About this tool
Percent change is the workhorse of comparison: stock returns, salary raises, price changes, weight loss. Always divide by the original value (A), not the new value (B). Going up 50% then down 50% does not get you back to start.
How it works
Enter two values. The calculator computes the absolute difference, the percent change, the multiplier, and the reverse change (what percent change goes from B back to A - usually different).
Quick math reference
| Operation | Formula | Example |
|---|---|---|
| Percentage of a number | value x percent / 100 | 20% of 150 = 150 x 0.20 = 30 |
| Percentage increase | (new - old) / old x 100 | from 80 to 100 = +25% |
| Percentage decrease | (old - new) / old x 100 | from 100 to 80 = -20% (not -25%) |
| Reverse percentage | value / (1 + rate) | $120 after 20% tax was $100 originally |
| Compound growth | P x (1 + r)^n | $1,000 at 7% for 10 years = $1,967 |
| Average (mean) | sum / count | (2+4+6+8) / 4 = 5 |
| Weighted average | sum(weight x value) / sum(weight) | Grade: (3x80 + 2x90) / 5 = 84 |
Why percentage gain != percentage loss
A 50% loss requires a 100% gain to recover. This asymmetry surprises most people:
- Down 10% -> need +11.1% to break even
- Down 20% -> need +25%
- Down 33% -> need +50%
- Down 50% -> need +100%
- Down 75% -> need +300%
- Down 90% -> need +900%
This is why limiting drawdowns matters more than capturing every up-day in investing.
Useful approximations
- Rule of 72: doubling time = 72 / rate. At 7%, money doubles in ~10.3 years. At 9%, in 8 years.
- Rule of 114: tripling time = 114 / rate.
- Rule of 144: quadrupling time = 144 / rate.
- Inflation halving: at 3% inflation, purchasing power halves in 24 years (72/3).
The formula explained
This calculator uses the following formula:
Percent change = ((B - A) / A) × 100 - positive means increase, negative means decrease
The reason this formula works is rooted in the underlying physics, finance, or biology of the problem. Behind every calculator is a published, peer-reviewed equation or a widely accepted convention. We do not invent formulas; we apply standard ones from textbooks, government tables, professional bodies, and academic literature.
If you are curious about the math, the simplest way to verify is to plug in two known numbers and compare against a known result. The calculator should match published examples to within rounding precision.
Frequently asked questions
Why is reverse change different?
Going from 100 to 150 is +50%. Going from 150 back to 100 is -33%. The base changes, so the percent does too.
Percentage points vs percent?
Going from 5% to 10% is +5 percentage points but +100% relatively. Always say which one you mean.
Compounding percent changes?
Multiply: a 10% gain followed by 10% gain is (1.1 × 1.1) - 1 = 21%, not 20%.
Negative numbers?
If A is negative, signs flip. Best practice: avoid percent change between numbers with different signs - use absolute change.
Is the calculator's precision exact?
JavaScript uses IEEE 754 double-precision floats. Most operations are accurate to ~15 significant digits. Currency calculations may show tiny rounding errors (0.1 + 0.2 = 0.30000000000000004) - this is normal and rounded for display.
Does the order of operations follow standard math rules?
Yes. Parentheses first, then exponents, then multiplication/division (left to right), then addition/subtraction. The calculator parses expressions accordingly.
What's the difference between mean, median, and mode?
Mean is the arithmetic average. Median is the middle value when sorted. Mode is the most frequent value. For skewed data (incomes, house prices), the median is more representative than the mean.
How do I calculate percentage difference between two numbers?
Use (new - old) / |old| x 100. The denominator is the ORIGINAL value, not the average. Going from 50 to 60 is a 20% increase. Going from 60 to 50 is a 16.7% decrease, not 20%.
How accurate is the Percentage Change Calculator?
It applies the standard formula. Accuracy is limited only by your input precision. For decisions with material consequences (taxes, medical, legal, structural), use the result as a starting point and verify with a qualified professional in the relevant field.
Is the Percentage Change Calculator free to use?
Yes. 100% free, no signup, no payment, no API key. The site is funded by display ads around the tool but not inside the calculation flow.
Are my inputs saved anywhere?
No. All inputs stay in your browser tab. Closing the tab discards them. The site uses Google Analytics for traffic measurement (anonymized) but the analytics never see what you type into the form.
Can I use the Percentage Change Calculator on my phone?
Yes. The tool is responsive and tested on iOS Safari, Android Chrome, and major desktop browsers. Touch targets meet Apple's 44pt and Google's 48dp minimum.
Does the Percentage Change Calculator work offline?
Yes. Once the page has loaded, it works without internet. The calculation runs in JavaScript on your device.
How do I report a bug or suggest improvement to the Percentage Change Calculator?
Email hi@3tej.com with the URL of this page and a description of what you saw vs expected. We typically respond within 72 hours.
Can I share results from the Percentage Change Calculator?
Take a screenshot or copy the output. The page doesn't generate shareable URLs for specific calculations - inputs stay in your browser only.
Why are the results different from another percentage change tool?
Most likely: different formula assumptions, different default values, different rounding rules, or different applicable rates. Check the methodology if both tools document it. Both can be valid for different scenarios.