Statistics & graphs · SL/HL
Standard Deviation & Standard Error Calculator
Paste the replicate values. Sample SD uses n − 1; SE = sample SD/√n.
Your values
Start with the example or enter your own values. Use a dot for decimals and e for scientific notation.
Calculated locally. No account or input upload.
Result & working
ExampleThe calculator is loading. The worked example is also shown below.
Step-by-step working
The formula
sample SD = √[Σ(x−x̄)²/(n−1)]
SE = sample SD/√n
| Symbol | Meaning |
|---|---|
| SD | Spread of individual values around the mean. |
| SE | Uncertainty in the estimated mean due to sampling variability. |
When to use this calculator
State whether error bars represent SD, SE or another quantity; these are not interchangeable.
Worked example
The page opens with these example values. The result below is pre-generated for reference.
- mean = 5
- Σ(x−x̄)² = 0.1
- sample SD = √[0.1/(5−1)] = 0.1581139
- SE = SD/√n = 0.1581139/√5 = 0.07071068
sample SD = 0.1581139
Common mistakes
- Do not report error bars without saying what they show.