Effect Size Calculator

This free effect size calculator handles three metrics from a single interface. Follow these steps to get your result.

Effect size is a standardized measure of the magnitude of a difference between groups or the strength of a relationship between variables. Where significance testing answers whether an observed result is likely due to chance, measuring effect size answers how large that result actually is. The two pieces of information are complementary, not interchangeable.

The distinction matters because significance is sensitive to sample size. A large enough sample will produce a statistically significant result even for a between-group difference so small it carries no practical meaning. Conversely, a study with low statistical power may fail to reach significance despite an effect size that would be considered meaningful in its field. A trivial effect size can be significant. A meaningful effect size can go undetected. Neither situation is visible from the p-value alone.

For that reason, effect size reporting is required by the APA Publication Manual (7th ed.) and expected by most peer-reviewed journals across psychology research, education research, behavioral science, and the social sciences. In quantitative research, reporting a result without a corresponding effect size is increasingly treated as an incomplete analysis.

This calculator covers three metrics used across the most common research designs:

Each metric, its required inputs, and its interpretation are covered in the sections below.

Cohen's d is the most widely used effect size formula for comparing two independent groups. It expresses the mean difference between a control group and a treatment group, or any two conditions, in standard deviation units. The result is a single standardized number that describes how far apart the two group means are relative to the spread of the data.

Required Inputs

To calculate Cohen's d from means, you need four values: M1 (mean for Group 1), M2 (mean for Group 2), SD1 (standard deviation for Group 1), and SD2 (standard deviation for Group 2). Enter these directly into the calculator. The tool handles the pooled standard deviation calculation internally.

The Formula

The denominator is the pooled standard deviation, calculated as:

The pooled SD is the root mean square of both group standard deviations. Use it when the two groups have approximately equal variances, which covers most standard two-sample research designs. If one group's variance is substantially larger than the other, the pooled SD will misrepresent the typical spread, and a weighted version or an alternative metric may be more appropriate.

Assumptions

Cohen's d assumes normally distributed data within each group. The formula for Cohen's d with independent groups also produces the most accurate results when group sizes and standard deviations are similar. When sample sizes are small or unequal, the d statistic carries a small upward bias, which is the condition under which Hedges' g becomes the preferred alternative.

What the Result Means

The output is in standard deviation units. A Cohen's d of 0.5, for example, means the two group means differ by half a standard deviation. A d of 1.0 means the groups differ by a full standard deviation. To put those numbers in context: a d of 0.2 is considered small by Cohen's 1988 conventions, a d of 0.5 sits in the medium range, and d of 0.8 or above is large. A worked example helps here: if an intervention group scores a mean of 75 and a control group scores 65 with a pooled SD of 20, Cohen's d is 0.5, a medium effect.

These thresholds are reference points drawn from Cohen (1988), not fixed rules. The meaning of a medium effect size varies considerably across fields. In a tightly controlled laboratory experiment, a d of 0.5 may be modest. In a large-scale educational or clinical intervention, the same value may represent a substantial practical gain. Always interpret Cohen's d alongside comparable published findings in the same domain.

Effect Size for T-Test Results

Cohen's d is the standard effect size for t-test designs. When you run an independent samples t-test and want to calculate effect size from the t-statistic directly rather than from group means, the calculator can also accept t and sample size inputs depending on your available data. The output is the same standardized mean difference expressed as Cohen's d.

Hedges' g is a bias-corrected version of Cohen's d. The two metrics measure the same thing — the standardized mean difference between two independent groups — but Hedges' g applies a correction factor, commonly noted as J, that reduces the slight upward inflation present in Cohen's d when sample sizes are small.

Why the Correction Is Needed

Cohen's d is known to overestimate effect size in small samples. This is a systematic bias, not random error, meaning d will consistently read slightly larger than the true population effect when sample sizes are limited. The degree of overestimation is small in large samples and becomes more pronounced as n decreases. Small sample effect size correction addresses this directly. Hedges' g multiplies Cohen's d by the correction factor J, which is derived from the total sample size, pulling the estimate closer to the unbiased population value.

The practical difference between d and g narrows as sample size increases. In samples of 50 or more per group, the two values are nearly identical for most purposes. Below roughly 20 observations per group, the gap becomes meaningful enough that effect size bias correction should be applied, and Hedges' g becomes the appropriate metric to report.

