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Cohen's d Calculator

Get Cohen's d for two groups from summary statistics, with the matching t-test and a size label.

Test
Data entry
Method
Group 1
Group 2
Alternative hypothesis
Significance level (α)

Student's two-sample t-test (equal variances)

t = 1.8686, p = 0.067
Degrees of freedom
58
Critical values
-2.002 and 2.002
Difference of means
7
Standard error
3.7461
95% interval
-0.4987 to 14.5
Cohen's d
0.482 (small)

p = 0.067 ≥ α = 0.05, so fail to reject H0: μ1 = μ2. There is not enough evidence that the two population means differ. The sample means differ by 7 (95% interval from -0.4987 to 14.5). Cohen's d = 0.482, a small effect.

Student or Welch?

The variances differ by a factor of 1.15 and the group sizes are similar, so Student and Welch give nearly the same answer. Welch is still the safer default.

Methodtdfp-value
Welch1.868657.7260.067
Student1.8686580.067

Rejection region and t statistic

Rejection region and t statisticRejection region and t statistic. The two tails is shaded. The t is 1.869.-4-3-2-101234t (df = 58)t = 1.869

The shaded area is the rejection region (total area 0.05): values below -2.002 or above 2.002. The dashed line is your statistic.

Step-by-step working

  1. 1Hypotheses
    H0: μ1=μ2H_0:\ \mu_1 = \mu_2H0​: μ1​=μ2​
    ↓
    H1: μ1≠μ2H_1:\ \mu_1 \neq \mu_2H1​: μ1​=μ2​

    two-tailed test at α = 0.05

  2. 2Group summaries
    xˉ1, s1, n1 and xˉ2, s2, n2\bar x_1,\ s_1,\ n_1\ \text{and}\ \bar x_2,\ s_2,\ n_2xˉ1​, s1​, n1​ and xˉ2​, s2​, n2​
    ↓
    105, 15, 30 and 98, 14, 30105,\ 15,\ 30\ \text{and}\ 98,\ 14,\ 30105, 15, 30 and 98, 14, 30
  3. 3Pooled variance
    sp2=(n1−1)s12+(n2−1)s22n1+n2−2s_p^2 = \dfrac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}sp2​=n1​+n2​−2(n1​−1)s12​+(n2​−1)s22​​
    ↓
    sp2=29(15)2+29(14)258=210.5s_p^2 = \dfrac{29(15)^2 + 29(14)^2}{58} = 210.5sp2​=5829(15)2+29(14)2​=210.5
  4. 4Standard error
    SE=sp2(1n1+1n2)SE = \sqrt{s_p^2\left(\dfrac{1}{n_1}+\dfrac{1}{n_2}\right)}SE=sp2​(n1​1​+n2​1​)​
    ↓
    SE=3.7461SE = 3.7461SE=3.7461
  5. 5Degrees of freedom
    df=n1+n2−2df = n_1 + n_2 - 2df=n1​+n2​−2
    ↓
    df=58df = 58df=58
  6. 6t statistic
    t=xˉ1−xˉ2SEt = \dfrac{\bar x_1 - \bar x_2}{SE}t=SExˉ1​−xˉ2​​
    ↓
    t=105−983.7461=1.8686t = \dfrac{105 - 98}{3.7461} = 1.8686t=3.7461105−98​=1.8686
  7. 7p-value and critical value
    p and tc (df=58)p\ \text{and}\ t_c\ (df = 58)p and tc​ (df=58)
    ↓
    p=0.06673, tc=−2.002 and 2.002p = 0.06673,\ t_c = -2.002\ \text{and}\ 2.002p=0.06673, tc​=−2.002 and 2.002
  8. 8Confidence interval
    (xˉ1−xˉ2)±tα/2 SE(\bar x_1 - \bar x_2) \pm t_{\alpha/2}\,SE(xˉ1​−xˉ2​)±tα/2​SE
    ↓
    7±2.002×3.7461=[−0.4987, 14.5]7 \pm 2.002\times 3.7461 = [-0.4987,\ 14.5]7±2.002×3.7461=[−0.4987, 14.5]
  9. 9Cohen's d
    d=xˉ1−xˉ2spd = \dfrac{\bar x_1 - \bar x_2}{s_p}d=sp​xˉ1​−xˉ2​​
    ↓
    d=714.509=0.4825d = \dfrac{7}{14.509} = 0.4825d=14.5097​=0.4825

    small effect

  10. 10Decision
    p≥αp \geq \alphap≥α
    ↓
    fail to reject H0\text{fail to reject } H_0fail to reject H0​
  1. Tools
  2. Statistics
  3. T-Test Calculator
  4. Cohen's d Calculator

About Cohen's d Calculator

This Cohen's d calculator turns two group means, standard deviations and sizes into a standardised effect size, and runs the matching two-sample t-test. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.

