In a book of Werner Gruber about the physics of cooking, I found the following formula for cooking eggs.

\(t = 0.0016 \, d^2 \, \ln \left(\dfrac{2(T_W-T_0)}{T_W-T_1}\right)\)

The temperatures are in Celsius, the diameter d is in mm. The result is the time in minutes. A reasonable value for TW (tempeature of water) is 95°. If you take the egg out of the refrigerator, you set T0=6°. If you want a soft-boiled egg, you want T1=62°. Set T1=82° for a hard-boiled egg.

I tested the case d=45, and got a perfectly soft egg in 5 minutes 27 seconds, as predicted. Insert the egg into boiling water, of course. Crack the egg at the larger end a bit and put it slowly into the water. Cool down with cold water, when it is finished.

I believe there are apps for this. But I had to test this in Euler. Surprisingly, the times change a lot with each millimeter.

>function tegg(d,tw=95,ts=6,ti=62) := 0.0016*d^2*log(2*(tw-ts)/(tw-ti))
% As an example, we compute the times in minutes for eggs from 40mm to
% 50mm. Then we compute the minutes and the seconds, and print with
% writetable().
>de=(40:50)'; te=tegg(de);  ...
>tem=floor(te); tes=round((te-tem)*60); ...
>writetable(de|tem|tes,labc=["d","min","sec"])
          d       min       sec
         40         4        19
         41         4        32
         42         4        45
         43         4        59
         44         5        13
         45         5        28
         46         5        42
         47         5        57
         48         6        13
         49         6        28
         50         6        44
% We might give the user some constants to play with.
>softegg=62; hardegg=82; fridge=6; room=20;
>writetable(tegg(45,ts=[fridge,room],ti=[softegg,hardegg]'), ...
>   labc=["fridge","room"],labr=["soft","hard"])
               fridge      room
       soft      5.46      4.91
       hard      8.48      7.92

Of course, measuring the diameter is not very easy. It is easier to take the weight w of the egg. It would be a nice job to develop a good formula for d depending on w.