Parameters of Gaussian Kernel in the Context of Image Convolution
When dealing with Gaussian Blur in the Image Processing context the following holds:


The Standard Deviation, $ \sigma $, is sometimes called radius. I think this goes back to Photoshop.
If you implement this using FIR Filter (Well, Gaussian Kernel is infinite so you approximate it) usually the radius of the filter will be something like ceil(4 * kernelStd). This is because the Kernel almost vanishes after $ 4 \sigma $.


Some in practice remarks:


The Gaussian Kernel is Separable hence if implemented as FIR filter it is implemented as 2 1D Convolutions - Along rows and along columns.
You may have a look at the Image Convolution GitHub Repository for efficient C Code.
There are many other way to approximate the Gaussian Blur which are much faster (Though sometimes there is accuracy vs. speed balance, most of the time negligible). You may have a look at Fast Gaussian Blur GitHub Repository for IIR and Box Blur implementations which are insensitive to the radius parameter.