Hick’s law (the Hick-Hyman law)

In short

With two buttons in front of you, you choose right away. With sixteen, you pause for a moment. Hick’s law describes how this pause grows with the number of options.

It is also called the Hick-Hyman law. Both names describe the same principle.

Measure it yourself in the test below. First do a few rounds with 2 options, then with 16.

Live demo: find the right fruit

Choose a number of options and press Start. A target name appears at the top, with the options below. Find the target and press it. A wrong option counts as an error, and the round goes on.

Decision time test

This test works with JavaScript. If it’s off, the text below explains the same idea with the formula and examples.

Time is measured from pressing Start to pressing the right option. The time to read the target name is included. This isn’t a controlled experiment: do a few rounds with each number and look at the mean. With the keyboard, focus is on the first option and Tab moves on. Then time grows faster, because you go through the options one by one.

With 16 options, your mean is very likely higher than with 2. But the difference doesn’t grow as much as the number of options. The formula below shows why.

This test has a weakness: the options are reshuffled every round. Part of the measured time therefore goes into searching. I come back to this difference in the section on limits.

The formula: what is measured?

The Wikipedia article on Hick’s law gives the formula for equally probable options as:

T = b × log₂(n + 1)

• T: mean reaction time.
• n: number of equally probable options.
• b: a constant determined from the data.

The +1 in the formula has a reason. The person doesn’t know which option they will choose, nor whether they should respond at all. The +1 covers this second uncertainty; the article bases this explanation on the 1983 book by Card, Moran and Newell.

The Interaction Design Foundation, on the other hand, writes the formula as RT = a + b × log₂(n). Here a and b are constants that depend on the task and conditions. Both notations describe the same idea: time grows with the logarithm of the number of options.

• 2 options1.58 bits
• 4 options2.32 bits
• 8 options3.17 bits
• 16 options4.09 bits

Figure: values of log₂(n + 1) for the four numbers from the demo. The calculation is mine. While the number of options rises eightfold, the value doesn’t even triple.

The practical consequence: doubling the options adds roughly a fixed amount of time. In the figure’s calculation, the step from 8 to 16 adds 0.92 bits, and the step from 2 to 4 adds 0.74 bits.

Origin: Hick 1952, Hyman 1953

The first source of the law is the paper by psychologist William Edmund Hick, “On the Rate of Gain of Information”. It appeared in March 1952 in the Quarterly Journal of Experimental Psychology: volume 4, issue 1, pages 11–26.

According to Wikipedia, Hick used 10 lamps arranged in a circle in his experiment. Each lamp was paired with a Morse key pressed with its own finger. A random lamp lit up, and the participant pressed the right key.

The second source is psychologist Ray Hyman’s 1953 paper “Stimulus information as a determinant of reaction time”. It is in volume 45 of the Journal of Experimental Psychology (issue 3, pp. 188–196).

Hyman asked his participants to say the name of the light that lit up. In later trials, the number of each kind of light was varied. Hyman found a linear relationship between reaction time and the amount of information transmitted. That is why the law carries both names.

According to the same article, psychologists saw a similarity between this phenomenon and information theory. The time needed to process a given number of bits is called the “rate of gain of information”. That is also the title of Hick’s paper.

Applying it in the interface: examples

The examples are typical and don’t target any particular app. For each, I ask: is the person making a quick decision here, or looking for something they already know?

1. The home screen of a banking app

People who sign in usually come for one thing: sending money or checking the balance. If the home screen has twenty shortcuts of the same size, the person chooses among all of them every time they open it.

Laws of UX is clear: when a quick response matters, limit the options. Here I keep the two or three most frequent tasks large and group the rest under “All features”.

2. The shipping method at a store’s checkout

If the payment page asks about five shipping methods and two delivery times at once, the person gets stuck before paying. Laws of UX recommends highlighting the recommended option.

For that, it is enough to preselect one option and show it with a “Recommended” label.

Splitting a long form into steps follows the same logic. The form side is covered in the form design pattern.

3. The list of services in a city’s app

A city’s app can have 60 services, from dog licences to residential parking permits. Reducing them is often impossible, because each one matches a real need.

If the person already knows what they want, the problem isn’t the decision but the search. That is why I recommend grouping and a search field together. Forming the groups is information architecture work.

Limits and misconceptions

The law applies to equally probable options. The Interaction Design Foundation says so clearly. If the person knows beforehand what they want, they act faster than the law predicts.

Deciding and searching aren’t the same. According to Wikipedia, finding a word in a randomly ordered list means going through the entries one by one. That takes linear time, and the law doesn’t apply here.

Alphabetical order changes things. According to the same article, a person can subdivide an alphabetical list whose names they know and find the entry in logarithmic time. The article also notes that the law is cited as a justification for menu design decisions. For a randomly ordered list, it doesn’t apply.

With familiar items, the effect shrinks. The article names studies of verbal responses to familiar stimuli as an exception. There, there was no relationship, or only a subtle one, between reaction time and the number of items.

With long lists, its importance fades. According to the Interaction Design Foundation, the law matters less for long lists such as a contact list, and more for short ones such as a menu or action buttons.

Too much simplification has a price too. Laws of UX warns against simplifying to the point of abstraction. Hiding options can mean the person doesn’t find what they are looking for.

A note: the Wikipedia article itself is flagged as lacking enough inline citations. That is why I took its findings as a general tendency. I also checked the bibliographic details in the Crossref records.

My note

The Hick mistake I see most often in audits: screens where everything carries the same weight. With eight identical buttons, the person reads them all. Making one of them primary often shortens the decision.

The second mistake is applying the law to long lists. Teams try to shorten a 40-item menu when the problem is the search. There, good grouping and a search field do more than cutting items.

I don’t use the law as a numeric rule. When I review a screen, it makes me ask a single question: is the person deciding here, or searching? I ask this question of every screen in a heuristic evaluation.

If you want this question asked of your own product from outside, take a look at the UX Audit.

Related pages

Hick describes the time to decide what to press. The time to get there is described by Fitts’s law. Together, the two explain the cost of a button.

Why users quickly choose familiar patterns is explained on the pages about Jakob’s law and the mental model. The other laws are in the list of laws of UX.