Percentage Calculator: Formula, Examples and How to Use It
Percentages express a quantity as parts per hundred. They are useful for discounts, exam scores, price changes, survey results and comparing values. This guide explains which calculation to use for each question instead of treating every percentage problem the same way.
1. Find a percentage of a number
Use this when the question asks “What is X% of Y?” Convert the percentage to a decimal by dividing by 100, then multiply it by the base number.
Example: 15% of 240 = (15 ÷ 100) × 240 = 0.15 × 240 = 36. The answer is 36, in the same units as the original number.
2. Calculate a percentage of a total
To find what percentage one value represents of another, divide the part by the total and multiply by 100. The total should be the correct whole for the comparison.
Example: 42 correct answers out of 60 = (42 ÷ 60) × 100 = 70%. If the total is zero, this percentage is undefined.
3. Work out a discount
Calculate the saving first, then subtract it from the original price.
Example: A ₹1,500 item has a 20% discount. Saving = ₹1,500 × 0.20 = ₹300; sale price = ₹1,200 before any additional taxes, delivery fees or charges.
4. Percentage increase or decrease
For a change between an old value and a new value, use the old value as the base. A positive result is an increase; a negative result is a decrease.
Example: A value changes from 80 to 100. Change = 20; 20 ÷ 80 × 100 = 25% increase. If the old value is zero, the percentage change formula cannot be used.
Common mistakes to avoid
Do not confuse percentage points with percent change. A rate rising from 10% to 12% rises by 2 percentage points, which is a 20% relative increase from the original rate. Always check which number is the base, and keep the same units on both values.
For ordinary non-negative values, 10% should be one tenth and 50% should be one half. Estimating first can reveal a misplaced decimal or incorrect base.
Frequently asked questions
Can a percentage be greater than 100%?
Yes. For example, 150% of 40 is 60. A part can exceed a reference total, or a value can increase by more than its original amount.
Why does the base value matter?
The same difference can represent different percentages when the starting values differ. A rise of 10 from 20 is 50%, while a rise of 10 from 100 is 10%.
When is percentage change undefined?
When the original or starting value is zero, the standard percentage-change formula divides by zero. Describe the absolute change instead or choose a meaningful non-zero reference.
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