Meta-Analysis Calculator
A meta-analysis calculator combines the effect sizes from your included studies into one pooled estimate with a confidence interval, then quantifies how much the studies disagree. Enter your data, choose a model, and read the pooled result and heterogeneity statistics straight away.
1. Choose your data
2. Enter studies
| Study | Events (T) | Total (T) | Events (C) | Total (C) | |
|---|---|---|---|---|---|
Pooled estimate
Per-study contribution
| Study | OR | 95% CI | Weight |
|---|---|---|---|
| Anderson 2018 | 0.57 | [0.29, 1.09] | 18.6% |
| Becker 2019 | 0.58 | [0.23, 1.41] | 9.9% |
| Carter 2020 | 0.72 | [0.43, 1.20] | 30.9% |
| Diaz 2020 | 0.39 | [0.13, 1.18] | 6.4% |
| Evans 2021 | 0.73 | [0.40, 1.31] | 22.9% |
| Foster 2022 | 0.88 | [0.38, 2.04] | 11.3% |
Random-effects pooling uses DerSimonian-Laird tau-squared and inverse-variance weights. Switch to fixed effect only when between-study heterogeneity is negligible.
How to run your meta-analysis
The calculator works the same way whether you have raw counts or already-published effect sizes. Follow these six steps and the pooled result updates as you enter each study.
- 1. Choose your effect measure. Pick the outcome type that matches your data: odds ratio, risk ratio, or risk difference for binary events, a mean difference or standardised mean difference for continuous outcomes, or a pre-computed estimate such as a hazard ratio when you only have a published value and its interval.
- 2. Enter one row per study. For binary outcomes type the events and totals in each arm. For continuous outcomes type the mean, standard deviation, and sample size for each group. For pre-computed effects, paste the estimate with its lower and upper confidence limits and the calculator recovers the standard error.
- 3. Select a model. Start with a fixed-effect model if you believe every study estimates the same underlying effect, or a random-effects model if the studies differ in population, dose, or follow-up. The section below on choosing a model explains how to decide.
- 4. Read the pooled estimate. The headline number is the combined effect with its 95 percent confidence interval. For ratio measures it is pooled on the natural-log scale and back-transformed, so an odds ratio of 1.0 still marks the line of no effect.
- 5. Check the heterogeneity panel. Look at Cochran's Q, I-squared, and tau-squared together before you trust the summary. High heterogeneity is a signal to prefer random effects and to read the prediction interval.
- 6. Export or visualise. Send the same numbers to the interactive forest plot builder to draw the squares and summary diamond, or test for small-study effects with a funnel plot for publication bias.
Reading the pooled output
The pooled estimate is the headline number, but it is only trustworthy once you have weighed the heterogeneity beside it. A high I-squared value tells you the studies are estimating genuinely different effects, which is the moment a random-effects model earns its place and the prediction interval becomes the honest summary of what to expect next. The per-study weights show which trials are driving the result, so a single large study dominating the pool is easy to spot. A confidence interval that crosses the line of no effect, 1.0 for ratios or 0 for differences, means the pooled effect is not statistically significant at the level you chose.
If you are unsure which model to choose, the guide to fixed-effect versus random-effects assumptions walks through the decision, and the explainer on what I-squared really measures covers how to interpret the heterogeneity output.
A worked example: pooling three studies
Suppose three trials report a mean difference between treatment and control on the same continuous scale. Study A found 2.0 with a standard error of 0.50, Study B found 3.0 with a standard error of 0.40, and Study C found 1.0 with a standard error of 0.80. Each study's weight under a fixed-effect model is the inverse of its variance, so the most precise study, B, carries the most weight.
| Study | Mean difference | Standard error | Variance | Weight (1 / variance) |
|---|---|---|---|---|
| A | 2.0 | 0.50 | 0.25 | 4.00 |
| B | 3.0 | 0.40 | 0.16 | 6.25 |
| C | 1.0 | 0.80 | 0.64 | 1.56 |
The fixed-effect pooled estimate is the weighted average of the three effects, which works out to 2.40 with a 95 percent confidence interval of 1.83 to 2.97. Cochran's Q comes to 5.95 on two degrees of freedom, giving an I-squared of 66 percent, so two thirds of the variation across these studies reflects real differences rather than chance. That is substantial heterogeneity, which is the cue to switch models.
