Percentages without the head-scratching.
Twenty percent off. A 15% increase. A report saying something grew by five percentage points. These are small calculations that are surprisingly easy to mix up.
Pick the question you have and I’ll show the answer and how the math works.
What kind of percentage do you need?
Four percentage questions that come up all the time
Find a percentage: 20% of $150 is $30. Multiply 150 by 20, then divide by 100.
Find a share: 15 people out of 60 is 25%. Divide 15 by 60 and multiply by 100.
Find a change: Going from $80 to $100 is a 25% increase, because the $20 rise is one-quarter of the original $80.
Go backward: If a $100 price increased 20% to $120, divide $120 by 1.2 to find the original. If a $100 price dropped 20% to $80, divide $80 by 0.8.
Percent versus percentage points
Here’s a sneaky difference. Suppose a survey result goes from 20% to 25%. That’s a rise of 5 percentage points, but it’s a 25% relative increase because 5 is one-quarter of 20. This distinction matters whenever you’re comparing rates, not just dollar amounts.
Starting from zero needs special care. Going from zero sales to ten sales is an increase of ten, but the relative percentage change from zero is undefined. The calculator says so instead of inventing a percent.
Percentages are straightforward arithmetic; financial, tax, scientific and medical applications may require specific rounding rules. This tool doesn’t replace those rules.
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