Expected Frequency Calculator

Enter the total in the i-th row, the total in the j-th column, and the grand total into the calculator to determine the expected frequency for a given cell. The calculator is found below.

Expected Frequency Calculator

Single Cell Contingency Table Chi-Square Test

Enter any 3 values to calculate the missing variable

Row Value Column Value Total Value Expected Frequency Preset Scenario None Wikipedia Example (20,40,100 → 8) Example (100,125,250 → 50)

Build your table and enter observed counts to get expected frequencies for each cell.

Rows 23456 Columns 23456 Preset Dataset None A/B Test Conversions (2×2) Study Preference by Group (3×2) Defect Types by Line (3×3)

Enter observed counts to compute expected frequencies, χ², degrees of freedom, and p-value.

Rows 23456 Columns 23456 Preset Dataset None A/B Test Conversions (2×2) Study Preference by Group (3×2) Defect Types by Line (3×3) Calculate Reset

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Expected Frequency Formula

The following equation can be used to calculate the expected frequency of a contingency table.

E = \frac{R_i \times C_j}{N}

• Where E is the expected frequency (expected count) for cell (i, j)
• Ri is the total in the i-th row
• Cj is the total in the j-th column
• N is the grand total

To calculate the expected frequency, multiply the total of the i-th row by the total of the j-th column, then divide the result by the grand total.

In a contingency table, this expected frequency calculation must be performed once per cell. For an r × c table, you will do the calculation r × c times (for example, a 32 × 32 table has 1024 cells).

Expected Frequency Definition

Expected frequency (or expected count) is the average number of times an outcome would occur over many repetitions, often computed under a null hypothesis. For example, the probability of drawing any specific card from a standard 52-card deck in one draw is 1/52 ≈ 0.01923 ≈ 1.923%. If you make n draws with replacement, the expected number of times that specific card appears is n/52.

Expected frequencies are most often used when analyzing contingency tables. You can see an example of this below.

FAQ

What is an expected frequency?

An expected frequency (expected count) is the number of observations you would expect in a category or contingency-table cell under a stated model (often a null hypothesis).

How is expected frequency calculated?

For a contingency-table cell (i, j), expected frequency is calculated as E = (row total × column total) / grand total, and you repeat this for each cell.