Standard Deviation Calculator
Paste numbers separated by commas or spaces to see the mean, the variance, and the standard deviation for a sample or a population.
How to use
- Paste or type into the number box. Commas, spaces, and semicolons all separate values. The placeholder example is 2, 4, 4, 4, 5, 5, 7, 9.
- Set Type to Sample (n−1) or Population (n). Sample divides the sum of squared differences by one less than the count. Population divides by the count itself.
- Press Calculate. For the placeholder list the mean is 5. The population variance is 4 and the population standard deviation is 2. The sample variance is 32/7, about 4.571429, and the sample standard deviation is about 2.13809.
- The main line is labeled with a sigma. The detail line repeats the mean, the variance, and n. You need at least two numbers. One number, or a box that parses to fewer than two numbers, shows Enter at least 2 numbers.
When it helps
Compare a short lab set or a quiz column when you already have the raw scores. Switching Type on the same paste shows why a sample spread is larger than a population spread: the divisor shrinks from n to n−1 while the squared gaps stay the same.
The page will not turn the spread into a letter or a percentile rank. If you need "this score is what percent of that total" before you paste, use the percentage calculator. A one-off square root or power that is not a full list belongs on the scientific calculator.
Limits
Sample mode needs at least two numbers because it divides by n−1. The form applies that same two-number minimum to Population as well, so a one-value population is refused even though some textbooks would call its variance zero. The message is Enter at least 2 numbers in both cases.
There is no frequency table, no histogram, and no button to remove an outlier. Each pasted value counts once. The result uses the symbol sigma even when Type is Sample, where a textbook might write s. Grouped data such as "12 students scored 80" must be expanded into repeated numbers.
Questions
Which Type should I pick?
Sample (n−1) when the list is a subset of a larger group. Population (n) when the list is everyone you care about. The mean is the same either way; the variance and the standard deviation change.
Why were some tokens ignored?
The box splits on commas, spaces, and semicolons, then keeps only tokens that parse as numbers. A label such as score is discarded instead of failing the whole list.
Can I calculate with a single measurement?
No. Fewer than two numbers stops at Enter at least 2 numbers, including when Type is Sample (n−1), where dividing by zero would be meaningless.