The central hub of the Research Gold analysis pipeline. Calculate and convert between Cohen's d, Hedges' g, odds ratios, risk ratios, and correlation coefficients, then send results directly to the Forest Plot, Funnel Plot, or Heterogeneity tools. Choose your confidence level (80%, 90%, 95%, or 99%) for all interval estimates. Import multiple studies at once via CSV/Excel batch mode, convert from t-statistics or F-statistics in the “From Stats” tab, and export everything as CSV or Excel.
Move data between tools automatically. Compute effect sizes, then send results to Forest Plot, Funnel Plot, or Heterogeneity analysis with one click.
No data in pipeline yet. Compute effect sizes or convert data in any tool, then send it downstream.
Calculate effect size for a single study. Switch to Batch Mode to process multiple studies from a spreadsheet.
Enter means, standard deviations, and sample sizes for two independent groups.
Load sample data to see how the tool works, or clear all fields to start fresh.
Analysis Pipeline
Select from means & SDs, 2×2 table data, correlations, or use the “From Stats” tab to convert t-statistics, F-statistics, chi-square values, or p-values directly into Cohen’s d.
Input values for a single study, or switch to batch mode to import a CSV or Excel file. Fuzzy column matching automatically maps your headers to the required fields.
The calculator returns the effect size, confidence interval (selectable at 80%, 90%, 95%, or 99%), variance, and standard error. All inputs are auto-saved to your browser so you never lose work.
Copy individual results to clipboard, or export the full results table as CSV or Excel for use in other software.
Click “Send to Forest Plot,” “Send to Funnel Plot,” or “Send to Heterogeneity” to push your computed effect sizes directly into the next stage of the analysis pipeline.
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Get a Free QuoteUse SMD (Cohen's d or Hedges' g) for continuous outcomes measured on different scales. Use OR or RR for dichotomous outcomes. Use correlation (r) for association studies.
Point estimates alone are insufficient. The confidence interval tells readers how precise your estimate is and whether it crosses clinically meaningful thresholds. This tool lets you select 80%, 90%, 95%, or 99% confidence levels to match your reporting requirements.
Cohen's d slightly overestimates effect sizes in small samples. Hedges' g applies a correction factor (J) that approaches 1 as sample size increases.
Odds ratios and risk ratios should be log-transformed before meta-analytic pooling. The calculator provides both the natural log and the raw ratio.
An effect size calculator standardizes treatment effects across studies so that results measured on different scales, in different populations, and under different conditions can be meaningfully compared and pooled. In the Cochrane Handbook for Systematic Reviews of Interventions (Higgins et al., 2023), effect size computation is identified as one of the foundational steps in quantitative synthesis: without a common metric, meta-analysis cannot proceed. The choice of metric depends on the outcome type. For continuous outcomes measured on different scales, the standardized mean difference, reported as either Cohen's d or its small-sample-corrected counterpart, is the standard approach. For binary outcomes such as response versus non-response, the odds ratio or risk ratio captures the relative likelihood of the event between groups.
Cohen (1988) introduced the d statistic as a scale-free measure of the distance between two group means, expressed in pooled standard deviation units. While widely adopted, Cohen's d exhibits an upward bias when sample sizes are small. Hedges & Olkin (1985) proposed a correction factor J, computed as J = 1 − 3/(4df − 1), that shrinks d toward zero, producing what is now universally known as the Hedges' g calculator output. When group variances are unequal and the control condition provides the more natural reference, Glass's delta uses only the control group standard deviation as the denominator, offering an alternative that avoids pooling heterogeneous variances. The correction is negligible for studies with more than about 50 participants per arm, but for the small trials common in behavioral and educational research, the difference can be substantial. Best practice in contemporary meta-analysis, as outlined in PRISMA 2020 (Page et al., 2021), is to report Hedges' g alongside its 95% confidence interval and variance estimate so that downstream pooling uses the most accurate inputs.
