image processing - How to find width of (1D discrete) Gaussian Kernel for a certain sigma? -

is there rule of thumb or mathematical equation tells me how wide (1d discrete) gaussian kernel should sigma?

lets say, choose sigma of 1.87, should kernel 5 values/steps/pixels wide, 7 oder rather 25 in order perform standardized image smoothing? thank you.

pick threshold consider ignorable, t = 0.01. solve exp(-x^2/(2s^2)) / sqrt(2pi s^2) < t:

|x| < s sqrt(-2 ln(sqrt(2pi s^2) t))

the right hand side gives width. s = 1.87 , t = 0.01, gives width of 4 pixels.