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I am looking for a value to specify as a maximum time between presses for it to count as a multi-press when pressing an hardware button on e.g. a mobile phone. An example would be to execute an action by pressing twice (or more) on the home button.

Of course the optimal value will differ a lot depending on the user, but I find the value commonly used for mouse clicks being 500ms, and I think 300ms is sometimes used for double tapping on a touch screen. But what about a HW button on e.g phone?

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I just timed pressing my phone's volume button. I have a fairly squishy case with a poor design that makes for uncrisp button presses, so these values are on the slow side.

10 presses at a speed I would consider to feel like "double-clicking" took 2.4 seconds, so ~240ms.

10 presses at a speed where I was trying to enter presses as fast as possible, while intentionally NOT "double-clicking", took 4.4 seconds, so ~440ms.

Hence ~300 is probably a safe value, especially given that my case slows me down, so even ~240 is slower than it could be for the average user.

Microsoft's default is indeed 500ms, but that's very generous. Try it yourself and you'll see you can double-click things much slower than you thought. The only reason it doesn't get triggered accidentally is that few things in their UX require do anything when clicked on 2 or more times (i.e. as opposed to one double-click). One exception is clicking twice on a filename to edit it. Try doing so and you'll see how much time you have to leave between clicks to edit that filename. I sometimes end up accidentally opening a file or folder instead of renaming it. Conclusion: 500ms is really high.

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In a hardware button there are multiple variables to consider, including materials, resistance of such materials to pressure, elevation of the button (more elevation equals to higher reaction times) and so on. You'll also need to consider the location of the button, which fingers will be used to activate such button and many more.

The point is that there isn't a formula, but many formulas (such as Fitt's law or Accot–Zhai steering law ), and of course, direct measure of user interactions on real life prototypes.

Once you solve the problem, the 300 ms time you mention (as in the answer from Luke Sawczak) is an industry standard, and you should get as close to that number as possible.

However...

If you value accessibility, it is recommended to choose a slightly higher time (even if you add a bit more resistance) to help people with physical and neurological disabilities. Keep in mind many users can't control their movements, so this is a very important concern. You can adjust the time from within the interface, of course.

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