Under a random-effects model the calculator estimates a between-study variance, tau-squared, of about 0.57 and rebalances the weights so the studies count more equally. The pooled estimate shifts to 2.16 and the confidence interval widens to 1.10 to 3.22. The interval is wider on purpose: it now reflects both the uncertainty within each study and the genuine spread between them. This is exactly why a random-effects result looks less precise when heterogeneity is real, and why reporting the fixed-effect interval in that situation overstates your confidence.
Fixed-effect or random-effects: which model
The two models answer different questions. A fixed-effect model assumes there is one true effect and every study is a noisy estimate of it, so the only reason results differ is sampling error. It is defensible when the trials are near replicates of each other, with the same population, intervention, and outcome definition. A random-effects model assumes the true effect itself varies from study to study around an average, and it estimates that spread as tau-squared using the DerSimonian-Laird method before widening the weights and the interval.
In practice most systematic reviews combine studies that differ in design and setting, so a random-effects model is the more honest default whenever the I-squared statistic is moderate or high. Choosing fixed effects under real heterogeneity produces a confidence interval that is too narrow and a false sense of precision. The reverse mistake is milder: running random effects on truly homogeneous studies gives almost the same answer as fixed effects, because tau-squared estimates near zero. When in doubt, the random-effects result is the safer one to report.
Common mistakes to avoid
- Pooling ratio measures on the raw scale. Odds ratios and risk ratios are skewed, so they must be combined on the natural-log scale and back-transformed. The calculator does this automatically, but if you average raw ratios by hand the pooled value will be biased toward the larger numbers.
- Reading I-squared as an amount of effect. The I-squared statistic measures the proportion of variation that is not due to chance, not how big or important the effect is. A small, consistent effect can have a high I-squared, and a large effect can have a low one.
- Confusing the confidence interval with the prediction interval. The confidence interval describes the average effect; the prediction interval describes the range a future study might find. With real heterogeneity the prediction interval is much wider and is the one that answers what to expect next.
- Pooling too few studies under random effects. With only two or three studies, tau-squared is estimated very imprecisely, so treat a random-effects interval from a tiny set of trials as a rough guide rather than a firm answer.
- Ignoring a single dominant study. Check the weights. If one large trial carries most of the weight, the pooled result is really that trial with a little adjustment, and the summary diamond can hide that fact.
Want the pooled analysis written up, not just computed?
The calculator gives you the numbers. If you need a methodologist to confirm the model choice, extract the effect sizes correctly, and write a results section that holds up in peer review, we can take it from here.
Get help with your meta-analysisFrequently asked questions
How does a meta-analysis calculator pool effect sizes?
It weights each study by the inverse of its variance, so more precise studies count more, and combines the weighted effects into a single pooled estimate. Ratio measures such as odds ratios are pooled on the natural-log scale and back-transformed for display. A random-effects calculation first estimates the between-study variance, tau-squared, with the DerSimonian-Laird method, then widens the weights and the confidence interval to reflect that extra variation.
Which heterogeneity statistics does it report?
Every calculation returns Cochran’s Q with its degrees of freedom and p-value, the I-squared statistic as a percentage, tau-squared as the absolute between-study variance, and H-squared. With a random-effects model, three or more studies, and genuine heterogeneity, it also reports a 95 percent prediction interval for the true effect of a new study.
Do I need raw data or can I enter effect sizes directly?
Either works. You can enter events and totals for binary outcomes, means with standard deviations and sample sizes for continuous outcomes, or a pre-computed effect with its confidence interval for any measure, including hazard ratios. The calculator derives the standard error it needs from whatever form you provide.
How many studies do you need for a meta-analysis?
You can pool as few as two studies, and the calculator will combine them, but the result is only as reliable as the evidence behind it. With two or three studies the between-study variance is estimated poorly, so a random-effects interval is wide and unstable. Cochrane guidance treats any number of studies as eligible for pooling, while noting that heterogeneity and the prediction interval become much more informative once you have around five or more.
Why is my random-effects interval wider than the fixed-effect one?
Because it carries more information. A fixed-effect interval reflects only the sampling error within each study. A random-effects interval adds the estimated spread between studies, tau-squared, on top of that. When the studies genuinely disagree, that extra term is large and the interval widens, which is the honest way to report an average effect drawn from varied trials.