About the Percentage Calculator
Percentages are one of the most useful pieces of everyday maths — they turn up in discounts, taxes, tips, interest, exam marks, statistics and news headlines. Yet the different “shapes” of percentage question trip people up constantly. This calculator handles the three core ones in one place: finding a percentage of a number, working out what percentage one number is of another, and calculating percentage increase or decrease — each with the formula and a worked example so the method sticks.
The three core calculations
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 15% of 200 = 30 |
| X is what percent of Y? | (X ÷ Y) × 100 | 45 of 180 = 25% |
| Percentage change | ((new − old) ÷ old) × 100 | 80 → 100 = +25% |
Percentage of a number
This is the most common case: a discount, a tip, a tax, a share of a total. Convert the percentage to a decimal by dividing by 100, then multiply. So 15% of 200 is 0.15 × 200 = 30. The same method finds a 7% sales tax on a ₹1,200 bill (₹84) or 60% of 50 marks (30).
What percentage one number is of another
Here you have a part and a whole and want the proportion. Divide the part by the whole and multiply by 100. If you scored 45 out of 180, that is (45 ÷ 180) × 100 = 25%. This is how you turn raw counts into comparable rates — marks into a percentage grade, or one figure into a share of a budget.
Percentage increase and decrease
To measure change, divide the difference by the original value (not the new one) and multiply by 100. Going from 80 to 100 is a 25% increase, because the 20 gained is measured against the starting 80. Going from 100 to 80 is a 20% decrease, because the 20 lost is measured against the starting 100. A subtle but important point follows: a percentage rise and the equal-sized fall are not symmetrical. A 20% drop from 100 lands at 80, and it then takes a 25% rise — not 20% — to climb back. This asymmetry explains why an investment that falls 50% needs to double (rise 100%) just to break even.
Percent versus percentage points
One of the most frequently muddled distinctions: a percentage point is the simple difference between two percentages, while a percent is a relative change. If an interest rate moves from 5% to 6%, that is an increase of one percentage point but a 20% increase in relative terms. Getting this right matters whenever you read about interest rates, poll numbers or market shares.
Reversing a percentage
Sometimes you know the figure after a change and want the original — the pre-tax price, or the price before a discount. Divide by the growth factor rather than subtracting the percentage. A price of ₹120 that already includes a 20% markup started at 120 ÷ 1.20 = ₹100; a sale price of ₹80 after a 20% discount started at 80 ÷ 0.80 = ₹100. Subtracting 20% of the final figure would give the wrong answer, a common and costly mistake.
Everyday uses
Once you recognise which of the three shapes a problem is, almost any everyday percentage becomes straightforward — discounts, GST, service charges, exam results, growth rates and more. For specific jobs, the Discount Calculator and Tip Calculator apply these same ideas with a tailored interface. Everything here runs instantly and privately in your browser.
Frequently Asked Questions
How do I find X% of a number?
Multiply the number by the percentage written as a decimal: X% of Y = (X ÷ 100) × Y. For example, 15% of 200 = 0.15 × 200 = 30.
How do I work out what percentage one number is of another?
Divide the part by the whole and multiply by 100: (part ÷ whole) × 100. For example, 45 out of 180 is (45 ÷ 180) × 100 = 25%.
How is percentage increase or decrease calculated?
Take the change, divide by the original value, and multiply by 100: ((new − old) ÷ old) × 100. A rise from 80 to 100 is a +25% increase; a fall from 100 to 80 is a −20% decrease. Note the two are not symmetrical, because the base differs.
Why isn’t a 20% drop cancelled by a 20% rise?
Because each percentage is taken from a different base. If 100 falls 20% to 80, a 20% rise on 80 only adds 16, giving 96 — not back to 100. To return to the original you would need a 25% rise.
What is the difference between “percent” and “percentage points”?
A percentage point is the arithmetic difference between two percentages, while a percent is relative. If a rate goes from 5% to 6%, that is a rise of 1 percentage point but a 20% increase. Mixing the two is a common source of confusion in news and finance.
How do I reverse a percentage — find the original before a change?
Divide by the growth factor. If a price is 120 after a 20% increase, the original was 120 ÷ 1.20 = 100. After a 20% discount to 80, the original was 80 ÷ 0.80 = 100.
Can I use this for discounts, tips, tax and marks?
Yes — they are all percentage problems. A 20% discount uses “percent of”; a test score uses “what percent”; a price change uses “increase/decrease”. For dedicated tools see the Discount and Tip calculators.