Cohen's d is the difference between the means divided by the pooled standard deviation, so it says how many standard deviations apart the groups are. Unlike a p-value it does not grow just because the sample is large, which makes it the right number to report next to a significance test.

The page opens on two groups of 30 with a seven-point gap and spreads near 15. The label (negligible, small, medium, large) uses Cohen’s benchmarks, which are rules of thumb rather than laws.

How to use Cohen's d Calculator

  1. 1Choose the test: one-sample, paired or two-sample.
  2. 2Choose raw data or summary statistics. For raw data, paste each list; for paired data, keep the two lists in the same order and the same length.
  3. 3For a one-sample test type the hypothesised mean. For two samples pick Welch or Student.
  4. 4Pick the alternative hypothesis (two-tailed, right or left) and the significance level.
  5. 5Read the t statistic, p-value, interval and Cohen's d, then open the working to see every formula.

Features

  • One-sample, paired and independent two-sample t-tests.
  • Welch (unequal variances) and Student (pooled) two-sample tests, compared side by side with a recommendation.
  • Raw data or summary statistics (mean, standard deviation, n).
  • Cohen's d with a size label, plus the standard error and a confidence interval.
  • Left, right or two-tailed tests, with the critical value for your significance level.
  • A bell curve with the rejection region shaded and the t statistic marked.
  • Step-by-step KaTeX working and a plain-English conclusion.

Cohen's d

The pooled standard deviation weights each group by its degrees of freedom.

s_p = √( ((n1 − 1) s1² + (n2 − 1) s2²) / (n1 + n2 − 2) )
d = (x̄1 − x̄2) / s_p

Worked examples

  • Group 1: mean 105, SD 15, n 30. Group 2: mean 98, SD 14, n 30 → gives d = 0.482 (small), t = 1.869, df = 58, p = 0.067

    A small effect that does not reach significance with 30 per group.

Privacy: how it works

  • The test is calculated by code in your own browser tab. Your data is not sent to Ulkaa or to any other server.
  • There is no account and nothing is stored. Closing the tab clears what you entered.

Tips

  • Use the paired test when the same people or items are measured twice. Using the two-sample test on paired data throws away the pairing and usually loses power.
  • Decide one-tailed or two-tailed before you see the data. A two-tailed test is the safe default.
  • Report the effect size and the interval with the p-value. A tiny p-value with a negligible Cohen's d is statistically significant but may not matter in practice.
  • If your lists have different lengths, that is fine for the two-sample test, but the paired test needs equal lengths.

Frequently asked questions

Is it really free?

Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.

Do I need an account?

No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.

Does it run in my browser?

Yes. Your data are processed by code running in your browser tab, on your own device.

Is my data uploaded?

No. Your data are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.

What is a good Cohen’s d?

By convention 0.2 is small, 0.5 medium and 0.8 large. Whether an effect matters depends on the field, the cost of the intervention and the outcome being measured.

Does the sign of d matter?

The sign shows which group is higher. A negative d means group 1 has the lower mean. The size label uses the absolute value.

More T-Test Calculator pages

  • T-Test CalculatorRun a one-sample, paired or two-sample t-test from raw data or summary statistics, with Cohen's d, the p-value and the working.
  • One-Sample T-Test CalculatorCompare the mean of one sample with a value you expect and see the t statistic, p-value and working.
  • Paired T-Test CalculatorPaste two matched lists and get the paired t statistic, p-value and working.
  • Two-Sample T-Test CalculatorCompare the means of two independent groups with the classic pooled Student t-test.
  • Welch's T-Test CalculatorCompare two means without assuming equal variances, with Welch-Satterthwaite degrees of freedom.

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