Height & Distance
Solve vertical heights, horizontal and slope distances, elevation differences and inaccessible-object problems from field observations.
Height, Distance & Vertical Angle
Enter any two compatible quantities. Vertical angle is measured from the horizontal; positive means elevation and negative means depression.
Observation
Leave exactly one of the three fields blank; the calculator derives it from the other two.
Instrument / Target Heights
If observing a target point, the point-to-point elevation difference is vertical difference + target height − HI when the supplied height is the vertical rise to the line of sight.
Inaccessible Height — Two Stations
For an object whose base is inaccessible, observe the top from two stations on the same straight line. Enter the horizontal station spacing and two angles of elevation.
Field observations
Geometry
For the standard “object beyond the nearer station” case, height above the station line is D·tanα·tanβ ÷ (tanα − tanβ). For an object between stations, the horizontal distances to the object are found from D and the two angles.
Slope Distance, Horizontal Distance & Height Difference
Convert between slope distance, horizontal distance, vertical difference and vertical angle using right-triangle trigonometry.
Known quantities
Leave exactly one field blank. The remaining three values must be geometrically compatible.
Check
The calculator checks the supplied values against the Pythagorean relationship and reports the corresponding slope ratio and grade.
Height from Two Vertical Angles
Determine the height of an object above a known horizontal plane when two observations are taken from stations with a known horizontal separation.
Observations
Station geometry
Angles are taken above the horizontal. The calculator solves the horizontal distance from each station to the vertical projection of the object and the common height above the station plane.
Height & Distance Reference
For a vertical angle θ from the horizontal: V = H tanθ, H = S cosθ and V = S sinθ. Sign convention: positive vertical difference is rise/elevation; negative is fall/depression.