Percentage Calculator
Solve the three everyday percent problems: what percent, percent of, and percent change.
What it does
Almost every percent question is one of three shapes. Sharing questions ask what share one number is of another. Taking questions ask for a slice of a number. Change questions ask how far a number moved in relative terms.
The tool above handles all three. Pick the shape, enter the two numbers, and the answer updates as you type. Each answer prints one line of working so you can check it.
Percent change deserves care because direction matters. A rise from 45 to 60 is plus 33.33%, while the fall back from 60 to 45 is minus 25%. Same gap in points, different base, different percent.
How to use
- Pick the problem type that matches your question.
- For shares: enter the part first, the whole second.
- For slices: enter the percent first, the base second.
- For change: enter the starting value first, the new value second.
Formula
- X / Y
- Share of a whole, times 100 for percent.
- X / 100 x Y
- Slice: rate times base.
- (Y - X) / X
- Change relative to the start, signed.
Change divides by the starting value, never the new one. That is why a 50% drop needs a 100% rise to recover: the base shrinks halfway down. Percent change from zero is undefined because division by zero has no answer.
Worked example
Example: price moves from $45 to $60
Start 45, new value 60, using the change form.
- Gap: 60 - 45 = 15.
- Divide by the start: 15 / 45 = 0.3333.
- Multiply by 100: 33.33%.
- Sign: positive, so a 33.33% rise.
- Reverse check: 25% down from 60 is 45, since 15 / 60 = 0.25.
Reference table
| Words | Math | Example |
|---|---|---|
| 50% of | half | 50% of 80 = 40 |
| 25% of | one quarter | 25% of 80 = 20 |
| 10% of | one tenth, move decimal one place | 10% of 80 = 8 |
| Percent change up | new above start | 45 to 60 is +33.33% |
| Percent change down | new below start | 60 to 45 is -25% |
Limits
- Change from zero is undefined.
- Percents across different bases do not add.
- Falls cannot pass minus 100% for positive quantities.
- Rounded inputs give rounded answers.
Common mistakes
- Dividing change by the new value instead of the start.
- Adding percents across different bases, such as plus 20% then minus 20% expecting flat.
- Reading points as percents. A move from 10% to 15% is 5 points but a 50% relative rise.
- Rounding mid way. Keep full digits until the last step, then round once.
- Forgetting the sign on change, which states rise or fall.
Try it yourself
Quick checks. Answers sit tucked under each question.
Percent change from 200 to 150?
(150 - 200) / 200 = -25%.
30% of 90?
0.30 x 90 = 27.
Questions
What is the difference between percent and points?
Points are the plain gap between two rates; percent change is relative. From 10% to 15% is 5 points, which equals a 50% relative rise.
Why is down 50% then up 50% not flat?
The bases differ. Down 50% halves the number, then up 50% adds half of the smaller value, landing at 75% of the start.
How do I find the original before a percent rise?
Divide the final value by one plus the rate. After a 20% rise to 60, the start was 60 / 1.20 = 50.
Can percent change exceed 100%?
Yes for rises. Doubling is plus 100%, tripling is plus 200%. Falls cannot pass minus 100% for positive quantities.
What does percent change from zero give?
No answer. Division by zero is undefined, so the tool asks for a non-zero start.