TestPulseHow to interpret KR-20 and KR-21
| Score | Verdict | Good enough for |
|---|---|---|
| 0.90 and above | Excellent | Certification and high-stakes exams |
| 0.80–0.89 | Good | Graded exams and hiring decisions |
| 0.70–0.79 | Acceptable | Screening tests and classroom quizzes |
| 0.50–0.69 | Low | Practice only; improve the test before relying on it |
| Below 0.50 | Poor | Scores are mostly noise |
Reliability rises with more good questions, so a 10-question quiz rarely reaches 0.80, while a 50-question exam should. Use results from at least 20–30 people; with fewer, the number bounces around.
The formulas
KR-20 (Kuder-Richardson Formula 20) = (k ÷ (k − 1)) × (1 − Σpq ÷ σ²), where k is the number of questions, p the share of people who got a question right, q = 1 − p, and σ² the variance of total scores (the standard deviation squared).
KR-21 = (k ÷ (k − 1)) × (1 − M × (k − M) ÷ (k × s²)), where M is the average number correct and s the standard deviation of total scores. It assumes every question is equally hard, so it is usually a little lower than KR-20.
Both formulas expect the standard deviation of the group itself (dividing by the number of people, not by one less). TestPulse calculates KR-20 automatically for every test. Read test reliability explained for more on what the number means.
Frequently asked questions
What is KR-20 (Kuder-Richardson Formula 20)?
KR-20 is the standard reliability measure for tests where each question is right or wrong. KR-20 = k ÷ (k − 1) × (1 − Σpq ÷ σ²), where k is the number of questions, p the share of people who got a question right, q = 1 − p, and σ² the variance of total scores.
How do I interpret a KR-20 score?
KR-20 runs from 0 to 1. 0.90 or higher is excellent (certification and high-stakes exams), 0.80–0.89 is good for graded exams and hiring decisions, 0.70–0.79 is acceptable for screening and quizzes, and below 0.70 the scores are too noisy to rely on alone.
What is KR-21?
KR-21 is a quick estimate of test reliability for right-or-wrong questions, using only the number of questions, the average score and the standard deviation. It assumes questions are of similar difficulty, so it slightly underestimates KR-20.
How can I raise reliability?
Add good questions on the same skill, remove confusing ones, replace questions that everyone gets right or wrong, and improve wrong answer options nobody picks.