No. 01
Working Memory and Digit Span — From 7±2 to 4±1
What digit span measures, and the conditions behind Miller's "magical number 7±2" and Cowan's "4±1", explained from the original research.
Holding a phone number in your head until you've dialed it, or keeping track of an intermediate result during mental arithmetic, relies on what psychologists call working memory. It is less a storage box than a workbench: you hold information briefly while you use and change it.
The idea of working memory
Baddeley and Hitch (1974) described short-term memory not as a single box but as a system with several parts: a phonological loop that holds speech sounds by rehearsing them, a visuospatial sketchpad that holds shapes and locations, and a central executive that coordinates the two and allocates attention. Baddeley (2000) later added an episodic buffer that binds information into a single scene.
Hearing digits and repeating them relies mainly on the phonological loop. As long as you silently rehearse the digits they stay in memory; once rehearsal stops, they fade within seconds.
A short history of the digit span task
Joseph Jacobs (1887) is credited with the first systematic measurement of digit span. He read increasingly long strings of digits to students and recorded the longest they could repeat without error. Because the method is simple and needs no equipment, digit span subtests later found their way into intelligence and neuropsychological tests, where they are still widely used.
Miller's "magical number 7±2"
Reviewing experiments on absolute judgment and immediate memory, George A. Miller (1956) pointed out that the number of items people can handle at once clusters around seven across many tasks. His paper's title, "The Magical Number Seven, Plus or Minus Two", became famous, and "7±2" became shorthand for memory capacity.
What Miller considered more important than the number itself was the unit he called the chunk. Memory span is limited by the number of meaningful groups rather than by the amount of information (bits), so regrouping items into larger chunks lets you fit more information into the same span. He himself admitted that the coincidence of "seven" was somewhat rhetorical.
Cowan's "4±1"
Re-examining many studies, Nelson Cowan (2001) proposed that when rehearsal and grouping are prevented, people hold 3 to 5 items, about 4, in the focus of attention at once. On this view, the spans of around 7 seen in digit span tasks reflect pure storage capacity plus silent rehearsal and natural grouping.
| Figure | Proposed by | Conditions | What it refers to |
|---|---|---|---|
| --- | --- | --- | --- |
| 7±2 | Miller (1956) | Immediate memory with rehearsal and grouping allowed | Memory span (items or chunks) |
| 4±1 | Cowan (2001) | Rehearsal and grouping suppressed | Chunks held in the focus of attention at once |
The two figures don't contradict each other; they measure under different conditions. The test on this site doesn't prevent rehearsal or grouping, so it is closer to Miller's conditions.
How to read your digit span score
- Your score is the longest length you got exactly right at least once. A single wrong digit makes the whole try incorrect.
- The same person varies by a digit or two from day to day. An average and trend over several tests are more reliable than one score.
- In standardized intelligence tests, the digit span subtest is given by a trained examiner at a fixed pace and procedure, and scores are interpreted with age-based norm tables. This site doesn't use such norms, so it doesn't show comparisons like "top X%".
- Your result is not evidence of your intelligence or of any memory disorder. If you feel your memory has noticeably declined, talk to a professional.
Sources: Jacobs (1887) Mind 12:75–79 · Miller (1956) Psychological Review 63(2):81–97 · Baddeley & Hitch (1974) Psychology of Learning and Motivation 8:47–89 · Baddeley (2000) Trends in Cognitive Sciences 4(11):417–423 · Cowan (2001) Behavioral and Brain Sciences 24(1):87–114