Circular curve layout table
and stations for a circular curve and a layout table at a chosen interval: station, deflection from the PC, chords, and coordinates when the position and back tangent are given.
Experimental: not yet fully verified. How results are checked
The curve runs from PC 11+00.59 to PT 13+62.38, 261.799 ft of arc.
| Station | Deflection from the PC | Chord from the PC | Chord from the last point |
|---|---|---|---|
| 11+00.59 | 0°00'00.0" | 0.000 ft | 0.000 ft |
| 11+50.00 | 2°49'52.5" | 49.394 ft | 49.394 ft |
| 12+00.00 | 5°41'45.7" | 99.251 ft | 49.979 ft |
| 12+50.00 | 8°33'39.0" | 148.859 ft | 49.979 ft |
| 13+00.00 | 11°25'32.2" | 198.096 ft | 49.979 ft |
| 13+50.00 | 14°17'25.5" | 246.837 ft | 49.979 ft |
| 13+62.38 | 15°00'00.0" | 258.819 ft | 12.384 ft |
- PT station
- Tangent T
- Curve length L
Provenance
- Computed by
- survey.curves.curve-layout 1.0.0, core 0.1.0
- Model
- Arc definition: T = R tan(Δ/2), L = RΔ; deflection from the PC δ = s/(2R) for arc s; chord 2R sin δ; coordinates from the PC along the back tangent rotated by δ (Ghilani & Wolf 2021, ch. 24)
- Accuracy
- Exact for the elements given
- Notes
- 1 shown with the answer
- Cites
- Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Arc definition: T = R tan(Δ/2), L = RΔ; deflection from the PC δ = s/(2R) for arc s; chord 2R sin δ; coordinates from the PC along the back tangent rotated by δ (Ghilani & Wolf 2021, ch. 24)
Accuracy: Exact for the elements given
Worked example: R = 500 ft, Δ = 30°, PI at 12+34.56, staked every 50 ft. Source: add-survey-suite layout-table scenario. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Deflection Δ
- 30°00'00"
- Station interval
- 50 ft
- PI station
- 12+34.56
- Radius R
- 500 ft
You get
- PC station
- 11+00.59
- PT station
- 13+62.38
- Tangent T
- 133.975 ft
- Curve length L
- 261.799 ft
Review: Not yet independently reviewed by a licensed surveyor.
Last verified: 2026-09-23, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Changes
- 2026-09-23, fixed: Survey tools cite Ghilani and Wolf's Elementary Surveying, 16th edition (2021), but their method notes said "Ghilani & Wolf 2018". The notes now give 2021, the edition cited. No results change. Changelog
Checked against: 6 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Elementary Surveying: An Introduction to Geomatics, Ghilani, C. D., and Wolf, P. R., Pearson, 16th edition. Chapter 24 (horizontal curves: stationing, deflection angles, chords, and layout by coordinates).
Terms
- PC: point of curvature
- On a horizontal curve, where the curve leaves the back tangent. Source: Elementary Surveying: An Introduction to Geomatics
- PI: point of intersection
- On a horizontal curve, where the two straight tangents would meet. Source: Elementary Surveying: An Introduction to Geomatics
- PT: point of tangency
- On a horizontal curve, where the curve joins the forward tangent. Source: Elementary Surveying: An Introduction to Geomatics
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.
PC — point of curvature
On a horizontal curve, where the curve leaves the back tangent.
Source: Elementary Surveying: An Introduction to Geomatics
PI — point of intersection
On a horizontal curve, where the two straight tangents would meet.
Source: Elementary Surveying: An Introduction to Geomatics
PT — point of tangency
On a horizontal curve, where the curve joins the forward tangent.
Source: Elementary Surveying: An Introduction to Geomatics
Learn the concept: Horizontal curves explained