to 100)”.

Y cannot be zero in the “what percent” and “change” modes, since dividing by zero has no answer.

Mistakes to watch for

• Percentage points versus percent. If an interest rate moves from 4% to 5%, that is one percentage point, but a 25% increase in the rate.
• Reversing a change. A 50% drop needs a 100% rise to get back, because the base shrank.
• Adding percentages. A 10% rise followed by a 10% fall is not back to the start; it ends at 99% of the original.

Frequently asked questions