Work out theodolite angle reduction instantly with clear inputs, formula shown and shareable results.
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.
Mean direction
Mean = face left - (face left - (face right - 180)) / 2
Collimation error
Error = half the difference between the reduced faces, in arc seconds
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.
It removes collimation, horizontal axis and vertical index errors. It does not remove centring errors, pointing errors or the effect of an unlevelled instrument.
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.