Stadia / Tacheometry Reduction Calculator
Reduce upper, middle and lower readings on a plumb vertical staff to horizontal distance, signed vertical difference and staff-station RL. Enter the signed vertical angle, station RL, instrument height and the instrument's own K and C constants.
Uses only this tool title and its public link. Inputs, results, coordinates and filenames are not included. Sharing starts only when you press the button.
Free advisory field tool — every result is computed in your browser from the inputs you provide and is advisory and unverified, not for survey deliverables. Where a published guideline applies, results only ever read “within guideline” or “exceeds guideline — review”. The full working is shown for every calculation so each step can be re-checked. Registered surveyor confirmation required before reliance.
Horizontal distance, signed VD and staff-station RL
Angle 30°00′00.00″. VD is from the instrument axis to the centre-hair point on the staff: positive upward, negative downward. The middle reading is then subtracted to obtain the staff-station RL.
- Staff intercept s (m)
- 1
- Upper - middle interval (m)
- 0.5
- Middle - lower interval (m)
- 0.5
- Midpoint imbalance (m)
- 0reported only; no limit applied
- Horizontal distance HD (m)
- 76.732051
- Signed vertical difference VD (m)
- 44.30127axis to centre-hair point
- Instrument-axis RL (m)
- 51.5
- Staff-station RL (m)
- 94.30127
This reduction does not assess staff plumb, reading quality, instrument calibration, curvature/refraction, datum, geoid, epoch, CRS, grid/ground scale or project acceptance criteria.
Show the working
- staff intercept ss = upper - lower1
- upper-to-middle intervalupper - middle0.5
- middle-to-lower intervalmiddle - lower0.5
- midpoint imbalance(upper - middle) - (middle - lower)0
- stadia productR = K × s100
- line-of-sight distance to centre-hair pointI = R × cos(θ) + C88.6025403784
- horizontal distance HDHD = I × cos(θ)76.7320508076
- signed vertical difference VDVD = I × sin(θ)44.3012701892
- instrument-axis RLaxis RL = station RL + HI51.5
- staff-station RLstaff RL = axis RL + VD - middle reading94.3012701892
Working trace rendered from the same computation as the result above — re-check any step by hand before relying on it.
How to use the stadia reduction calculator
Enter one three-wire staff observation, the signed vertical angle, elevations and instrument constants, then review the reduction.
Enter the staff readings
Enter upper, middle and lower metre readings from the same plumb vertical staff observation in descending order.
Enter angle and constants
Supply the signed vertical angle, station RL, instrument height and the K and C constants determined for the instrument.
Review the reduced values
Inspect the staff intercept, midpoint imbalance, horizontal distance, signed vertical difference, staff-station RL and working trace.
Questions about Stadia reduction
What does a stadia reduction calculator in Australia calculate?
This stadia reduction calculator uses a vertical staff observation to calculate horizontal distance, signed vertical difference and staff-station RL for review in Australia.
Which instrument constants are used?
The calculation uses the multiplying constant K and additive constant C entered by the user. It does not supply or infer values for an instrument.
Does the reduction account for every field correction?
No. Staff plumb, calibration, curvature and refraction, datum, geoid, grid scale and project criteria remain outside this bounded reduction.
Safety & scope
SurveyMarkup helps prepare and review working information. Every professional decision remains with the registered surveyor, and original data and final outputs require qualified review.
Assistance only - professional review remains required.