Convert a Confidence Interval to a Standard Error Carefully

Inspect how the interval was constructed

A confidence interval can sometimes supply a missing standard error, but its endpoints are not sufficient by themselves. First record the estimate, confidence level, effect measure, and stated analysis method. Inspect the methods section or supplement for a normal approximation, t distribution, bootstrap, profile likelihood, or another construction.

The familiar conversion applies to an interval formed as estimate plus or minus a critical value times its standard error, on the appropriate analysis scale. Cochrane's effect-measure chapter explains recovering standard errors from intervals, including ratio measures on a logarithmic scale.

Convert a difference on its reported scale

For a normal-approximation two-sided 95% interval, divide the interval width by twice 1.959964. In a fictional example, a difference of 3.00 has endpoints 1.04 and 4.96. The width is 3.92, so the recovered SE is approximately 1.00. Rounded endpoints explain the tiny difference from exactly one.

The confidence-interval-to-SE calculator supports normal critical values for 90%, 95%, and 99% intervals. Select the reported level; do not treat every interval as 95%. Preserve more input digits when the source provides them, and round only the final displayed result.

Use logarithms for ratio intervals

For a ratio analyzed on the log scale, the corresponding calculation uses log(upper) minus log(lower), divided by twice the critical value. The result is an SE for the log ratio, not an SE on the original ratio scale. Both endpoints must be positive.

Check that the point estimate is reasonably centered on the relevant scale. Pronounced asymmetry, beyond ordinary rounding, is a reason to investigate the interval method rather than force a conversion. This diagnostic is useful but does not prove the method.

Know when to stop

An interval for a small-sample mean commonly uses a t critical value. NIST's confidence-limit explanation shows the dependence on sample size and degrees of freedom. The normal-only calculator does not recover that exact SE.

Do not apply the width shortcut automatically to bootstrap, exact, profile-likelihood, or transformed intervals whose construction is unknown. Seek the reported SE or contact the authors. Save the original interval, conversion scale, critical value, and assumption in the extraction record so later reviewers can distinguish reported information from a reconstructed quantity.

Sources checked on 30 October 2026; numerical example independently recalculated.