Blazon Research Resources · Statistical conversion
How to calculate standard error from a confidence interval
The basic relationship
When a two-sided confidence interval has the form:
estimate ± critical value × SE
the standard error can be recovered from the confidence limits.
Normal/Wald confidence interval to SE
For a confidence interval based on the standard normal distribution:
SE = (upper limit − lower limit) / (2 × z*)
For a 95% confidence interval, z* ≈ 1.959964.
Example
If the 95% CI is 10 to 14:
SE = (14 − 10) / (2 × 1.959964) ≈ 1.0204
t-based confidence interval to SE
If the interval was calculated using a Student t critical value:
SE = (upper limit − lower limit) / (2 × t*)
The critical value depends on both the confidence level and the degrees of freedom.
Cochrane notes that confidence intervals for continuous outcomes in smaller trials may have been constructed using t distributions, and that using the large-sample normal constants in those cases is inappropriate. Cochrane Handbook, Chapter 6
How do you know which interval type to use?
| Situation | Likely approach | What to check |
|---|---|---|
| Large-sample model estimate | Often normal/Wald | Methods section or model documentation |
| Mean from a small sample | Often t-based | Degrees of freedom and stated CI method |
| Welch procedure | t-based with possibly fractional df | Reported Welch/Satterthwaite df |
| Profile likelihood / bootstrap / exact CI | Not necessarily recoverable with the simple formula | Original interval method |
Why does asymmetry matter?
If a point estimate is not centered between the reported confidence limits on the relevant analysis scale, the simple SE reconstruction may not describe the original interval-generating procedure. Small differences can arise from ordinary rounding, so Statistical Converter uses a rounding-aware consistency check rather than a fixed percentage cutoff.
Confidence intervals for OR, RR and HR are different
Odds ratios, risk ratios and hazard ratios are normally analysed on the natural-log scale. Their confidence intervals therefore need to be evaluated on that scale before reconstructing the SE. Cochrane recommends log-transforming ratio measures for analysis and describes reconstructing SEs from confidence intervals on the log scale. Cochrane Handbook, Chapter 6
Read: Convert OR, RR and HR for meta-analysis →
Frequently asked questions
How do I calculate SE from a 95% confidence interval?
For a normal/Wald 95% CI, divide the interval width by 2 × 1.959964. For a t-based CI, use the corresponding t critical value instead.
Can I always divide a 95% CI width by 3.92?
No. That is the large-sample normal approximation. Smaller-sample mean intervals may require a t critical value, and some interval methods are not symmetric Wald-style intervals. Cochrane Handbook, Chapter 6
Can degrees of freedom be fractional?
Yes. Procedures such as Welch’s t test can use fractional degrees of freedom, and the Statistical Converter accepts them.
What if the confidence interval looks asymmetric?
Check whether the estimate and limits could differ simply because of rounding. If not, the original interval may have been calculated using a method that cannot be reduced to a single symmetric SE.
Can I calculate a confidence interval from SE?
Yes, when you know the point estimate, confidence level and the appropriate normal or t critical value.
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