Calculate raw Cronbach’s alpha from item and total-score variances, or standardized alpha from average inter-item correlation. Inspect coefficient diagnostics and optionally model test length for a supplied target.

Cronbach’s alpha describes sample internal consistency, not validity or a single underlying dimension. Use consistently scored items from the same respondents; no universal acceptable cutoff is assumed.

Use the same respondents, scoring and variance divisor as the total-score variance.

Target alpha and length planning

Blank omits planning. Enter a target below 1; added items must be comparable to the existing items.

Related Calculators

Reliability Coefficient Formula

The following formula is used to calculate the Reliability Coefficient.

RC = (k / (k - 1)) × (1 - (Σσ² / σt²))

Variables:

  • RC is the Reliability Coefficient
  • k is the number of items or tests
  • Σσ² is the sum of the variances of each item or test
  • σt² is the total variance of the test scores

For raw Cronbach’s alpha, calculate item variances and the variance of the summed total scores using the same respondents, scoring and variance divisor. Divide the sum of item variances by the total-score variance, subtract that ratio from 1, then multiply by k/(k − 1). Standardized alpha instead uses the average Pearson correlation and can differ when item variances differ.

What is a Reliability Coefficient?

This calculator estimates Cronbach’s alpha, a sample internal-consistency coefficient used for scales such as questionnaires and tests. Coherent inputs give alpha no greater than 1, but alpha can be negative when net inter-item covariance is negative. Negative values warrant review of scoring directions and item relationships. Alpha depends on the sample, test length and intended use; it does not by itself establish validity, accuracy or a single underlying dimension. There is no universal acceptable cutoff.

How to Calculate Reliability Coefficient?

The following steps outline how to calculate the Reliability Coefficient.

  1. First, determine the number of items or tests (k).
  2. Next, calculate the sum of the variances of each item or test (Σσ²).
  3. Next, determine the total variance of the test scores (σt²).
  4. Next, use the formula RC = (k / (k - 1)) * (1 - (Σσ² / σt²)).
  5. Finally, calculate the Reliability Coefficient.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Number of items or tests (k) = 5

Sum of the variances of each item or test (Σσ²) = 10

Total variance of the test scores (σt²) = 3. Alpha = (5/4) × (1 − 10/3) = −2.916667. This is a negative-alpha example; inspect scoring direction and item relationships rather than treating it as a normal positive reliability estimate.