Same Inputs, Corrected Output

Hedges' g uses the same four inputs as Cohen's d: M1 and M2 (group means), SD1 and SD2 (group standard deviations). The calculator applies the correction internally. You enter your group summaries the same way, and the output accounts for the bias adjustment automatically.

Hedges' g vs. Cohen's d: Which to Use

The choice comes down to sample characteristics. Use Cohen's d when group sizes are large and roughly equal. Switch to Hedges' g when working with unequal sample sizes or small n, as those are the conditions where d's upward bias is most consequential. In practice, many researchers default to Hedges' g as their standard metric for two-group comparisons, particularly in meta-analysis contexts where effect size estimates from many small studies are pooled and bias compounds across studies. When in doubt between the two, Hedges' g is the more conservative and defensible choice.

Interpretation

Hedges' g is interpreted using the same conventional benchmarks as Cohen's d. A value around 0.2 indicates a small effect, 0.5 a medium effect, and 0.8 or above a large effect. Because the correction factor only slightly adjusts the raw d value, the magnitude category rarely changes between the two metrics. The difference matters most for precision in reporting and for downstream use in meta-analysis, not for the rough small/medium/large classification.

Eta-squared (η²) is the standard effect size for ANOVA designs. Where Cohen's d measures the standardized mean difference between two groups, eta-squared measures the proportion of total variance in an outcome that is explained by group membership. The result answers a different question: not how far apart two group means are, but how much of the overall spread in scores can be attributed to which group a participant belongs to.

When to Use Eta-Squared

Use eta-squared when your analysis involves a one-way ANOVA with three or more groups. It is not appropriate for two-group comparisons, where Cohen's d or Hedges' g is the correct metric. Effect size for ANOVA designs is most commonly reported as eta-squared, though alternatives exist and are discussed below.

Required Inputs

The calculator accepts two types of input for eta-squared: sum of squares between groups (SS_between) and total sum of squares (SS_total), if you have the ANOVA table already, or group-level summary values, from which the calculator derives the necessary sums of squares.

If your statistical software outputs an F statistic and degrees of freedom, you can also derive eta-squared from that output. The effect size from F statistic follows directly from the ANOVA table values, and many researchers enter those figures here when working from software output rather than raw data.

The Formula

The result ranges from 0 to 1. A value of 0 indicates that group membership explains none of the variance in the outcome. A value of 1 would indicate that group membership explains all of it. In practice, eta-squared values in social and behavioral research typically fall well below 0.5.

Effect Size Thresholds for Eta-Squared

Cohen's conventional benchmarks for eta-squared are:

These effect size thresholds follow the same logic as the small/medium/large framework applied to Cohen's d, and they carry the same caveat: treat them as reference points, not as fixed rules. A value of 0.06 in one research context may represent a meaningful result; in another, it may not.

Partial Eta-Squared: An Important Distinction

Most statistical software, including SPSS, R, and similar tools, reports partial eta-squared by default rather than eta-squared. The two are not the same. Partial eta-squared calculates the proportion of variance explained by a factor after removing the variance accounted for by other factors in the model. In a one-way ANOVA with a single factor, partial eta-squared and eta-squared are identical. In multi-factor designs, partial eta-squared values are typically larger than eta-squared values and are not directly comparable across studies that use different model structures. When reading software output, confirm which version is being reported before recording your effect size.

Omega-Squared vs. Eta-Squared

Eta-squared has a known positive bias: it tends to overestimate the true population effect size, particularly in smaller samples, in the same way that Cohen's d overestimates before Hedges' correction is applied. Omega-squared (ω²) is the less biased alternative for ANOVA designs, applying a correction to bring the estimate closer to the population value. The omega-squared vs. eta-squared choice mirrors the Cohen's d vs. Hedges' g choice: for larger samples the difference is small, for smaller samples the correction matters. This calculator reports eta-squared; if your sample is small or you are contributing results to a meta-analysis, consider computing omega-squared as well for comparison.