For dichotomous outcomes, the odds ratio calculator computes the ratio of the odds of an event in the treatment group to the odds in the control group. Odds ratios are the default metric in Cochrane Reviews because they possess desirable mathematical properties: they can be log-transformed to produce an approximately normal sampling distribution, making them suitable for inverse-variance-weighted pooling. Software such as Comprehensive Meta-Analysis (CMA) and the metafor package in R automates this pooling across studies, and network meta-analysis extends the process by requiring all included comparisons to use a consistent effect size scale so that indirect treatment effects can be estimated without introducing metric artefacts. When clinical interpretability is a priority, odds ratios can be converted to numbers needed to treat using our NNT calculator, giving clinicians a concrete measure of treatment benefit. For association studies, the correlation coefficient r is the natural effect size; it can be converted to and from Cohen's d via the formula d = 2r / sqrt(1 - r squared), a transformation supported by our correlation to effect size converter.
Variance estimation is inseparable from effect size calculation. Every pooled estimate in a meta-analysis weights each study by the inverse of its variance, so an error in variance computation propagates directly into the summary result. For standardized mean differences, variance depends on both the sample sizes and the effect size itself; for log odds ratios, it depends on the cell counts in the 2x2 table. When original studies report standard errors rather than standard deviations, the SE-to-SD converter facilitates the necessary back-calculation. Similarly, studies reporting medians and interquartile ranges instead of means and SDs require estimation methods such as those described by Wan et al. (2014), available through our median and IQR converter.
Beyond computation, interpreting effect sizes requires domain expertise. Cohen's benchmarks (0.2 for small, 0.5 for medium, 0.8 for large) were intended as rough guides for power analysis planning, not as universal thresholds for clinical significance. A d of 0.3 in a preventive cardiology trial may save thousands of lives at population scale, while a d of 0.8 in an underpowered pilot study may reflect nothing more than measurement noise. Researchers should also be aware that effect size inflation from selective reporting, where only the largest or most significant effects reach publication, can systematically exaggerate the true magnitude of treatment differences in the published literature. The Cochrane Handbook urges reviewers to contextualize effect sizes relative to clinically important differences, baseline risk, and the precision of the estimate. Combining accurate effect size calculation with thoughtful clinical interpretation is what elevates a meta-analysis from a statistical exercise to a genuine contribution to evidence-based practice.
In practice, effect size calculation is rarely a standalone task. It is one stage in a longer pipeline that spans data extraction, quantitative synthesis, and visualization. This calculator is designed to serve as the central hub of that pipeline. After extracting raw study data (means, standard deviations, sample sizes, or 2×2 table counts), researchers compute standardized effect sizes here and then pass them directly to downstream tools: the forest plot generator for visual synthesis, the funnel plot generator for publication bias assessment, or the heterogeneity calculator for I² and τ² estimation. This interoperability eliminates the error-prone step of manually re-entering data between tools. Batch import via CSV or Excel, with fuzzy column matching that automatically maps headers like “mean_treatment” or “SD (control)” to the correct input fields, makes it practical to process dozens or hundreds of studies at once, as is common in large-scale umbrella reviews and living systematic reviews. The “From Stats” tab further extends coverage by allowing researchers to convert t-statistics, F-statistics, chi-square values, or p-values into Cohen's d when original means and standard deviations are unavailable, a scenario that arises in roughly 30-40% of primary studies according to estimates from the Campbell Collaboration. All inputs are auto-saved to the browser, and all results can be exported as CSV or Excel, ensuring that no work is lost and that the audit trail from raw data to final forest plot remains transparent and reproducible.
An effect size is a standardized measure of the magnitude of an observed effect. In meta-analysis, effect sizes allow researchers to combine and compare results across studies that may use different measurement scales or report different statistics. Common effect sizes include standardized mean differences (for continuous outcomes), odds ratios and risk ratios (for binary outcomes), and correlation coefficients (for associations).
Hedges' g is generally preferred in meta-analysis because it corrects for the small upward bias in Cohen's d that occurs with small sample sizes. The correction factor J = 1 - 3/(4*df - 1) is close to 1 for large samples, so the two measures converge as sample size increases. For individual studies with n > 50 per group, the difference is negligible.
