Dual n-back scoring: formulas, examples and calculator

Start with one stream and one comparison rule

Dual n-back asks you to judge position and sound separately. For each stream, a target is an item that matches the item exactly N turns earlier. A response is a press on the corresponding control within the response window. The same turn can contain a target in one stream, in both, or in neither. Before interpreting a percentage, establish which stream, which eligible turns and which response window it describes. A percentage without its counting rule leaves out information you need to interpret it.

The four possible outcomes

A hit means you pressed for a real match. A miss means a real match passed without the required response. A false alarm means you pressed when there was no match at the required distance. A correct rejection means there was no match and you did not press. These four counts form a complete record for the eligible comparisons in one stream. They describe outcomes, not their causes: a false alarm might involve confusion about N, an accidental tap or an uncertain decision. The count alone cannot tell you which happened.

A worked example: 100 eligible comparisons

Imagine one stream with 20 matches and 80 non-matches. You correctly identify 16 matches, miss 4, press incorrectly on 8 non-matches and correctly leave 72 non-matches alone. The four counts add up to 100: 16 + 4 + 8 + 72. These are invented teaching values, not results from users or a recommended target. Keeping a complete example makes it easier to see how the same performance can produce different percentages without either calculation being arithmetically wrong.

Hit rate and false-alarm rate use different denominators

The hit rate is hits divided by all real matches: 16 / (16 + 4) = 80%. The false-alarm rate is false alarms divided by all non-matches: 8 / (8 + 72) = 10%. Do not divide both counts by 100 and call them these rates. Sixteen hits out of 100 comparisons is the proportion of all comparisons that ended in a hit; it is a different quantity. If there were no real matches, the hit rate has no denominator and is undefined. The same applies to the false-alarm rate if there were no non-matches.

Overall accuracy and active accuracy answer different questions

Overall accuracy counts both kinds of correct outcome: (hits + correct rejections) / all comparisons. The example gives (16 + 72) / 100 = 88%. Another rule, labelled active accuracy in the calculator, is hits / (hits + misses + false alarms). It excludes correct rejections, giving 16 / (16 + 4 + 8), approximately 57.1%. This is not the statistical metric called precision, whose denominator is hits + false alarms. Check the definitions supplied by the app or study before comparing a displayed result with either formula.

Why never pressing can look deceptively good

Keep the example’s 20 matches and 80 non-matches, but imagine never pressing. The counts become 0 hits, 20 misses, 0 false alarms and 80 correct rejections. Overall accuracy is 80%, even though every match was missed. Active accuracy is 0%, hit rate is 0% and false-alarm rate is 0%. The example demonstrates the importance of the denominator; it does not imply that an app necessarily awards 80% for doing nothing. A target-sensitive scoring rule can treat the same behaviour quite differently.

Try the counts without confusing them with an app result

The calculator below works on one stream. Its starting values reproduce the 100-comparison example. Change a count to explore the four formulas, or use the never-press example to keep the number of targets constant while changing the response pattern. Zero-denominator results are shown as undefined rather than silently converted to a good or bad score. This is a teaching tool, not an import of your app history, a reconstruction of every app version or a clinical assessment. The values stay in your browser.

Read position and sound before combining them

Calculate each stream separately when the underlying counts are available. If you combine streams, decide whether you are pooling counts or averaging percentages. Those procedures can differ when the denominators differ. For example, a stream with 9 hits in 10 target trials has a 90% hit rate, while another with 1 hit in 2 target trials has a 50% hit rate. Their simple average is 70%; their pooled hit rate is 10 / 12, approximately 83.3%. Report which calculation you used. Neither should be silently substituted for the other.

A good score depends on the task settings

N, the number of active streams, pace, number of eligible trials, target frequency and scoring formula all affect the meaning of a score. A result from a different setup is not automatically better or worse than yours. Check how initial turns without enough history are treated, whether simultaneous matches need two responses and whether missed responses are counted separately by stream. For comparisons over time, keep those settings as consistent as practical and record changes instead of treating every percentage as interchangeable.

Read the settings before comparing scores

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Actual app capture · September 2026 · interface language may differ · EN · 2026-09-06

Variability is information, not a diagnosis

A session can vary with attention, familiarity with the controls, interruptions or other conditions. A score alone does not establish why it changed, and there is no basis here for assigning a fixed effect to sleep, caffeine or a particular day. Look at several comparable sessions before interpreting a trend. A plateau does not identify a biological ceiling, and a lower result does not by itself show a loss of general memory ability. If a session feels uncomfortable or frustrating, a shorter session or a break is a practical option rather than a guaranteed scoring strategy.

What to keep in a simple practice record

Keep the date, N, active streams, pace, eligible trial count and the formula used. When available, keep the four outcome counts for each stream; the rates can then be recalculated without guessing their denominators. Add a brief note about an interruption or a settings change if it will help you interpret the session later. A personal best can be motivating, but it is not the same as a typical result. A few comparable records are more informative than a collection of percentages with no description of the task.

What these numbers can and cannot establish

These scores describe responses to a particular task under particular rules. Improvement on that task is not, by itself, a measured increase in IQ or proof of better performance at school or work. The research guide explains the distinction between practice gains and transfer to other outcomes. Use the scores to understand your responses and the exercise’s rules. For your actual session result, refer to the definitions and per-stream breakdown shown by the app; the calculator is there to make the arithmetic transparent.

Further reading

• Kane et al. (2007), Working memory, attention control, and the n-back task, Journal of Experimental Psychology: Learning, Memory, and Cognition
• Cowan (2010), The Magical Mystery Four: How is working memory capacity limited, and why?, Current Directions in Psychological Science
• scikit-learn documentation — classification metrics and confusion matrices (mathematical definitions)