Hick's Law Reaction Time Calculator

Hick’s law (Hick-Hyman law), established in 1952, describes how reaction time grows with the number of equally likely choices. More options means more information to process, and processing takes time.

The formula:

RT = a + b x log2(n + 1)

where RT is reaction time in milliseconds, n is the number of equal-probability response alternatives, a is the base reaction time (the floor with no uncertainty at all, typically 150-200 ms), and b is the information processing rate (ms per bit, typically 150-200 ms/bit).

Why log base 2? Each doubling of choices adds exactly one bit of information. Going from 2 to 4 choices adds one bit. Going from 4 to 8 adds another. The brain processes this information at a roughly constant rate, so RT grows linearly with bits.

Typical parameter values:

• a: 150-200 ms (varies by individual and modality)
• b: 150-200 ms/bit for finger responses
• Simple reaction time, meaning one stimulus and one response: 150-250 ms

What n = 1 actually means, because it looks wrong. Put 1 into the formula and you get a + b·log2(2) = a + b, about 335 ms on typical values. Set that beside the 150-250 ms quoted above for simple reaction time and it looks like the law has failed at the easiest possible case.

It has not. The two numbers describe different tasks. Simple RT is measured with the response certain: a light comes on, you press, and the only question is how fast. The +1 inside the logarithm is Hyman’s 1953 addition for the uncertainty of whether to respond at all, so n = 1 in this formula is a go/no-go task, where a signal might or might not be the one you act on. Go/no-go really is slower than simple RT, by roughly the 100 ms the formula puts between them, and that is a measured difference rather than an artefact.

The practical consequence: if you want a prediction for a plain simple-RT task, use a on its own, not the formula. The calculator flags this when you enter 1.

Applications outside psychology. UX designers use Hick’s law to justify limiting navigation menu items. Too many choices increases the time users take to decide. Martial artists use it to explain why an oversized technique library becomes a liability in a fight, since scanning more options costs time you do not have.

The law breaks down with practice. Expert chess players do not scan moves sequentially; they pattern-match to familiar positions and bypass the linear search. When response options are predictable, RT no longer follows the log2 relationship.