Calculate percentages, increases and decreases
30
15% of 200 is 30
Percentage questions come in several shapes and they are easy to mix up. Asking what fifteen percent of two hundred is, and asking what percent thirty is of two hundred, produce different answers from the same two numbers. This handles five distinct forms — percentage of, is-what-percent, change between two numbers, and adding or subtracting a percentage — and writes each answer out as a sentence you can copy into a message or an invoice.
The trap of compounding percentages
Percentages do not add up the way intuition suggests, because each one applies to whatever the number is at the time. A shirt marked up 50% and then discounted 50% ends at 75% of its original price, not back where it began. A salary rising 10% for three years rises by 33%, not 30%. And a portfolio that falls 50% needs a 100% gain to recover. In each case the base changed between the two operations, and the second percentage is measured against the new base rather than the old one.
Percent against percentage points
This distinction matters whenever a rate is the thing changing. If a home loan rate moves from 8% to 9%, that is one percentage point — but also a 12.5% increase in the rate, and it raises the interest on a ₹50 lakh loan by considerably more than the small-sounding single point implies. Financial coverage often reports the point change because it is the smaller number, while the effect on your EMI follows the proportional one. When a figure seems surprisingly small or large, checking which of the two is being quoted usually explains it.
Reversing a percentage
Removing a percentage is not the same as subtracting it, and this is where GST and discounts trip people up. If a bill of ₹1,180 includes 18% GST, the base is ₹1,180 divided by 1.18, which is ₹1,000 — not ₹1,180 minus 18%, which gives ₹967.60 and is simply wrong. The same applies to discounts: to find the original price of an item bought at ₹2,000 after 20% off, divide by 0.8 to get ₹2,500, rather than adding 20% to get ₹2,400.
Frequently asked questions
- What is the difference between 'X% of Y' and 'X is what % of Y'?
- The first multiplies: 15% of 200 is 30. The second divides: 30 is 15% of 200. Same three numbers, opposite operations, and mixing them up is the most common percentage error there is.
- How do I calculate percentage increase?
- Subtract the old value from the new, divide by the old, and multiply by 100. Going from 100 to 150 is a 50% increase. Note it is divided by the starting number, not the ending one.
- Does a 50% rise then a 50% fall return me to where I started?
- No, and this catches people out constantly. 100 plus 50% is 150; 150 minus 50% is 75. The percentages apply to different bases, so they never cancel out.
- What is the difference between percent and percentage points?
- If a rate moves from 5% to 7%, that is a rise of two percentage points but a 40% increase. News reports frequently confuse the two, and the difference can be large.
- How do I remove GST from a total?
- Divide by 1 plus the rate, not by subtracting the rate. For 18% GST, divide the total by 1.18. Subtracting 18% from the inclusive figure gives the wrong answer.
- How do I work out a discount?
- Use the subtract option. 20% off ₹2,500 leaves ₹2,000. To find the original price from a discounted one, divide rather than add the percentage back.
- Is any of this sent to a server?
- No. It is arithmetic done in this page, so it works with your connection off and nothing you type is recorded.