Math
Percentage Calculator
Three percentage questions in one place: what is X% of a number, what percentage one number is of another, and how much something changed in percentage terms.
How to use this calculator
- Pick the type of question you want to answer.
- Enter the two numbers. The labels change to match the question.
- Read the result and the sentence that explains it in plain words.
Formula
X% of Y = X × Y ÷ 100 · X is (X ÷ Y × 100)% of Y · Change = (New − Old) ÷ Old × 100
- X, Y
- the two values you enter
- Old, New
- the before and after values in a percentage change
Percentage change is negative when the value falls.
Worked example
A salary rises from ₹50,000 to ₹57,500 a month.
- Difference57,500 − 50,000 = 7,500
- Divide by original7,500 ÷ 50,000 = 0.15
- Convert to percent0.15 × 100
That is a 15% increase.
The three questions
Almost every percentage problem is one of these three, and they use the same relationship rearranged.
- X% of Y: use it for discounts, tips, commission and tax on a known base.
- X is what % of Y: use it for marks out of a total, market share, or a part of a budget.
- Percentage change: use it for growth, price rises, and any before-and-after comparison.
Percentage points are not percentages
If an interest rate moves from 4% to 5%, that is a rise of one percentage point, but a 25% increase in the rate itself. Both statements are correct and they mean very different things. News reports about rates, vote shares and unemployment usually mean percentage points.
Why a rise and a fall of the same percentage do not cancel out
A 20% fall followed by a 20% rise does not return to the starting value. ₹100 falls to ₹80, and 20% of ₹80 is only ₹16, so you end at ₹96. The second percentage applies to a smaller base. Recovering a 20% fall actually needs a 25% rise.
Things to keep in mind
- Percentage change needs a non-zero starting value. Growth from zero cannot be expressed as a percentage.
- Results are shown to four decimal places where needed; round to the precision your situation requires.
Frequently asked questions
How do I calculate percentage of marks?
Use the second mode: enter the marks you scored and the total marks. If you scored 437 out of 500, that is 437 ÷ 500 × 100 = 87.4%.
How do I find the original price before a percentage increase?
Divide the new value by (1 + rate ÷ 100). A price of ₹1,180 after an 18% increase came from ₹1,180 ÷ 1.18 = ₹1,000. The GST calculator does exactly this for tax.
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- Old or new tax regime: which one fits youThe new regime has lower rates, the old one has deductions. Here is how to work out which leaves you with more, using your own numbers.1 min read
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