Type your numbers in, separated by commas, and get the spread back: mean, variance, standard deviation and standard error in one press. This is the calculator you want open when a lab report asks you to show the variability of your trials and you have six readings sitting in a table.
It is for intro stats, biology and psych labs, and for anyone double-checking a spreadsheet result. One box, one button, no settings to pick. It wants at least two values, comma separated.
The one detail worth knowing before you press anything: it divides by n-1, so you are getting sample standard deviation, not population. If those six numbers are the whole population you care about, the figure will read slightly high. The section near the bottom covers which one you actually need.
Calculate standard deviation, variance, and standard error from a data set. Enter comma-separated values.
How it works
Enter something like 12, 15, 18, 14, 16, 20 and press Calculate. The tool splits the text on commas, trims the spaces, and rejects anything that is not a number. Two values is the minimum, and if you type fewer it says so instead of quietly dividing by zero.
From there it runs five steps. Add the values, divide by n, and you have the mean. Take each value minus the mean, square it, and add those squares up. Divide that sum by n-1 for the sample variance. Take the square root for the standard deviation. Then divide the standard deviation by the square root of n for the standard error. Every one of those five numbers comes back rounded to four decimal places.
Reset clears the box and the result. Nothing is stored and nothing is sent anywhere, which is a small mercy when the numbers are your own grades.
A worked example
Six trial readings: 12, 15, 18, 14, 16, 20. They add to 95, so the mean is 95 ÷ 6 = 15.8333.
Each value minus the mean comes out at -3.8333, -0.8333, 2.1667, -1.8333, 0.1667 and 4.1667. Square those and you get 14.6944, 0.6944, 4.6944, 3.3611, 0.0278 and 17.3611, which add to 40.8333. Divide by five rather than six, because n-1 is 5 here, and the sample variance is 8.1667. Square root of that is a standard deviation of 2.8577.
Standard error is 2.8577 ÷ √6 = 2.8577 ÷ 2.4495 = 1.1667. You quote that second figure when the claim is about how well this sample mean estimates the true mean, and it should be much smaller than the standard deviation, because averages are steadier than individual readings. If your standard error ever comes out larger than your standard deviation, something is off in the input.
A second set, five quiz scores: 88, 92, 79, 95, 84. Mean is 438 ÷ 5 = 87.6, the squared deviations add to 161.2, so the variance is 161.2 ÷ 4 = 40.3000, the standard deviation is 6.3482, and the standard error is 2.8390. Read that as a spread of about six points around an average that is itself good to roughly three points.
Sample or population, and the other traps
The divisor is the whole argument. Dividing by n-1 corrects the fact that a sample tends to sit closer to its own mean than to the population mean, and it gives an unbiased estimate of the population variance. Divide the same six numbers by six instead and you get a variance of 6.8056 and a standard deviation of 2.6087, about nine percent smaller. When you are reporting a lab result, a run of measurements taken as a sample of a larger process, use what this tool gives you.
The four decimal places are arithmetic precision, not measurement precision. Your balance reads to two decimals, your graduated cylinder to half a millilitre, so round to whatever your equipment justifies before you write the number in a report.
Two more things people get wrong. Standard error does not describe how spread out your data is, it describes how reliable the mean is, and it shrinks as the square root of n, so going from 6 readings to 24 only halves it. And standard deviation will happily report a huge number if one value is a typo.
Other tools
- Stress level checker — when the numbers that matter are about you rather than a data set
- T-test calculator — the next step, comparing the means of two samples
- Task priority matrix — for the rest of the lab report sitting around the analysis
Frequently asked questions
What is the difference between standard deviation and standard error?
Standard deviation describes how spread out your individual values are. Standard error describes how much the sample mean would vary if you drew the sample again. Same data, two different claims: one about the observations, one about the average.
Which one should I put in my lab report?
Whichever your instructor asks for. Reporting the spread of your trials is a standard deviation; stating how precise an estimate is, usually in a caption, is a standard error. A paper that quotes both wants both.
Why does it divide by n-1?
Because a sample underestimates the spread of the population it came from. Dividing by n-1, sometimes called Bessel’s correction, removes that bias. With three values you are dividing by two, so the gap between the two methods is obvious.
How many values do I need for this to mean anything?
Two is the mathematical minimum, and it is not statistics. Under about five the standard deviation barely holds still and moves if one value changes. Around twenty to thirty is where the figure starts behaving.
Does the order of the numbers matter?
No. The mean, variance, standard deviation and standard error are all order-independent, so 12, 15, 18 gives the same answer as 18, 12, 15. Only the values and their count change the result.