How to Calculate Percentages: 5 Everyday Sums

What a percentage is, and which formula to use

A percentage (%) means “out of 100”. 15% is 15 out of 100, or 15 ÷ 100 = 0.15. Almost every percentage sum comes down to one question: which number is the base, or “whole”? Get that right and the rest is simple division and multiplication. Nearly every everyday question is one of these 5:

Choose the question and enter two numbers, and the Percentage Calculator does all 5 with the working shown. Below, each one is worked by hand.

1. A percent of a number, and 2. what percent

What is P% of Y

Divide the percentage by 100 and multiply by the number. 15% of 2,000 = 15 ÷ 100 × 2,000 = 300. And 12.5% of 240 = 0.125 × 240 = 30.

A quick mental check: 10% means divide by 10. 10% of 2,000 is 200, 5% is half that, 100, so 15% is 200 + 100 = 300.

X is what percent of Y

Divide the part by the whole and multiply by 100. Scoring 45 in a 60-mark exam is 45 ÷ 60 × 100 = 75%. The whole can’t be 0. If the part is bigger than the whole, the answer is over 100%: 50 is 250% of 20.

3. Percentage increase or decrease

Percentage change = (new value − starting value) ÷ starting value × 100. A positive answer is an increase, a negative one a decrease.

• From 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase.
• From 100 to 80: (80 − 100) ÷ 100 × 100 = −20%, that is a 20% decrease.

The difference is 20 both times, but the percentages differ, because you divide by the starting value and the starting value is different each time. If the starting value is 0, there is no percentage change. If it is negative, the calculator divides by its size, so going from −50 to −25 is a 50% increase, because the value really did go up.

4. Increasing or decreasing a number by a percent

To increase, multiply by (1 + P ÷ 100); to decrease, multiply by (1 − P ÷ 100). That saves working out the percentage separately and then adding or subtracting it.

• 1,000 increased by 10%: 1,000 × 1.10 = 1,100.
• 200 decreased by 15%: 200 × 0.85 = 170 (30 less).

Decreasing by more than 100% takes you below zero: 100 decreased by 150% is −50. That is correct maths, but things like prices or weights can’t go below zero, so if you get an answer like this, check the question again.

5. Reverse percentage: finding the original number

When you know a part and its percentage but not the whole, divide the part by (percentage ÷ 100). If 25 is 20% of a number, the number is 25 ÷ 0.20 = 125.

Shops make you do this often. If the price after a 15% discount is ৳170, you are paying 85% of the original price. So the original price = 170 ÷ 0.85 = ৳200. To see the sale price and how much you save directly, the Discount Calculator helps.

Common mistakes

• Adding and subtracting percentage changes. 100 increased by 25% is 125, but decreasing that by 25% takes off 25% of 125, which is 31.25, leaving 93.75, not 100. Getting back to 100 takes a 20% decrease. In the same way, two 10% rises make 21%, not 20% (1,000 → 1,100 → 1,210).
• Mixing up percent and percentage points. An interest rate going from 9% to 10% is a rise of 1 percentage point. As a percentage change it is (10 − 9) ÷ 9 × 100 ≈ 11.11%. Check which one a news report or offer means.
• Using the wrong base in a reverse percentage. Adding 15% back on to a ৳170 sale price gives ৳195.50, not the original ৳200, because the 15% was of ৳200, not ৳170. Divide, don’t add.
• Dividing a change by the new value. The rise from 80 to 100 is 20 ÷ 80 = 25%, not 20 ÷ 100 = 20%. Always divide by the starting value.

3 steps before any percentage sum

1. Decide which number is the base, or “whole”: the starting price, the total marks, or an unknown original.
2. Check whether you know the percentage or are looking for it, and pick the formula from the table above.
3. Check the answer makes sense, for example with a rough 10% estimate.

Rather than working it by hand, enter your numbers in the Percentage Calculator. Alongside the answer you get a sentence and the full working, so it is always clear which number was used as the base.