Contingency Table Calculator

Work out contingency table instantly with clear inputs, formula shown and shareable results.

About Contingency Table Calculator

A two-by-two contingency table cross-tabulates two binary variables. Comparing each cell with its expected count under independence gives a chi-square statistic on one degree of freedom, and phi rescales it as a correlation.

Formulas

Expected count

E = row total × column total / grand total

Phi coefficient

φ = √(χ² / N)

Worked example

With the default values below, Contingency Table Calculator returns Chi-square statistic (1 df) of 16.66666667. Change any input above and every figure here is recalculated in your browser.

Inputs used

Cell a (row 1, column 1)minimum 0: 40
Cell b (row 1, column 2)minimum 0: 10
Cell c (row 2, column 1)minimum 0: 20
Cell d (row 2, column 2)minimum 0: 30

Results

Chi-square statistic (1 df): 16.66666667
p value: 0.00004456
Phi coefficient (effect size): 0.40824829
Grand total: 100

Step by step

1Values used
2Expected count
3Phi coefficient
4Chi-square statistic (1 df)= 16.66666667
5p value= 0.00004456
6Phi coefficient (effect size)= 0.40824829
7Grand total= 100

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For the table 40, 10, 20, 30?

The expected counts are 30, 20, 30 and 20, so χ² = 100/30 + 100/20 + 100/30 + 100/20 ≈ 16.667 on 1 df, giving p ≈ 0.00004 and a phi of 0.4082.

When should I use Fisher's exact test?

When any expected count falls below about 5, where the chi-square approximation becomes unreliable.