SD, SE & CI Converter
Convert between standard deviation, standard error and confidence interval.
Enter your values to see the result.
Follows the Cochrane Handbook (section 6.5.2): SD = √n × SE, and SE = (upper − lower) ÷ (2 × critical value). For ratios such as odds ratios use the meta-analysis effect converter, which works on the log scale.
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Understand the method, inputs and limits behind your result.
- Formula
- SE = SD/√n and SD = SE√n. For a two-sided mean confidence interval, SE = (upper − lower)/(2 × selected critical value).
- Variables
- I have the: SD, SE, CI
- Mean
- Sample size (n)
- Standard deviation
- Standard error
- CI lower
- CI upper
- Confidence level: 90%, 95%, 99%
- Use the t distribution (recommended when n < 60)
- Units
- Use the units shown beside each input. Counts and ratios are dimensionless unless labeled otherwise.
- Example
- A mean of 52.3 with a 95% CI of 48.8 to 55.8 from 25 people gives an SE of 1.70 and an SD of 8.48 using the t distribution.
- Assumptions
- Follows the Cochrane Handbook (section 6.5.2): SD = √n × SE, and SE = (upper − lower) ÷ (2 × critical value). For ratios such as odds ratios use the meta-analysis effect converter, which works on the log scale.
- Last reviewed
- Review date not yet recorded.
Methodology & References
The method depends on the selected model and input options. Review the assumptions and references above before interpreting the result.
- Choose whether you have the SD, the SE or a confidence interval.
- Enter the mean, the sample size and the value you have.
- Read the other two measures.
Interpretation and limitations
- When should I use t rather than z? The Cochrane Handbook recommends t for samples under about 60, because the interval was probably calculated with t.
- Can I use this for odds ratios? No. Ratio intervals are symmetric on the log scale, so use the meta-analysis effect converter.
References
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Clear instructions
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How to use the SD, SE & CI Converter
Convert between standard deviation, standard error and confidence interval.
- 1 Choose whether you have the SD, the SE or a confidence interval.
- 2 Enter the mean, the sample size and the value you have.
- 3 Read the other two measures.
Example and practical tips
A mean of 52.3 with a 95% CI of 48.8 to 55.8 from 25 people gives an SE of 1.70 and an SD of 8.48 using the t distribution.
Further reading
Frequently asked questions
When should I use t rather than z?
The Cochrane Handbook recommends t for samples under about 60, because the interval was probably calculated with t.
Can I use this for odds ratios?
No. Ratio intervals are symmetric on the log scale, so use the meta-analysis effect converter.
Practical guides
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How to Use SD, SE & CI Converter
Convert between standard deviation, standard error and confidence interval of a mean, using t or z, following the Cochrane Handbook formulas.
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