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Theodolite and total station

Intermediate Surveying Reviewed 24 Oct 2026 2 min read

A theodolite measures horizontal and vertical angles precisely using a telescope that rotates about vertical and horizontal axes over graduated circles. A total station adds electronic distance measurement (EDM) and a computer to an electronic theodolite, so a single pointing gives angle, distance and therefore coordinates of the target. It is the workhorse of engineering surveying: control, topographic detail, setting out and monitoring.

Setting up involves centring over the station mark with an optical or laser plummet and levelling with the plate bubble or electronic tilt sensor. Angles are measured on both faces (face left and face right) and averaged, which cancels collimation, trunnion axis and index errors. EDM works by measuring the phase of a modulated infrared or laser signal reflected by a prism, or, in reflectorless mode, by the target surface itself. Atmospheric corrections for temperature and pressure, and a prism constant, must be set.

Diagram: Indiacon original, not to scale.

With coordinates of the station and a backsight point, the total station computes new coordinates directly. For setting out, it guides the operator to where a design point lies by showing the offset to move. Robotic total stations follow the prism automatically and allow one-person work and continuous deformation monitoring. Accuracy is specified as an angle (for example 1 or 5 arc-seconds) and as a distance accuracy of a few millimetres plus a few parts per million.

Key formulas
  • Horizontal distance: H = S cos α (α = vertical angle)
  • Height difference: V = S sin α; reduced level = RL_station + hi + V − h_target
  • Coordinates: E₂ = E₁ + H sin θ; N₂ = N₁ + H cos θ
  • Face left and face right mean cancels instrumental errors
Solved example

Problem. From a station at E 1000.000, N 2000.000, RL 50.000 with instrument height 1.520 m, a prism at height 1.800 m is observed: bearing 62° 10′, slope distance 145.320 m, vertical angle +3° 20′. Find its coordinates and RL.

  1. H = 145.320 × cos 3° 20′ = 145.074 m; V = 145.320 × sin 3° 20′ = 8.449 m.
  2. E = 1000 + 145.074 × sin 62° 10′ = 1000 + 128.31 = 1128.31.
  3. N = 2000 + 145.074 × cos 62° 10′ = 2000 + 67.70 = 2067.70.
  4. RL = 50.000 + 1.520 + 8.449 − 1.800 = 58.169 m.

Answer. E 1128.31, N 2067.70, RL 58.17 m

Quick quiz

1Why observe on both faces?

To cancel instrumental errors by averaging.

2What does EDM measure?

Distance, from the phase or time of a reflected signal.

3What does a robotic total station add?

Automatic target tracking for one-person work and monitoring.

Code note

    Clauses and documents to read

    • ISO 17123-3 and 17123-4 (field test procedures for theodolites and EDM, cited by number)

    Cited by number and clause only. We do not reproduce clause text, tables or figures (BIS Act 2016, s.10(5) and s.11). Check the current edition and amendments before use.

    References and further reading

    Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.

    • S. K. Duggal, Surveying (Vols 1 and 2), McGraw Hill Education (India), latest edition.
    • B. C. Punmia, A. K. Jain, A. K. Jain, Surveying (Vols 1 to 3), Laxmi Publications, latest edition.
    • C. D. Ghilani, P. R. Wolf, Elementary Surveying: An Introduction to Geomatics, Pearson, latest edition.

    Free and official sources

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