Stadia Distance

This relation gives the horizontal distance to a staff point when a tacheometer is sighting a level rod and the distance between the upper and lower stadia hair readings is known. The factor 100 comes from the instrument constant for standard stadia systems, while the cos²θ term corrects the line-of-sight reading to a horizontal distance when the telescope is inclined by angle θ. It works because the intercepted staff interval is proportional to the sloping sight distance, and projecting that sloping distance onto the horizontal introduces the cosine correction twice.

Use this in tacheometric surveying when you have stadia readings on a vertically held staff and need the horizontal distance to the point. It is especially useful on uneven ground, where the line of sight is not horizontal but you still want plan-distance for mapping or setting out.

• Using the angle in degrees without evaluating cos²θ correctly
• Forgetting that s is the stadia intercept, not a single staff reading
• Applying the formula to a sloping distance instead of the horizontal distance