Cohen (1988) proposed benchmarks: d = 0.2 (small), 0.5 (medium), 0.8 (large). For odds ratios: OR ≈ 1.5 (small), 2.5 (medium), 4.3 (large). For correlations: r = 0.1 (small), 0.3 (medium), 0.5 (large). These are rough guides -- clinical significance depends on context.
Yes, this calculator supports conversion between Cohen's d and correlation r using the formula d = 2r/√(1-r²). Conversions between SMDs and odds ratios are also possible using the logistic approximation OR = exp(d × π/√3). Note that conversions assume certain distributional properties.
Yes, completely free with no sign-up required. All calculations run in your browser -- no data is sent to any server. You can use it for as many studies as you need.
Hedges’ g corrects Cohen’s d for small-sample bias using a correction factor J. For n < 20, Cohen’s d overestimates the true effect. For n > 50, the two are nearly identical. Hedges’ g is preferred in meta-analysis because it provides an unbiased estimate regardless of sample size.
Use the formula d = ln(OR) × √3 / π, where ln(OR) is the natural logarithm of the odds ratio. This approximation (Borenstein et al., 2009) assumes logistic distribution of the underlying continuous variable. The conversion is exact when groups are equal-sized and the outcome follows a logistic distribution.
There is no universal threshold. Cohen (1988) proposed d = 0.2 (small), 0.5 (medium), 0.8 (large), but these are conventions, not clinical benchmarks. The minimum clinically important difference (MCID) depends on the outcome measure, patient population, and clinical context. Always interpret effect sizes relative to your specific field.
Yes. Switch to batch mode and upload a CSV or Excel file containing your study data. The calculator uses fuzzy column matching to automatically map your column headers to the required input fields (e.g., it recognizes headers like 'mean_treatment', 'SD (control)', or 'n_experimental'). You can review and correct the mappings before processing. All computed effect sizes appear in a single results table that you can export or send to downstream tools.
Use the “From Stats” tab. Enter your t-statistic (or F-statistic, chi-square, or p-value) along with the sample sizes for each group. The calculator applies the appropriate conversion formula (for example, d = 2t / √(df) for a two-sample t-test) and returns Cohen’s d with its 95% confidence interval. This is useful when the original paper reports only test statistics rather than means and standard deviations.
Yes. After computing effect sizes, click “Send to Forest Plot,” “Send to Funnel Plot,” or “Send to Heterogeneity” to push your results directly into the next tool in the analysis pipeline. The data transfers automatically so you don’t need to re-enter anything. This pipeline workflow reduces transcription errors and saves time.
Yes. All inputs are auto-saved to your browser’s local storage as you type. If you close the tab or navigate away, your data will be restored when you return. No data is sent to any server; everything stays on your device.
Need to convert correlations into standardized mean differences? Our correlation to effect size converter handles Pearson r, point-biserial, and phi conversions. For clinical trials, the NNT calculator translates odds ratios and risk differences into a number needed to treat that clinicians can act on. Visualize pooled results with our forest plot generator. If your studies report standard errors instead of standard deviations, use the SE/SD converter before calculating effect sizes. For time-to-event outcomes, extract hazard ratios from Kaplan-Meier curves using the survival curve digitizer.
Reviewed by
Dr. Sarah Mitchell holds a PhD in Biostatistics from Johns Hopkins Bloomberg School of Public Health and has over 15 years of experience in systematic review methodology and meta-analysis. She has authored or co-authored 40+ peer-reviewed publications in journals including the Journal of Clinical Epidemiology, BMC Medical Research Methodology, and Research Synthesis Methods. A former Cochrane Review Group statistician and current editorial board member of Systematic Reviews, Dr. Mitchell has supervised 200+ evidence synthesis projects across clinical medicine, public health, and social sciences. She reviews all Research Gold tools to ensure statistical accuracy and compliance with Cochrane Handbook and PRISMA 2020 standards.
Our PhD team runs complete meta-analyses: data extraction, effect size computation, forest plots, sensitivity analysis, and a manuscript ready for journal submission. Average turnaround: 2-4 weeks.