Convert between standard deviation (SD), standard error (SE), 95% confidence interval width, and sample size. Enter any two known values and the tool computes the remaining two instantly.
Enter any two of the four values below. The tool will compute the remaining values using the relationships SE = SD / √N and CI half-width = 1.96 × SE.
Example: SD = 10, N = 25 → SE = 2.0, 95% CI half-width = 3.92. All calculations assume a normal (z-based) approximation with z = 1.96 for the 95% confidence level.
Check which statistics your source paper reports: SD, SE, sample size, or confidence interval bounds.
Fill in exactly two of the four fields. You can also enter CI lower and upper bounds instead of the half-width.
Click Calculate to derive the missing values. The tool shows all four quantities plus the formulas used.
Click Copy to copy all computed values to your clipboard for pasting into your extraction spreadsheet.
Standard deviation quantifies variability within a sample, while standard error quantifies uncertainty of the sample mean. They are related by SE = SD / √N but answer fundamentally different questions.
Most pooling methods weight studies by the inverse of their variance (SE²). When a paper reports only the SD, you must convert to SE using the sample size before entering data into your meta-analysis.
A 95% CI of (lower, upper) implies SE = (upper – lower) / 3.92. This is invaluable when papers report CIs but not the SE or SD directly. Always check whether the CI is z-based or t-based.
Watch for papers that label SE as “SD” or vice versa, report SE of the median rather than the mean, or use non-standard confidence levels (90% or 99%). Always verify by cross-checking sample size, SD, and CI when multiple statistics are available.
An SE to SD converter addresses one of the most common data-extraction obstacles in systematic reviews: primary studies report variability in inconsistent formats. Standard deviation describes the dispersion of individual observations around the sample mean, while standard error quantifies the precision of that mean as an estimate of the population parameter. The Cochrane Handbook (Higgins et al., 2023, Chapter 6) defines the relationship as SE = SD / √N and notes that meta-analytic software weights each study by the inverse of the squared SE, making accurate conversion critical for valid pooling. Altman & Bland (2005), writing in the BMJ, warned that confusing SD with SE is among the most frequent statistical errors in published clinical research—a mistake that inflates or deflates a study's apparent precision and can bias the pooled estimate. In random-effects meta-analysis, the Knapp–Hartung adjustment uses study-level SEs to construct pooled confidence intervals with a t-distribution rather than a normal approximation, improving coverage when the number of studies is small. When only a p-value and point estimate survive from the original report, our p-value to confidence interval converter reconstructs the 95 % CI, from which the SE can then be derived using this tool.
A standard error calculator must also handle the reverse pathway: deriving SD from a reported confidence interval. The formula SE = (upper − lower) / 3.92 assumes a z-based 95 % CI; for small samples where a t-distribution was used, the critical value must be adjusted for the appropriate degrees of freedom. Wan et al. (2014) demonstrated that many studies report medians and interquartile ranges instead of means and standard deviations, requiring an intermediate estimation step before SE can be computed. Our median/IQR to mean/SD estimator implements the validated Wan, Luo, and Hozo methods for this conversion, producing a mean and SD that can then flow into the SE = SD / √N formula. For cluster-randomised trials, the effective sample size must be reduced by the design effect (1 + (m − 1) × ρ) before computing the SE, and cluster-robust standard errors should be used to account for the hierarchical data structure. RevMan and Comprehensive Meta-Analysis (CMA) both require the SE or its components (SD and N) as mandatory inputs for inverse-variance pooling. The Cochrane Handbook (Higgins et al., 2023, Chapter 6) recommends documenting every imputation and conversion step in a supplementary table so that the analytic chain remains fully reproducible, a standard that PRISMA 2020 (Page et al., 2021) reinforces through its data-preparation checklist item.
