When do I use KR-20 instead of Cronbach’s alpha?

Use KR-20 when each item has only two values (right and wrong, yes and no). Use Cronbach’s alpha when items have more options, like a 1-to-5 Likert scale. With 0/1 data, both give the same result.

Yes. SPSS has no KR-20 button, but Cronbach’s alpha on 0/1 data matches the KR-20 this tool calculates.

How many people do I need?

A pilot test usually uses 20 to 30 people similar to your final sample. With fewer than 10 the result is unstable.

What if my answers are letters (a, b, c, d)?

Convert them in Excel first: 1 if the answer matches the key and 0 if not. Then paste that table.

All tools

Kuder-Richardson KR-20 calculator

KR-20 measures the reliability of a test where each question is scored right or wrong (or yes and no). Paste your data from Excel: one row per person and one column per item, with 1 for a right answer and 0 for a wrong one. If the first row has the question names, it is skipped automatically.

Paste your data (1 = right, 0 = wrong)

The calculation runs in your browser. We don’t store what you type.

How it’s calculated

KR-20 = k / (k − 1) × (1 − Σ p·q / σ²), where k is the number of items, p the share who got each item right, q = 1 − p and σ² the variance of total scores.

KR-21 is a simplified version that assumes every item has the same difficulty: KR-21 = k / (k − 1) × (1 − M (k − M) / (k σ²)), with M the mean score.

Item difficulty is the share of people who got it right. Discrimination is the item’s correlation with the score on the rest of the test (corrected point-biserial).

"KR-20 if item deleted" repeats the calculation without each question, so you can see which ones lower reliability.

How to read the result

Read it like Cronbach’s alpha: 0.9 or more excellent, 0.8 good, 0.7 acceptable, 0.6 questionable and below 0.6 low.
Difficulty: 0.30 to 0.70 is ideal. An item almost everyone gets right (over 0.90) or almost nobody does (under 0.10) adds little.
Discrimination (Ebel): 0.40 or more very good, 0.30 to 0.39 good, 0.20 to 0.29 review, and below 0.20 the item should be rewritten or dropped.
If KR-20 rises noticeably without an item and that item also discriminates poorly, it is the first one to fix.

Frequently asked questions

When do I use KR-20 instead of Cronbach’s alpha?: Use KR-20 when each item has only two values (right and wrong, yes and no). Use Cronbach’s alpha when items have more options, like a 1-to-5 Likert scale. With 0/1 data, both give the same result.
Does it match SPSS?: Yes. SPSS has no KR-20 button, but Cronbach’s alpha on 0/1 data matches the KR-20 this tool calculates.
How many people do I need?: A pilot test usually uses 20 to 30 people similar to your final sample. With fewer than 10 the result is unstable.
What if my answers are letters (a, b, c, d)?: Convert them in Excel first: 1 if the answer matches the key and 0 if not. Then paste that table.

Is it for your thesis?See the step-by-step guide to running your thesis survey: sample, questionnaire, consent, pilot test and analysis.Thesis surveys

Know what you want to ask?

Build the survey in SurvIQ, share it by link, WhatsApp or QR code, and watch results come in live. The Free plan is free forever.

Create a free survey

More tools

Aiken’s V calculatorContent validity from expert judges, item by item.Normality test (Shapiro-Wilk and Kolmogorov-Smirnov)Check whether your data is normally distributed before choosing a statistical test.Likert scale score rangesTurn scores into levels (low, medium, high) with ranges ready for your thesis.Compare two percentagesFind out if the difference between two groups is real or could be chance.Chi-square calculatorCheck whether two categorical variables are related.Correlation calculator (Pearson and Spearman)See whether two numeric variables rise or fall together, with the p-value.