Is the formula for object image size given focal length, etc. independent of sensor size?

I am trying to figure out how big an object of, say, 50cm height at 100m distance and 600mm focal length would appear on a camera's sensor. The ubiquitous formula

object size in image = focal length * object size / object distance

yields

object size in image = 600mm * .5/100 = 3mm

What I am wondering: Are these 3mm entirely independent of sensor size?

E.g., a specific superzoom model has a 1/2.3" sensor (= 4.55mm height according to one source) and a maximum zoom quoted to have a "35mm equivalent focal length of 600mm". Would the object actually cover 3/4.55 = approx. 66% of this sensor's height = 66% of the image, or does the relation between the sensor size and the "35mm equivalent" have to be taken into account somehow?

(My apologies if this has been asked before - I have found many related questions, but not this one.)

Answer

The answer to your question generally is yes. However as you mention, the ratio of how much of the overall image your subject takes up will depend on your sensor size. What you do have to watch out for is that the "35mm equivalent focal length" should not be used but the actual focal length as quoted on the camera specs - this is usually something in the single digits of millimetres.

The 35mm equivalent is for comparison purposes only because it reflects the equivalent area of 35mm film (or a full-frame digital sensor) - i.e. 36 x 24mm. People tend to be most familiar with the range of focal lengths at this sensor size e.g. 24mm is wide, 50mm is normal, anything about 100mm is telephoto and so on. This is simply the real focal length multiplied by a factor that represents the ratio between the camera's real sensor size and the nominal 35mm sensor size.