How to measure the diameter of a shaft without a caliper?

[Baluncore]

Another way:
Place two straight edges against the diameter of the shaft, one on each side. Adjust the edges to be approximately parallel. Use a ruler to measure the edge separation on both sides of the shaft, then average those to find the shaft diameter.

 

[BillTre]

Take it to a hardware store. Test their calipers on you shaft to get a feel for the one you might buy.
Cheep calipers are pretty lousy in my experience.

 

[renormalize]

Cheep calipers are pretty lousy in my experience.

 

[OmCheeto]

Another way would be to place the rod between a pinhole source of light and a white wall, with the rod being moved incrementally, and measurements being made of the width of the shadow. Might require some fancy maths. I believe marcus, MGB mfb, and I worked through a problem like this in the trip to Ceres thread.

I can't find the post, but it's basically:
at an infinite distance, the shadow will yield an accurate diameter.
at near distances, the shadow will yield inaccurate diameters.

Hence, maths.

 

[Baluncore]

Another way would be to place the rod between a pinhole source of light and a white wall, ...

You could check your measurements by employing the white wall as the background, then observing the shaft through a lens, one focal length from the shaft and one focal length from a projection screen. If my Fourier optics is not too cloudy, on the screen you will see repeated bands, the pitch of which will be the diameter of the shaft, (the inverse spatial frequency of the shaft).
https://en.wikipedia.org/wiki/Fourier_optics#Applications_of_Fourier_optics_principles

There are also many ways to measure the height of a building with a barometer.