Yes—using the simple pinhole/similar-triangles model, the relationship is:

s · f = b · D

So the required distance is:

D = (s · f) / b

Where:

• s = subject size you want to fit (width or height)
• f = focal length
• b = matching sensor dimension (sensor width for subject width, sensor height for subject height)
• D = distance from the lens/pinhole to the subject

Equivalent rearrangement if you want focal length instead:

f = (D / s) · b

This comes directly from similar triangles and is the standard approximation for framing calculations.

For real lenses, it is usually a good practical estimate, especially at normal shooting distances. At close-focus/macro distances, internal focusing and lens design can make the exact result differ somewhat, so treat it as approximate rather than exact.

You generally do not need extra camera-body dimensions for the basic estimate; the sensor size and focal length are the key inputs.