Statistics

ANOVA Calculator

The ANOVA Calculator runs a one-way analysis of variance on two or three groups of comma-separated numbers, returning the F statistic, both degrees of freedom, and the mean squares between and within groups.

What this calculator does

The ANOVA Calculator estimates your result instantly from the values you enter, using standard statistics formulas. The ANOVA Calculator runs a one-way analysis of variance on two or three groups of comma-separated numbers, returning the F statistic, both degrees of freedom, and the mean squares between and within groups. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.

ANOVA Calculator

Result

—
F Statistic
—
df Between
—
df Within
—
Mean Sq. Between
—
Mean Sq. Within

About ANOVA Calculator

Enter two or three groups of numbers and this tool performs a one-way analysis of variance, comparing the variation between the group means to the variation within the groups. It reports the F statistic along with the supporting degrees of freedom and mean squares.

The third group is optional, so you can compare either two or three sets of observations.

Formula & Mathematical Calculation

F Statistic = f(Group 1 (comma-separated), Group 2 (comma-separated), Group 3 (optional))

Calculated according to standard stats formulas implemented in the calculator core.

Calculation Example

With Group 1 = 2, 4, 6 (mean 4) and Group 2 = 8, 10, 12 (mean 10), the grand mean is 7 across N = 6 values in k = 2 groups. The between-groups sum of squares is 3×(4−7)² + 3×(10−7)² = 27 + 27 = 54, and the within-groups sum of squares is 8 + 8 = 16.

With df between = 1 and df within = 4, the mean squares are 54 ÷ 1 = 54 and 16 ÷ 4 = 4, giving F = 54 ÷ 4 = 13.5.

Key Benefits

  • Performs a one-way ANOVA on two or three groups at once
  • Breaks out both degrees of freedom and the between and within mean squares
  • Returns the F statistic ready to compare against a critical value
  • Accepts groups of unequal size entered as comma-separated numbers

How to Use this Calculator

  1. Enter Group 1
    Type the first group of numbers into the Group 1 field, separated by commas.
  2. Enter Group 2
    Type the second group of numbers into the Group 2 field.
  3. Add Group 3 if needed
    Optionally type a third group into the Group 3 field; leave it blank to compare only two groups.
  4. Calculate
    Press Calculate and read the F Statistic, df Between, df Within, and mean square boxes.

Assumptions & Limitations

What the calculation assumes

  • Every value you enter is treated as an exact, known amount.
  • Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
  • Results use standard published formulas and account only for the values entered above.
  • Rounding is applied for display; the underlying calculation uses your full precision.
  • Results are returned in the same units you enter, unless the tool states the output unit.

What it does not cover

  • ANOVA Calculator produces a calculated result for reference and learning, not a certified or official measurement.
  • Real-world outcomes differ when tolerances, rounding rules or local standards apply.
  • Definitions and standards vary by region and change over time; verify the convention that applies to your case.
  • Figures are only as accurate as the inputs you supply — check them before acting on the result.
  • For work where the result carries real consequences, confirm it against an authoritative source.

Frequently Asked Questions

You can compare two groups, or add an optional third group; at least two non-empty groups are required.

F is the ratio of the between-groups mean square to the within-groups mean square; the tool suggests comparing it to the critical F value at your significance level to test whether the group means differ.

Degrees of freedom between groups is the number of groups minus one, and within groups is the total number of observations minus the number of groups.

No; it reports the F statistic, degrees of freedom, and mean squares, which you compare against a critical F value or an F table yourself.

Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.