It depends on how good your eyes are for one thing. Assuming you have great eyesight, you may want to refer to: https://en.wikipedia.org/wiki/Optimum_HDTV_viewing_distance which contains some useful charts.
Personally I'd say from experience in trying to do something similar that it should be around 60-70 inches.
Your premise however is not entirely correct and can be avoided with other approches:
- reduce the brightness of your screen to about 50%
- reduce the ambient light in the room to a level just above what you might consider dim
The strain you talk about is most often caused by users either not blinking enough, poor environmental lighting, or both. Reflections off of lots of surfaces from high levels of ambient light will also add to eye strain.