I² Heterogeneity Calculator for Meta-Analysis

I² is the percentage of total variability across studies that is attributable to genuine heterogeneity (real differences between studies) rather than chance (sampling error). It does not measure the size of the treatment effect, and it is not, by itself, a test of whether pooling those studies is appropriate.

How to calculate I² with this calculator

1. Enter one row per study: the effect size and its standard error (not the standard deviation or the sample size).
2. For odds ratios, risk ratios and hazard ratios, enter the log of the ratio and the standard error of the log.
3. Use at least two studies. Rows with a missing or non-positive standard error are ignored.
4. Read Q, I² and τ² from the result panel below the table, then interpret them alongside how comparable the studies are.

Cochran's Q, I², and Tau²

Cochran's Q is a heterogeneity test statistic: the inverse-variance-weighted sum of squared deviations of each study's effect from the pooled fixed-effect estimate. It depends on the number of studies, so it is not directly comparable across meta-analyses of different sizes.

I² converts Q into a percentage that is comparable across meta-analyses. Higgins et al. (2003) suggested 25%, 50% and 75% as rough markers of low, moderate and high heterogeneity, and the Cochrane Handbook gives overlapping ranges (0–40% might not be important, 30–60% moderate, 50–90% substantial, 75–100% considerable). Both are guides, not strict rules, as explained below.

Tau² (τ²) is the DerSimonian–Laird estimate of the actual variance between true study effects, used to derive random-effects weights. Tau² is scale-dependent: its numeric value is tied to the effect measure and scale you extracted (e.g. log odds ratio vs. mean difference), so a τ² from one meta-analysis cannot be compared directly to a τ² measured on a different scale or outcome.

How I² is calculated

Cochran's Q is computed as the inverse-variance-weighted sum of squared deviations from the fixed-effect pooled estimate:

Q = Σ w_i(θ_i − θ̂)²,   w_i = 1/SE_i²

I² is then derived from Q and the degrees of freedom, df = k − 1 (k = number of studies):

I² = max(0, (Q − df) / Q) × 100%

Tau² (τ²) is the DerSimonian-Laird estimate of between-study variance, used to derive random-effects weights in a full meta-analysis.

Worked example

The four studies pre-filled in the calculator above (effects 0.42, 0.55, 0.38, 0.61 with standard errors 0.12, 0.15, 0.10, 0.18) give Q = 1.79, which is below k−1 = 3 — so I² floors at 0% and τ² = 0: these studies agree with each other more than chance alone would predict, i.e. low heterogeneity.

A moderate case: five studies with effects 0.20, 0.50, 0.30, 0.65 and 0.25 and standard errors 0.10, 0.12, 0.09, 0.15 and 0.11. The fixed-effect pooled estimate is 0.336, Cochran's Q = 8.87 on df = 4, so I² = (8.87 − 4) / 8.87 × 100% = 54.9% and τ² = 0.015. That sits in the overlap of the Cochrane Handbook's “moderate” (30–60%) and “substantial” (50–90%) ranges. It does not, on its own, decide the model or whether pooling is appropriate; that depends on whether the studies are answering a comparable question in the first place.

Contrast case

Four studies with the same standard errors as the calculator's default rows, but effects of 0.10, 0.45, −0.05 and 0.70, give Q = 17.32 on df = 3, I² = 82.7% and τ² ≈ 0.083, with a fixed-effect estimate of 0.178. That is high heterogeneity: the studies range from −0.05 to 0.70, and a single pooled figure of 0.18 would hide that spread.

How to report heterogeneity

Report Q with its degrees of freedom and p-value, I², and τ² with the estimator used. For the five-study example above:

Heterogeneity was assessed with Cochran's Q (Q = 8.87, df = 4, p = 0.064) and I² (54.9%); the between-study variance was τ² = 0.015 (DerSimonian–Laird).

The calculator above returns Q, I² and τ². The p-value for Q comes from a chi-square distribution with k − 1 degrees of freedom, which you can look up in any statistics package. A Q test has low power with few studies, so a non-significant p does not rule out heterogeneity.

Why I² thresholds are not rules

A specific I² percentage does not, by itself, mandate a random-effects model or forbid pooling. I² is a summary of statistical inconsistency; it cannot see the reasons behind it. The same I² value can arise from very different underlying situations — a few outlying studies, genuinely different populations, or simply small-study imprecision inflating the percentage.

Clinical and methodological diversity still matter regardless of what I² reads: differences in populations, interventions, outcome definitions, follow-up length, risk of bias across the included studies, and the precision of each study's estimate all affect whether a pooled number is meaningful — none of that is captured by I² alone.

When not to pool studies

Consider a narrative synthesis instead of (or alongside) a pooled estimate when:

• studies measure clinically different populations, interventions, or comparators that are not meaningfully exchangeable;
• outcome definitions or timepoints differ enough that a single pooled number would not answer one question;
• heterogeneity is high and unexplained by pre-specified subgroups, methodology, or risk of bias;
• most included studies carry a high risk of bias, so pooling would give a falsely precise, unreliable estimate.

References

Higgins JPT, Thompson SG. Quantifying heterogeneity in a meta-analysis. Stat Med. 2002;21(11):1539-1558. doi.org/10.1002/sim.1186. Higgins JPT, Thompson SG, Deeks JJ, Altman DG. Measuring inconsistency in meta-analyses. BMJ. 2003;327(7414):557-560. doi.org/10.1136/bmj.327.7414.557. Deeks JJ, Higgins JPT, Altman DG (editors). Chapter 10: Analysing data and undertaking meta-analyses. In: Cochrane Handbook for Systematic Reviews of Interventions. DerSimonian R, Laird N. Meta-analysis in clinical trials. Control Clin Trials. 1986;7(3):177-188. doi.org/10.1016/0197-2456(86)90046-2.

Extracted your effect sizes yet? Use the data extraction template to record events/totals or means/SDs consistently, then the effect size calculator to get Cohen's d, Hedges' g, or a risk/odds ratio from each study before computing heterogeneity here. Planning a new study instead? See the sample size calculator. Or start a free EvidenceFlow review to keep the full workspace — extraction, pooling, and PRISMA reporting — in one place.