Standard Deviation Calculator
Paste or type a list of numbers to get the standard deviation and variance for both a sample and a whole population, along with the mean, count, sum and a table showing the working.
Runs in your browser. Your files are never uploaded.
Loading Standard Deviation Calculator…
How to use Standard Deviation Calculator
- Enter your numbers separated by commas, spaces or new lines.
- Read the sample and population standard deviation and variance.
- Check the mean, count, sum and range.
- Use the table to see each value’s deviation from the mean and its square.
The formulas
First find the mean, which is the sum divided by the count. Next find each value’s deviation from the mean and square it. Add the squared deviations together. Dividing that total by n gives the population variance, and by n − 1 gives the sample variance. The standard deviation is the square root of the variance.
Worked example: for 2, 4, 4, 4, 5, 5, 7, 9 the mean is 40 / 8 = 5. The squared deviations are 9, 1, 1, 1, 0, 0, 4, 16, which sum to 32. The population variance is 32 / 8 = 4, so the population standard deviation is 2. The sample variance is 32 / 7 ≈ 4.571, so the sample standard deviation is about 2.138.
Reading the result
- About two thirds of values lie within one standard deviation of the mean when data are roughly bell-shaped; this is a rule of thumb, not a guarantee for every data set.
- Compare spread between data sets only when they use the same units and similar means.
- Outliers inflate the standard deviation because deviations are squared.
- Variance is in squared units, which is why the square root is usually reported.
Limits and privacy
The calculator treats every entry as an equally weighted observation; it does not handle frequency tables or weighted data. Non-numeric entries are flagged instead of ignored so mistakes are visible. Calculations use standard floating-point numbers, so extremely large values may lose precision. Your data never leaves your browser.
Why use this standard deviation calculator tool
- Both formulas. Shows population (divide by n) and sample (divide by n − 1) results side by side.
- Full working. A table lists each value, its deviation from the mean and the squared deviation.
- Flexible input. Accepts commas, spaces, semicolons and new lines, so you can paste from a spreadsheet column.
- Large lists. Handles up to 100,000 values; the table shows the first 200 for readability.
Frequently asked questions
Sample or population: which should I use?
Use the population formula when your numbers are the whole group you care about. Use the sample formula when they are a sample drawn from a larger group, because dividing by n − 1 corrects the tendency of a sample to underestimate spread.
What does standard deviation mean?
It is a typical distance of values from the mean, in the same units as the data. A small value means the data are tightly clustered; a large one means they are spread out.
Why is the sample result blank for one value?
The sample formula divides by n − 1, which is zero for a single value, so sample statistics are undefined.
More free tools
Calorie and BMR Calculator
Estimate your basal metabolic rate with the Mifflin-St Jeor equation, daily calories for your activity level, and calorie targets for losing or gaining weight.
Open toolPregnancy Due Date Calculator
Estimate your due date from the first day of your last period (with cycle length) or conception date, see weeks pregnant today and trimester dates.
Open toolFraction Calculator
Free fraction calculator for mixed numbers and fractions. Add, subtract, multiply or divide and get the simplified fraction, mixed number, decimal and steps.
Open tool