What is a Weber fraction?

It is the smallest relative difference between two quantities you can reliably tell apart. A Weber fraction of 0.15 means you can just distinguish 100 dots from 115. Lower is sharper. Most adults fall between 0.10 and 0.30.

Why flash the dots so briefly?

Half a second is too short to count. That forces you to use your approximate number system - the fast, innate sense of "roughly how many" - which is exactly what the test is measuring.

Does it matter that the dots are different sizes?

The dot sizes and total area are varied on purpose so you cannot use "more blue stuff" as a shortcut for "more blue dots". The judgement has to be about count.

Is a sharp number sense the same as being good at maths?

They are linked but not the same. In children, a sharper Weber fraction predicts later arithmetic achievement, and the correlation persists more weakly into adulthood. But formal maths relies far more on learned symbolic skills than on this fast, wordless sense of quantity.

Number Sense Test - Your Approximate Number Acuity

Two clouds of dots flash by. Which colour had more? This test estimates your Weber fraction, a precise measure of the brain's approximate number system.

How the scores are spread

Where players land on this test. Take it to see your own mark on the curve.

Lower is better · reference sample of 25,000

What this test measures

A field of blue and yellow dots flashes for half a second. You report which colour was more numerous. The ratio between the two counts ranges from very easy (more than 2 to 1) to hard (about 1.1 to 1).

From your pattern of right and wrong answers across the ratios, the test estimates your Weber fraction by maximum likelihood. Lower means you can discriminate closer quantities.

How to get a clean score

Do not try to count - you cannot, and attempting it makes you slower and less accurate.
Take in the whole field at once rather than scanning.
Guess when you are unsure. The estimate needs your genuine near-threshold performance, and refusing to answer the hard trials biases it.

How to improve your score

Mostly this is a fixed acuity, but a few things help you hit your true ceiling. Let your gaze rest in the centre and take in both colours at once rather than sweeping across the field - the estimate is a whole-scene impression, not a scan. Answer every trial, including the ones that feel like coin flips, because the Weber-fraction estimate needs your genuine near-threshold guesses and goes wrong if you only commit when you are sure. Training studies show small improvements with heavy practice, but expect your number to be fairly stable.

What the number tells you

The approximate number system is shared with infants and many animals and underlies our intuition for quantity. In children, a sharper Weber fraction predicts later maths achievement. In adults it is fairly stable, and this task is the standard way to measure it outside a lab.

FAQ

What is a Weber fraction?: It is the smallest relative difference between two quantities you can reliably tell apart. A Weber fraction of 0.15 means you can just distinguish 100 dots from 115. Lower is sharper. Most adults fall between 0.10 and 0.30.
Why flash the dots so briefly?: Half a second is too short to count. That forces you to use your approximate number system - the fast, innate sense of "roughly how many" - which is exactly what the test is measuring.
Does it matter that the dots are different sizes?: The dot sizes and total area are varied on purpose so you cannot use "more blue stuff" as a shortcut for "more blue dots". The judgement has to be about count.
Is a sharp number sense the same as being good at maths?: They are linked but not the same. In children, a sharper Weber fraction predicts later arithmetic achievement, and the correlation persists more weakly into adulthood. But formal maths relies far more on learned symbolic skills than on this fast, wordless sense of quantity.

Reference sample: SYNTHETIC. Lognormal, mean 0.20 / sd 0.09 for the Weber fraction from a dot-comparison task. Anchored to adult ANS acuity estimates (w ~0.1-0.3).