FFileTools

IMAGE PROCESSING REFERENCE

Gaussian Blur Kernel Size Calculator

Use this reference to estimate a practical Gaussian kernel size from a blur sigma. It is a mathematical reference, not a claim that every image editor maps its user-facing blur slider directly to sigma.

Formula

For a common three-sigma cutoff, radius = ceil(3 × sigma), so kernel size = 2 × radius + 1. The odd kernel size keeps a central pixel in the middle of the filter.

Blur kernel size table

SigmaRadiusKernel size
0.525 × 5
1.037 × 7
1.5511 × 11
2.0613 × 13
2.5817 × 17
3.0919 × 19
3.51123 × 23
4.01225 × 25
4.51429 × 29
5.01531 × 31
5.51735 × 35
6.01837 × 37
6.52041 × 41
7.02143 × 43
7.52347 × 47
8.02449 × 49
8.52653 × 53
9.02755 × 55
9.52959 × 59
10.03061 × 61
10.53265 × 65
11.03367 × 67
11.53571 × 71
12.03673 × 73
12.53877 × 77
13.03979 × 79
13.54183 × 83
14.04285 × 85
14.54489 × 89
15.04591 × 91
15.54795 × 95
16.04897 × 97
16.550101 × 101
17.051103 × 103
17.553107 × 107
18.054109 × 109
18.556113 × 113
19.057115 × 115
19.559119 × 119
20.060121 × 121

Why kernel size matters

Larger kernels examine more neighbouring pixels and can increase the computational work required for a blur. Real implementations may use separable filters, approximations, downsampling, GPU acceleration, or different cutoff rules.

For the browser blur tool, measure the actual implementation when comparing performance rather than assuming this table predicts processing time.