Test Reliability (KR-20) Calculator
Kuder-Richardson Formula 20 (KR-20) estimates the internal consistency reliability of a test whose items are scored right or wrong. It tells you how consistently the items work together to measure the same underlying ability. KR-20 is the binary-item special case of Cronbach's alpha and ranges from 0 to 1, where higher is more consistent. This calculator takes the number of items, the summed item variances, and the total score variance, then returns KR-20 along with a plain-language interpretation band. Enter your values to evaluate a test.
KR-20 formula
KR-20 = (k / (k - 1)) * (1 - (sum of item variances / total variance))
Item variance for a binary item = p * q (q = 1 - p)
Variance ratio = sum of item variances / total variance
Result ranges from 0 (no consistency) to 1 (perfect consistency)
The k / (k - 1) factor corrects for the number of items. As the summed item variance approaches the total variance, reliability falls toward zero.
Interpreting and using KR-20
- 0.90 and above is excellent and suitable for high-stakes decisions.
- 0.80 to 0.89 is good for most assessment uses.
- 0.70 to 0.79 is acceptable for many classroom and research contexts.
- Below 0.70 suggests the items may not measure a single consistent construct.
- Reliability rises with more items and with items that discriminate well between high and low scorers.
Test reliability: frequently asked questions
What is KR-20?
Kuder-Richardson Formula 20 (KR-20) is a measure of internal consistency reliability for a test scored right or wrong (dichotomous items). It estimates how consistently the items measure the same underlying construct. KR-20 is a special case of Cronbach's alpha for binary items and ranges from 0 to 1, with higher values indicating greater consistency.
What is the KR-20 formula?
KR-20 equals (k / (k - 1)) times (1 minus the sum of item variances divided by the total test variance), where k is the number of items. For binary items each item variance is p times q, where p is the proportion who got the item correct and q equals 1 minus p.
What is a good KR-20 value?
Interpretation depends on the purpose of the test. As a common rule of thumb, values of 0.70 and above are considered acceptable for many classroom and research settings, 0.80 and above is good, and 0.90 and above is excellent for high-stakes decisions. Very low values suggest the items are not measuring a single consistent construct.
How is KR-20 different from Cronbach's alpha?
KR-20 is used when items are scored dichotomously (correct or incorrect). Cronbach's alpha is the general form used when items can take a range of values, such as Likert ratings. For binary items the two formulas give the same result, so KR-20 is simply alpha applied to right or wrong scoring.
What inputs do I need?
You need the number of test items (k), the sum of the individual item variances (sum of p times q across items), and the variance of total test scores across test takers. Many statistics packages report these directly, or you can compute item variances from the proportion correct on each item.
Official sources
- National Center for Education Statistics: NCES assessment resources.
- U.S. Department of Education: ED.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.