Free-Station / 2-Point Resection
Calculate a 2D instrument station and orientation from two known plane-grid controls, two clockwise circle directions and two corrected horizontal distances. Review the coordinate residuals and the source-backed geometry cue before relying on the setup.
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.
Station, orientation and residuals
Included angle 45°00′00.00″: deviation from 90 degrees is 45 degrees - within guideline. The published two-control band is inclusive from 45 to 135 degrees.
Review both residual vectors and the baseline mismatch. Two controls are the minimum for this angle-and-distance fit, so the residual pair cannot identify which input caused a mismatch. No residual acceptance limit is applied.
- Station easting (m)
- 500001
- Station northing (m)
- 6960000
- Orientation correction
- 0°00′00.00″add to circle direction
- Included angle
- 45°00′00.00″
- Fixed scale
- 1held, not solved
- Known control baseline (m)
- 102
- Observed local baseline (m)
- 100
- Baseline mismatch (m)
- 2known - observed
- Baseline scale diagnostic
- 1.02reported only
- RMS horizontal residual (m)
- 1
| Control | Residual E (m) | Residual N (m) | Horizontal (m) |
|---|---|---|---|
| A | -1 | 0 | 1 |
| B | 1 | 0 | 1 |
Planimetric calculation only. It does not reduce slope distance, calculate elevation, model face observations or instrument weighting, or infer datum, zone, epoch or a grid-to-ground scale.
Show the working
- control A local xhorizontal distance A * sin(circle direction A)0
- control A local yhorizontal distance A * cos(circle direction A)100
- control B local xhorizontal distance B * sin(circle direction B)100
- control B local yhorizontal distance B * cos(circle direction B)100
- observed local baselinehypot(xB - xA, yB - yA)100
- known control baselinehypot(EB - EA, NB - NA)102
- fixed rotation cosineunit known baseline dot unit local baseline1
- fixed rotation sineclockwise 2D unit-baseline cross term1.4210854715202004e-16
- orientation correctionatan2(rotation sine, rotation cosine), normalized to 0-360 degrees0
- station eastingknown centroid E - rotated local centroid E500001
- station northingknown centroid N - rotated local centroid N6960000
- control A residual Eknown control E - fitted transformed local E-1
- control A residual Nknown control N - fitted transformed local N0
- control B residual Eknown control E - fitted transformed local E1
- control B residual Nknown control N - fitted transformed local N0
- RMS horizontal residualsqrt((residual A horizontal^2 + residual B horizontal^2) / 2)1
- baseline mismatchknown control baseline - observed local baseline2
- baseline scale diagnosticknown control baseline / observed local baseline (reported, not applied)1.02
- geometry deviation from 90 degreesabs(included angle - 90 degrees)45
- included anglesmaller folded separation between the two circle directions45
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 free-station calculator
Enter two known controls with their circle directions and corrected horizontal distances, then review the fixed-scale fit.
Enter both known controls
Enter the easting and northing for controls A and B in the same plane coordinate system and unit convention.
Enter instrument observations
Supply the clockwise circle direction and corrected horizontal distance to each control using DD or DMS directions.
Review the fit diagnostics
Inspect the station, orientation, residual vectors, baseline mismatch and geometry cue against the field record and an independent calculation.
Questions about Free-station / 2-point resection
What does a free station calculator for Australia calculate?
This free station calculator performs a fixed-scale two-control plane calculation and reports the station, orientation, residuals and baseline diagnostics for review in Australia.
Does the calculation solve a scale factor?
No. Scale is held at one and a separate baseline scale diagnostic is reported. Corrected observations and any project grid-to-ground treatment remain external inputs.
What does the included-angle cue mean?
It compares the two-control included angle with the published geometry band cited on the page. It does not apply a residual limit or select the observation quality for a job.
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.