Image blur radius calculator

The strength is interpreted as the Gaussian standard deviation, or sigma, in pixels. The result reports the radius needed to cover three standard deviations on each side and the corresponding odd kernel size. It is designed for developers configuring image libraries, shaders, canvas filters, and processing pipelines that expose different blur controls. No image is uploaded or inspected, and the same input always produces the same output.

Translate blur strength into implementation dimensions

Image tools often describe the same Gaussian blur with different controls. One interface asks for sigma, another asks for a radius, and a convolution function may require the complete kernel width. This calculator makes those representations explicit. It treats strength as sigma in pixels, then selects a radius large enough to include values from minus three sigma through plus three sigma. That interval contains virtually all of the useful weight of a Gaussian distribution while keeping the convolution finite. The radius is calculated as the ceiling of three times the strength, because a fractional boundary still needs a whole pixel position in a discrete image kernel. The kernel size is then twice the radius plus one: one side, the center pixel, and the matching positions on the other side. For example, a strength of two produces a radius of six and a thirteen-pixel kernel. This conversion gives implementations a clear, reproducible rule instead of relying on an undocumented slider.

Read the radius and kernel size correctly

The `gaussian_radius` result is the number of neighboring pixel positions sampled in each direction from the center. It is not the complete width. A radius of six therefore reaches six pixels left and six pixels right in a horizontal pass, or six pixels above and below in a vertical pass. The `kernel_size` result includes both sides and the center, so it is always an odd positive integer. Many image libraries accept this full size directly, while others accept radius or sigma and construct their own coefficients. Check which quantity your target API expects before copying a value. The returned numbers describe kernel geometry, not the individual Gaussian weights. To build the weights, evaluate the Gaussian function at every integer offset from negative radius through positive radius, then normalize the values so their sum is one. For a two-dimensional blur, implementations commonly apply the one-dimensional kernel horizontally and vertically as separate passes, producing the same Gaussian result with much less work than a full square convolution.

Handle zero, fractions, and visual differences

A strength of zero represents no blur. It returns a radius of zero and a kernel size of one, which is an identity operation containing only the center pixel. Positive fractional strengths are supported and can be useful for subtle smoothing. Because the radius uses a ceiling, the kernel changes only when three times the strength crosses an integer boundary, even though the Gaussian coefficients would continue changing smoothly between those boundaries. Negative strength is rejected because a Gaussian standard deviation cannot be negative; the calculator never silently takes an absolute value or clamps the input. The estimate deliberately uses a three-sigma cutoff, a common practical balance between accuracy and computation. Another application may choose two sigma, four sigma, a fixed maximum radius, or a vendor-specific approximation, so equal slider labels do not guarantee identical pixels across programs. Color space, edge extension, alpha handling, coefficient precision, and downsampling can also change the visible result. Record those choices alongside the returned dimensions when exact reproduction matters.