You can calculate it using the simple lens formulae to a good approximation using a tape measure. Measure the height of an object, h, at a distance v away from your lens, where v is much greater than the focal length, f, say 15 metres for a 300mm lens. Calculate the height of the image, i, from the number of pixels it spans and the size of the pixels (which you can calculate yourself or read in websites). Then, f = vi/h. For an extra couple of % of accuracy you should use u = vi/h, where 1/v + 1/u = 1/f.
Thanks Alan, I might try that if focus breathing isn't the answer.
What variable is u?
f = distance * image height / object height