Effect size values are unitless numbers. Without a reference frame, knowing that Cohen's d is 0.43 or that eta-squared is 0.08 tells you very little on its own. Cohen's conventional benchmarks provide that reference frame, and understanding them is central to both interpreting a result and to planning a study through effect size power analysis.

Benchmarks for Cohen's d and Hedges' g

Benchmarks for Eta-Squared

These thresholds come from Cohen (1988) and represent the most widely cited reference points across psychology, social science, and behavioral research. They are the default frame of reference used when no field-specific norms exist.

What Is a Good Effect Size?

There is no universal answer. How big the effect size needs to be to matter depends entirely on the research context. A Cohen's d of 0.2 is conventionally small, but in a large-scale clinical trial measuring mortality or serious adverse outcomes, even a small standardized difference can translate to thousands of lives. A d of 0.8 is conventionally large, but in a tightly controlled laboratory study where every variable is held constant, that magnitude may be the expected baseline rather than a notable finding. Effect size significance, in the sense of whether a result is worth acting on, is a judgment that belongs to the researcher and the field, not to the benchmark table alone.

This is the core limitation of practical significance statistics framed around fixed cutoffs. Cohen himself noted that his benchmarks were rough guides intended for situations where no other basis for judgment existed. They were never meant to function as pass/fail thresholds.

Using Benchmarks for Power Analysis and Study Planning

Before data collection, effect size benchmarks serve a planning function. The minimum detectable effect size your study can reliably identify depends on your sample size, significance threshold, and desired statistical power. Researchers often use the medium benchmark (d ≈ 0.5) as a default planning assumption when prior literature provides no better estimate, but a more defensible approach is to base the target effect size on results from similar published studies in the same field. The benchmarks then serve as a sanity check, not a starting point.

Compare Results to Prior Literature, Not Just Benchmarks

The most reliable way to interpret your effect size is to position it against comparable published findings. If prior studies on a similar intervention or population report Cohen's d values clustering around 0.3 to 0.4, a result of 0.25 is informative relative to that range regardless of whether it sits in the "small" benchmark category. Effect size confidence intervals, which express the precision of the estimate rather than just the point value, provide additional context and are increasingly expected alongside the effect size value itself in peer-reviewed reporting.

Statistical significance and effect size measure different things. Treating them as equivalent is one of the most common errors in applied research, and understanding the distinction changes how you read both your own results and published findings.

What Each Measure Tells You

A p-value is the probability of observing your data, or data more extreme, under the assumption that the null hypothesis is true. It tells you whether a result is likely to have occurred by chance given your sample. It says nothing about the size of the effect.

Effect size tells you how large the observed difference or relationship actually is. It is the standardized magnitude of the result, independent of sample size. Where the p-value depends heavily on how many observations you collected, a properly computed effect size does not. That independence is what makes effect size values comparable across studies and what makes how to report effect size a question worth answering separately from significance testing.

Why Large Samples Distort Significance

A large enough sample will produce a statistically significant p-value for almost any nonzero difference, including differences so small they carry no practical weight. An unstandardized effect size, such as a raw mean difference of 0.3 points on a 100-point scale, may look negligible on its face. But with a sample of several thousand participants, that difference will reach p < 0.05 with little difficulty. The p-value confirms the difference is unlikely to be zero; it does not confirm the difference is worth acting on. Effect size makes that second judgment possible.

Why Small Samples Suppress Significance

The reverse problem occurs with small samples. A study with 15 participants per group may produce a Cohen's d of 0.6, which is a meaningful medium-to-large effect by conventional standards, while still failing to reach statistical significance because the test lacks the statistical power to reliably detect effects of that size. The effect is real and substantial; the significance test simply does not have enough information to confirm it with the required confidence. Low power causes genuine effects to go undetected, and p-values from underpowered studies should be interpreted with that limitation in mind.

Can Effect Size Be Negative?

Yes. Cohen's d and Hedges' g can be negative when the mean of Group 2 is larger than the mean of Group 1, because the formula subtracts M2 from M1. A negative value indicates the direction of the difference, not an error in the calculation. The magnitude of the effect is read from the absolute value. When reporting, the sign should be retained alongside the direction label to clarify which group scored higher.

