Calculator Input
Formula Used
SE = SD / √n
SD = SE × √n
Variance = SD²
Margin of Error = z × SE
CV% = (SD / |Mean|) × 100
Standard error measures how precisely a sample statistic estimates the population value. Standard deviation measures how spread out the original observations are. When you know standard error and sample size, you can recover the implied standard deviation by multiplying the standard error by the square root of the sample size.
This works only when the reported standard error follows the usual definition based on the same sample size.
How to Use This Calculator
- Enter the dataset label if you want named exports.
- Type the known standard error value.
- Enter the sample size used to compute that standard error.
- Optionally add the sample mean for CV and relative error outputs.
- Select confidence level and decimal places.
- Press the calculate button to show the result above the form.
- Use the CSV or PDF buttons to export the result summary.
Example Data Table
| Case | Standard Error | Sample Size | Standard Deviation | Variance |
|---|---|---|---|---|
| Survey Response Set | 1.20 | 25 | 6.00 | 36.00 |
| Clinical Measure | 0.85 | 64 | 6.80 | 46.24 |
| Manufacturing Sample | 2.10 | 36 | 12.60 | 158.76 |
| Exam Score Batch | 1.75 | 49 | 12.25 | 150.06 |
FAQs
1. What does standard error represent?
Standard error measures the uncertainty of a sample statistic, such as a mean. Smaller values usually mean the estimate is more precise for the given sample size.
2. How do I convert standard error to standard deviation?
Multiply the standard error by the square root of the sample size. The formula is SD = SE × √n.
3. Why is sample size required?
Standard error depends on both spread and sample size. Without n, you cannot recover the original standard deviation from the reported standard error.
4. Does confidence level change the standard deviation?
No. Confidence level affects the margin of error, not the converted standard deviation. The SD comes only from standard error and sample size.
5. What happens if I leave mean blank?
The core conversion still works. Only relative standard error and coefficient of variation need a non-zero mean.
6. Can I reverse the process later?
Yes. Once you know standard deviation and sample size, you can recalculate standard error with SE = SD / √n.
7. Is this valid for any reported standard error?
It is valid when the standard error follows the usual formula based on the same sample size. Always confirm the source method matches that assumption.
8. When should I report SE instead of SD?
Use SD to describe data spread. Use SE to describe estimate precision. They answer different questions and should not be used interchangeably.