Old value to new value
Percentage change asks how far a number moved relative to where it started:
(new − old) ÷ old × 100
The Bureau of Labor Statistics uses this two-point form for index changes. A rise is positive; a fall is negative. Going from 50 to 40 is a 20% decrease, not “20% of 40.”
Rounding and zero
The difference and the percent are computed with exact millionths, then rounded half up to six decimal places. A repeating fall from 3 to 1 is −66.666667%.
Starting at zero is rejected. There is no unique percent that turns 0 into another number.
Example
50 to 60 is an increase of 10, or 20%. 50 to 50 is no change. 1 to 0 is −100%.
Limits
This is not an average annual rate, a CAGR or an inflation adjustment. It does not weight intermediate values. For “what percent is A of B” use the percentage calculator. For a sale price, use the discount calculator.
Frequently asked questions
Is a 50% fall then a 50% rise a wash?
No. 100 to 50 is −50%. 50 to 75 is +50%. You are not back to 100, because the
second move uses a smaller base.
Why do you refuse a starting zero?
Dividing by zero is undefined. A change from 0 to 10 is an amount of 10, but
it is not a percent of the start.
Are inputs stored or sent to analytics?
No. Values stay in page memory. Analytics may use the calculator identifier
only.
Sources & review
- How to Calculate Percent Changes — U.S. Bureau of Labor Statistics
- Calculating percent changes — U.S. Bureau of Labor Statistics
Last reviewed: . The formula is reproduced above so you can check the math independently.
A two-point comparison of the numbers you enter. Not an average, compound or inflation-adjusted rate.