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Rounding percentages

2024-06-21 Tavian Barnes

Let's say you're downloading a file and you see this:

0%

How do you know the download actually started? Similarly, if you see
this:

100%

Is it actually done? Or did it download 999/1000 bytes and then hang?

I know this is a relatively minor thing, but I find myself frustrated
by UIs like this so often that I'm proposing these rules for rounding
percentages that are shown to users:

  * 0% means exactly zero percent. If the user sees 0%, they can
    assume that absolutely nothing has happened yet except rendering
    the progress bar.

  * 100% means finished. If the user sees 100%, the process is
    finished, done, over, complete. They shouldn't have to wait for
    anything else to happen to start using the thing. Don't show 100%
    and then call fsync() or something silly.

In between those values, interpolate as normal.

There are a few ways to implement this. With (truncating) integer
division, you just have to fix up the 0% case:

>>> def percent(progress, total):
...     ret = 100 * progress // total
...     if ret == 0 and progress > 0:
...         return 1
...     else:
...         return ret
...
>>> percent(0, 1000)
0
>>> percent(1, 1000)
1
>>> percent(999, 1000)
99
>>> percent(1000, 1000)
100

There's also a neat trick with floating point: the default rounding
mode is typically ties-to-even. So if we interpolate between 
[0.5,99.5][0.5, 99.5][0.5,99.5] instead of [0,100][0, 100][0,100],
the endpoints will round correctly and everything else will stay
within [1,99][1, 99][1,99]:

>>> def percent(progress, total):
...     return round(99 * progress / total + 0.5)
...
>>> percent(0, 1000)
0
>>> percent(1, 1000)
1
>>> percent(999, 1000)
99
>>> percent(1000, 1000)
100

(If your language has bad defaults, you may have to ask for the right
rounding mode explicitly.)