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Spearman-Brown Prophecy Formula Calculator

What is the Spearman-Brown prophecy formula?

ρ* = nρ / (1 + (n - 1)ρ), where ρ is the current reliability and n the factor by which the test is lengthened. Doubling a test with reliability .70 gives 2(.70)/1.70 = .82. To reach a target ρ*, the length factor is n = ρ*(1 - ρ) / [ρ(1 - ρ*)]. For a split half, n = 2.

How many items do you need to add to get alpha over .80? How reliable is the short form? Is the split-half correlation the test's reliability? The Spearman-Brown formula answers all three.

Enter the current reliability and length; the calculator gives the predicted reliability at the new length, the length for a target, the split-half correction, and a table across lengths.

Use the calculator All free tools

Built by Muhammad Shahzeb Anwar, MSc Industrial and Organizational Psychology. Test length is a design decision in every assessment, from classroom tests to selection tests and rating panels.

The calculator

Your test

Runs in your browser. Nothing you type is stored or sent anywhere.

Cronbach's alpha, KR-20, test-retest or inter-rater reliability, from 0 to 1.
The correlation between two halves of one test.

Three uses

Lengthening or shortening a test. A 20-item test with alpha .70 extended to 40 parallel items: n = 2, ρ* = 1.40/1.70 = .824. Cut a 40-item test with reliability .80 to 20 items: n = .5, ρ* = .40/.60 = .667.

Length needed for a target. From .70 to .90: n = .90 x .30 / (.70 x .10) = 3.86, so 20 items become 78. That is often the moment to write better items instead.

Split-half reliability. The correlation between two halves estimates the reliability of a half-length test. Stepping it up to full length is the Spearman-Brown formula with n = 2: a split-half r of .60 gives 2(.60)/1.60 = .75.

The same formula works for raters: the reliability of the average of k raters, from one rater's reliability, is the Spearman-Brown step-up with n = k. It is how the average-measures ICC relates to the single-measures ICC.

The assumption that matters

The prophecy assumes the new items are parallel to the old ones: measuring the same thing, equally well. In practice added items are usually a little weaker, so treat the prediction as a ceiling. Shortening works the other way: if you drop the weakest items, the short form keeps more reliability than the formula predicts.

Before you rely on this

What this will not tell you

This applies the formula; it cannot know whether new items will be as good as the old ones. It does not estimate validity, which rises much more slowly with length than reliability. Nothing you type leaves your browser.

Questions

Questions people actually ask

What does the Spearman-Brown formula predict?

The reliability of a test whose length is changed by a factor n, assuming the added or removed items are parallel to the rest.

How do I correct a split-half correlation?

Use Spearman-Brown with n = 2: full-test reliability = 2r / (1 + r). A split-half r of .60 gives .75.

How many items do I need for a reliability of .80?

Multiply the current number of items by n = .80(1 - r) / [r(1 - .80)], where r is the current reliability. From .60 with 10 items you would need about 27.

Does doubling a test double its reliability?

No. Reliability rises with diminishing returns: .50 becomes .67 when doubled, .70 becomes .82, and .90 only .95.

Can I use Spearman-Brown for raters?

Yes. The reliability of the mean of k raters follows the same formula with n = k, given one rater's reliability.

The papers behind the formula

Sources

The formula was published independently by Spearman and by Brown in the same issue in 1910. Checked on 2 November 2026.

  1. Spearman, C. (1910). Correlation calculated from faulty data. British Journal of Psychology, 3(3), 271-295: https://doi.org/10.1111/j.2044-8295.1910.tb00206.x
  2. Brown, W. (1910). Some experimental results in the correlation of mental abilities. British Journal of Psychology, 3(3), 296-322: https://doi.org/10.1111/j.2044-8295.1910.tb00207.x
Citation

Cite this tool

Free to use and free to quote. If a figure here is useful in something you are writing, a link back is all that is asked.

Muhammad Shahzeb Anwar, MSc Industrial and Organizational Psychology. Spearman-Brown Prophecy Calculator. Shahzeb Speaks. https://www.shahzebspeaks.com/spearman-brown-prophecy-calculator/

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Building or shortening a test?

The free item analysis calculator shows which items to cut first: the ones with low discrimination, which a short form can lose at the least cost in reliability.

Open the item analysis calculator