Effect size converter for meta-analysis
Studies rarely report results in the format a meta-analysis needs. These eight converters turn the statistics papers do report into the ones you need, using the formulas recommended in the Cochrane Handbook and the methodological literature.
Open the effect size converterThe eight converters
| Converter | You enter | Formula | Assumptions and cautions |
|---|---|---|---|
| Ratio and 95% CI to log effect and SE | RR, OR or HR with its 95% CI | ln(ratio); SE = [ln(upper) − ln(lower)] / (2 × 1.96) | Wald interval symmetric on the log scale; the tool warns when it is not. Source: Cochrane Handbook, Chapter 6, section 6.3.2. Wald approximation. |
| Baseline and follow-up SD to change SD | SD before, SD after, within-person correlation r | SD_change = √(SD₀² + SD₁² − 2·r·SD₀·SD₁) | r must be justified from the study or similar studies; test other values in sensitivity analysis. Source: Cochrane Handbook, Chapter 6, section 6.5.2.8. |
| Median and IQR to mean and SD | n, Q1, median, Q3 | mean = w(Q1+Q3)/2 + (1−w)·median, w = 0.7 + 0.39/n; SD = (Q3−Q1) / [2·Φ⁻¹((0.75n−0.125)/(n+0.25))] | Imputed estimate assuming roughly normal data; check skewness and run sensitivity analysis. Source: Mean: Luo D, et al. Stat Methods Med Res 2018;27:1785. SD: Wan X, et al. BMC Med Res Methodol 2014;14:135. |
| Median and range to mean and SD | n, minimum, median, maximum | mean = w(min+max)/2 + (1−w)·median, w = 4/(4+n^0.75); SD = (max−min) / [2·Φ⁻¹((n−0.375)/(n+0.25))] | Exploratory only; Cochrane advises against routine range-based SD estimation. Source: Mean: Luo D, et al. 2018. SD: Wan X, et al. 2014. |
| 95% CI of a mean to SD | n, lower and upper limit | SD = √n × (upper − lower) / (2 × t₀.₉₇₅, n−1) | Single group mean; uses the t distribution, which matters in small samples. Source: Cochrane Handbook, Chapter 6, section 6.5.2. |
| Standard error to SD | n, SE | SD = SE × √n | Papers sometimes label an SE as an SD; implausibly small spread suggests SE. Source: SD equals SE multiplied by the square root of n. |
| 2×2 table to risk ratio and odds ratio | events and totals in each arm | RR = (a/n₁)/(c/n₂); OR = a(n₂−c)/[(n₁−a)c]; 95% CI = exp(ln estimate ± 1.96 SE) | Stops on zero or full cells so you can apply a pre-specified method instead of an automatic correction. Source: Cochrane Handbook, Chapter 6. |
| Combine two groups into one | n, mean and SD of two arms | N = n₁+n₂; mean = (n₁m₁+n₂m₂)/N; SD = √{[(n₁−1)s₁² + (n₂−1)s₂² + (n₁n₂/N)(m₁−m₂)²]/(N−1)} | For multi-arm trials, so a shared control group is not counted twice. Source: Cochrane Handbook, Chapter 6, Table 6.5.a. |
Worked examples
These results come from running the converter’s own code.
- SE to SD: n = 100, SE = 2 gives SD = 20.
- 95% CI of a mean to SD: n = 25, 95% CI 10.2 to 14.6 gives SD = 5.33.
- Median and IQR to mean and SD: n = 60, Q1 = 4, median = 6, Q3 = 9 gives Estimated mean = 6.353; Estimated SD = 3.798.
- Ratio and CI to log effect: HR 0.75 (95% CI 0.60 to 0.94) gives Log effect = -0.288; SE of log effect = 0.115.
- 2×2 table: 15/100 events with the intervention and 25/100 with control gives Risk ratio = 0.6; RR 95% CI = 0.337 to 1.068; Odds ratio = 0.529; OR 95% CI = 0.26 to 1.078.
- Combining two arms: 30 participants, mean 12 (SD 4), and 32 participants, mean 14 (SD 5), gives Combined n = 62; Combined mean = 13.032; Combined SD = 4.618.
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All calculations run in your browser. The numbers you enter are not uploaded.
Frequently asked questions
How do I convert a standard error to a standard deviation?
Multiply the SE by the square root of the sample size: SD = SE × √n. For example, SE 2 with n = 100 gives SD 20.
Can I estimate a mean and SD from a median and IQR?
Yes, as an imputed estimate. The converter uses Luo et al. (2018) for the mean and Wan et al. (2014) for the SD. These assume roughly normal data, so assess skewness and run a sensitivity analysis.
Why does the 2×2 converter stop when a cell is zero?
Zero cells need a method chosen in advance, such as a continuity correction or a different effect measure. The tool stops rather than apply one silently.
How do I handle a trial with two intervention arms and one control?
Combine the two intervention arms into one group with the combine-groups converter, so the control group is not counted twice.
Are my numbers uploaded anywhere?
No. All calculations run locally in your browser.
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