Theodolite Angle Reduction Calculator

Work out theodolite angle reduction instantly with clear inputs, formula shown and shareable results.

About Theodolite Angle Reduction Calculator

Observing on both faces of the instrument and meaning the readings eliminates collimation error, because the error changes sign when the telescope is transited. The face right reading is first reduced by 180 degrees to bring it onto the same scale, and half the residual difference is the collimation error itself.

Formulas

Mean direction

Mean = face left - (face left - (face right - 180)) / 2

Collimation error

Error = half the difference between the reduced faces, in arc seconds

Worked example

With the default values below, Theodolite Angle Reduction Calculator returns Mean observed direction of 45.42750. Change any input above and every figure here is recalculated in your browser.

Inputs used

Face left readingaccepts 0–360 °: 45.4267 °
Face right readingaccepts 0–360 °: 225.4283 °
Reading on the reference objectaccepts 0–360 °: 0.5 °

Results

Mean observed direction: 45.42750 °
Included angle from the reference: 44.92750 °
Collimation error: -2.88 arc seconds
Difference between faces: -0.00160 °

Step by step

1Values used
2Mean direction
3Collimation error
4Mean observed direction= 45.42750 °
5Included angle from the reference= 44.92750 °
6Collimation error= -2.88 arc seconds
7Difference between faces= -0.00160 °

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Theodolite Angle Reduction figure worked out?

Mean = face left - (face left - (face right - 180)) / 2. Observing on both faces of the instrument and meaning the readings eliminates collimation error, because the error changes sign when the telescope is transited.

Does meaning the faces remove every error?

It removes collimation, horizontal axis and vertical index errors. It does not remove centring errors, pointing errors or the effect of an unlevelled instrument.

What values do I need to enter?

This calculator takes 3 inputs: Face left reading, Face right reading, Reading on the reference object. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.