Converting confidence interval to standard deviation is particularly valuable when extracting data from forest plots or summary tables in published meta-analyses that omit the underlying SD. Once SE and SD are known, the reviewer can compute standardised effect sizes—Cohen's d, Hedges' g, or log odds ratios—for pooling across studies. Our effect size calculator accepts means, SDs, and sample sizes for two groups and returns the standardised mean difference with its 95 % CI, closing the gap between raw extraction and analysis-ready input. Altman & Bland (2005) stress that the choice between SD and SE in graphical displays matters: error bars showing ±1 SD depict data spread, whereas bars showing ±1 SE (or the 95 % CI) depict estimation uncertainty, and conflating the two misleads readers about both the variability and the precision of the findings. When analytic formulas are unavailable or distributional assumptions are uncertain, bootstrap resampling offers a nonparametric alternative for SE estimation by repeatedly sampling with replacement from the observed data.
A robust data-extraction pipeline integrates SE/SD conversion with upstream and downstream tools. Upstream, a well-designed data extraction template should include dedicated columns for the reported variability measure, the sample size, and flags indicating whether the value is SD, SE, or CI-derived, so that conversions can be applied systematically rather than ad hoc. Downstream, the converted SDs feed into effect-size calculations that ultimately populate a forest plot, the primary visual output of any meta-analysis. The Cochrane Handbook (Higgins et al., 2023) notes that errors introduced during variability conversion propagate multiplicatively through the inverse-variance weighting scheme, making this seemingly simple arithmetic step one of the highest-leverage quality checks in the entire review process. By automating the conversion and displaying every formula used, this tool helps review teams satisfy the transparency and reproducibility requirements that PRISMA 2020 and Cochrane set for trustworthy evidence synthesis.
Standard deviation (SD) describes the spread of individual data points around the mean in a single sample. Standard error (SE) describes the precision of the sample mean as an estimate of the population mean. SE = SD / √N, so the standard error shrinks as sample size increases, even if the underlying variability stays the same. In meta-analysis, you typically need the SE (or its square, the variance) to weight each study.
If a paper reports a 95% confidence interval (lower, upper) for a mean, the SE can be back-calculated as SE = (upper – lower) / (2 × 1.96). This assumes the CI was constructed using a normal (z-based) approximation. For t-based intervals (common in small samples), use the t-critical value for the appropriate degrees of freedom instead of 1.96.
Most meta-analysis software expects the SE of the effect estimate (or the variance). If a study reports only the SD and sample size, you can convert to SE using SE = SD / √N. If the study reports means and SDs for two groups, you would first compute a standardized mean difference (e.g., Cohen’s d) and then its SE using the appropriate formula.
The SE = SD / √N formula assumes the data are approximately normal. For medians or heavily skewed data, the standard error has a different formula. If your paper reports median and interquartile range instead of mean and SD, use our Median/IQR to Mean/SD estimator first, then convert as needed.
This tool uses the 95% CI z-score of 1.96. For a 99% CI, the z-score is 2.576, and for a 90% CI it is 1.645. You can manually adjust: SE = CI half-width / z, where z corresponds to your confidence level. Then enter the SE and N into this tool to compute the SD.
Multiply the standard error by the square root of the sample size: SD = SE × √n. This reverses the relationship SE = SD / √n. You need the sample size (n) to perform this conversion. This is one of the most common transformations during data extraction for meta-analysis, as many studies report SE while pooling software requires SD.
Standard deviation (SD) measures the spread of individual data points around the sample mean — it describes variability in the data. Standard error (SE) measures the precision of the sample mean as an estimate of the population mean — it describes uncertainty in the estimate. SE always decreases with larger samples (SE = SD/√n), while SD remains roughly constant regardless of sample size.
For large samples (n ≥ 60), SD = √n × (upper limit – lower limit) / 3.92, where 3.92 = 2 × 1.96. For smaller samples, replace 1.96 with the t-value for n–1 degrees of freedom. This back-calculation is commonly needed when studies report only the mean and 95% CI without the SD, as described in the Cochrane Handbook Section 6.5.2.
Our statisticians handle the entire data extraction and conversion pipeline for your systematic review, from raw study reports to analysis-ready datasets.