Blazon Research Resources · Statistical conversion
How to convert standard error and standard deviation
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What is the difference between SD and SE?
The standard deviation (SD) describes variability among observed values. The standard error (SE) describes uncertainty in an estimated quantity. For an arithmetic mean calculated from independent observations, the standard error becomes smaller as the sample size increases because the mean is estimated more precisely.
This distinction matters in evidence synthesis and data extraction. Cochrane explicitly warns that confusing an SE with an SD can be misleading, and notes that review authors often need to reconstruct SDs when studies report alternative measures of variability or precision. Cochrane Handbook, Chapter 6
Convert SD to SE
For the standard error of an arithmetic mean:
SE = SD / √n
Example
If SD = 10 and n = 25:
SE = 10 / √25 = 2
Convert SE to SD
Rearranging the same relationship gives:
SD = SE × √n
Example
If SE = 2 and n = 25:
SD = 2 × √25 = 10
When is this conversion useful?
Common use cases include:
- extracting study-level data for meta-analysis when a paper reports SE instead of SD;
- checking whether a table has reported SD or SE;
- converting summary statistics into a common format before effect-size calculation;
- reconstructing study summaries for secondary analysis.
Cochrane specifically states that an SD can be recovered from the SE of a group mean by multiplying the SE by the square root of the sample size, while emphasizing that the SE must refer to the mean within a single intervention group. Cochrane Handbook, Chapter 6
What if the study reports a confidence interval instead?
A confidence interval can often be used to estimate the corresponding SE, but the calculation depends on how the interval was constructed. A large-sample normal/Wald interval uses a normal critical value, whereas smaller-sample intervals around means commonly use a t critical value. Treating every 95% CI as ±1.96 SE can therefore be inappropriate. Cochrane Handbook, Chapter 6
Read: How to calculate SE from a confidence interval →
When do you need another Blazon tool?
If you are working with pre/post measurements or change scores, a direct SD↔SE conversion may not be enough because the within-participant correlation can affect the required variance calculation.
Pre/Post & Change-Score Calculator → Study Effect Size Calculator →
Frequently asked questions
How do I convert SE to SD?
For the standard error of a sample mean, multiply SE by the square root of the sample size: SD = SE × √n.
How do I convert SD to SE?
Divide the SD by the square root of the sample size: SE = SD / √n.
Can I convert any SE to an SD?
No. The formula depends on what the SE represents. The simple SD↔SE relationship applies specifically to the SE of an arithmetic mean from independent observations.
Why do meta-analysts often need SD rather than SE?
Many continuous-outcome effect-size calculations require group SDs. Papers may report SEs or confidence intervals instead, so reviewers often need to reconstruct a usable measure of variability. Cochrane Handbook, Chapter 6
Does the Statistical Converter upload my values?
No. Calculations are performed locally in your browser, and no AI is used.
References
- Higgins JPT, Li T, Deeks JJ, eds. Chapter 6: Choosing effect measures and computing estimates of effect. In: Cochrane Handbook for Systematic Reviews of Interventions, version 6.5. Cochrane; 2024. Cochrane Handbook, Chapter 6