What is the range of longitude/latitude coordinates given a radius of area on Earth that I want to cover?

Given a pair of coordinates, I would like to have a range for both long/lat, that would cover, say 100 meters.

How can I do this?

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Assuming the earth is a perfect sphere of radius $R$, an arc of $\theta$ radians in a great circle will have length $\theta R$. So you want to solve $\theta R= 100 \, \text{m}$ for $\theta$.