Effect Size and P-Value Used Together

Neither measure alone gives a complete picture of a result. A p-value with no effect size tells you that something happened but not how much it mattered. An effect size with no significance test tells you the observed magnitude but not whether it is distinguishable from chance variation in this sample. Together, they answer the two questions a result needs to address: is this difference likely to be real, and is it large enough to matter?

The metric you select should match your study design, not your preference. Each of the three effect size types covered by this calculator is appropriate for specific conditions, and using the wrong one produces a result that is either technically incorrect or misleading when compared to other studies. The decision comes down to three factors: how many groups you are comparing, how large and balanced your samples are, and what kind of outcome you are measuring.

Cohen's d

Use Cohen's d when you are comparing two independent groups on a continuous outcome, your sample sizes are roughly equal, and the data within each group follow an approximately normal distribution. This covers the majority of standard experimental and quasi-experimental designs in psychology, education, and behavioral science: a treatment group versus a control group, two instructional conditions, two tested populations. Cohen's d is the conventional default for this design type and the metric most commonly reported in published literature for two-group comparisons.

Hedges' g

Use Hedges' g under the same two-group conditions as Cohen's d, but when your samples are small (roughly fewer than 20 observations per group) or unequal in size. As covered above, Cohen's d carries a small upward bias that compounds at small n. Hedges' g corrects that bias and should be the default choice in meta-analysis work, where pooling effect size estimates from multiple small studies makes that inflation consequential. When sample sizes are large and balanced, d and g will be nearly identical and either is acceptable, though Hedges' g is never the less defensible choice.

Eta-Squared

Use eta-squared when your analysis involves a one-way ANOVA with three or more groups. It is the appropriate effect size for variance-partitioning designs, where the question is how much of the total outcome variance is explained by group membership. It is not a substitute for Cohen's d in two-group designs, and the two metrics are not directly interchangeable in interpretation.

Designs Outside the Scope of This Calculator

For repeated measures designs, pre-post comparisons, or paired-sample analyses, none of the three metrics above is directly appropriate without adjustment. Repeated measures designs require effect size formulas that account for the correlation between measurements taken from the same participants. Using Cohen's d from independent groups in a paired design will underestimate the true effect because it does not remove within-subject variance from the denominator. If your design involves repeated observations, paired groups, or pre-post measurement, a dedicated repeated measures effect size calculator or manual adjustment is needed before the result can be interpreted or reported accurately.

A Note on Point-Biserial Correlation Effect Size

In some research contexts, particularly when one variable is continuous and the other is dichotomous, the point-biserial correlation effect size is used in place of Cohen's d. The two are mathematically related, and point-biserial r is sometimes preferred in correlational research designs or when results need to be expressed as a correlation coefficient for comparison across study types. This calculator does not compute point-biserial r directly, but the conversion section below covers how Cohen's d can be converted to r when that comparison is needed.

Cohen's d and the Pearson correlation coefficient (r) belong to different effect size families. Cohen's d describes a standardized mean difference between two groups. The correlation coefficient r describes the strength and direction of a linear relationship between two continuous variables. In most single-study contexts, the two are used for different designs and are not compared directly. The need to convert between them arises most often in meta-analysis, where studies using different designs and different reporting conventions need to be expressed on a common scale before their results can be aggregated.

The Formula

To convert Cohen's d to r, use the formula published by Cohen (1969):

From r², take the square root to obtain r. This is the r-squared effect size relationship made explicit: squaring the correlation gives the proportion of variance in one variable that is predictable from the other, which can then be traced back to the original d value through this conversion.

As a practical example: a Cohen's d of 0.5 produces an r of approximately 0.24. A d of 0.8 converts to approximately r = 0.37. The conversion is not linear, and the relationship between d and r compresses at higher values of d.

When to Use This Conversion

The primary use case is meta-analysis aggregation. When combining results across a set of studies, some may report Cohen's d from t-test comparisons while others report a correlation coefficient from regression or correlational designs. Converting all effect sizes to a common metric, typically r or d depending on the majority of included studies, allows meaningful pooling and comparison. This formula is the standard approach for that translation.

A secondary use case is cross-study comparison outside of formal meta-analysis. If a body of literature predominantly reports correlational effect sizes and your own study produces a Cohen's d, converting allows your result to be positioned accurately against that existing evidence base.

What This Conversion Is Not For