Stadia Distance Calculator

Work out stadia distance instantly with clear inputs, formula shown and shareable results.

About Stadia Distance Calculator

Tacheometry uses the staff intercept between two stadia hairs: horizontal distance is K s cos²θ + C cosθ, where K is typically 100 and C the additive constant of the telescope. The height difference uses K s cosθ sinθ, which is half K s sin 2θ. For a level sight the relation collapses to the familiar 100 times the intercept.

Formulas

Stadia distance

D = K s cos²θ + C cos θ

Height difference

V = K s cos θ sin θ + C sin θ

Worked example

With the default values below, Stadia Distance Calculator returns Horizontal distance of 84.4845. Change any input above and every figure here is recalculated in your browser.

Inputs used

Staff intercept between stadia hairsminimum 0.001 m: 0.845 m
Multiplying constantminimum 1: 100
Additive constantminimum 0 m: 0.3 m
Vertical angleaccepts -60–60 °: 3.5 °

Results

Horizontal distance: 84.4845 m
Difference in height: 5.1673 m
Slope distance: 84.6424 m
Distance if the sight were level: 84.8000 m

Step by step

1Values used
2Stadia distance
3Height difference
4Horizontal distance= 84.4845 m
5Difference in height= 5.1673 m
6Slope distance= 84.6424 m
7Distance if the sight were level= 84.8000 m

Assumptions and limits

The result is derived only from the 4 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 4 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 Stadia Distance figure worked out?

D = K s cos²θ + C cos θ. Tacheometry uses the staff intercept between two stadia hairs: horizontal distance is K s cos²θ + C cosθ, where K is typically 100 and C the additive constant of the telescope.

How accurate is stadia work?

About one in five hundred at best, so around 200 mm at 100 metres. It was a rapid detail survey method rather than a control technique, and total stations have made it largely historical.

What values do I need to enter?

This calculator takes 4 inputs: Staff intercept between stadia hairs, Multiplying constant, Additive constant, Vertical angle. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.