Circular Curve Set-Out Table Generator
Generates a full deflection-angle set-out table for a circular road curve — PC/PT chainages, cumulative deflection angles, chords, sub-chords, tangent offsets and coordinates — with a scaled plot and CSV export.
Curve inputs
Δ is the angle between the two straights (the deflection at the PI). The set-out uses the deflection-angle method: occupy the PC, backsight the PI, then turn each cumulative deflection and measure the chord. Everything runs in your browser.
Curve elements & stationing
Set-out plot
Set-out table
| Point | Chainage | Deflection | Chord (PC) | Sub-chord | Tangent X | Offset Y |
|---|---|---|---|---|---|---|
| PC | 0+884.530 | 0° 0' 0" | 0.000 | — | 0.000 | 0.000 |
| P1 | 0+900.000 | 2° 12' 57.319144" | 15.466 | 15.466 | 15.455 | 0.598 |
| P2 | 0+920.000 | 5° 4' 50.559456" | 35.424 | 19.992 | 35.284 | 3.137 |
| P3 | 0+940.000 | 7° 56' 43.799768" | 55.292 | 19.992 | 54.762 | 7.643 |
| P4 | 0+960.000 | 10° 48' 37.040081" | 75.023 | 19.992 | 73.692 | 14.071 |
| P5 | 0+980.000 | 13° 40' 30.280393" | 94.566 | 19.992 | 91.885 | 22.357 |
| P6 | 1+000.000 | 16° 32' 23.520706" | 113.873 | 19.992 | 109.161 | 32.418 |
| P7 | 1+020.000 | 19° 24' 16.761018" | 132.895 | 19.992 | 125.346 | 44.153 |
| P8 | 1+040.000 | 22° 16' 10.001330" | 151.585 | 19.992 | 140.279 | 57.445 |
| P9 | 1+060.000 | 25° 8' 3.241643" | 169.896 | 19.992 | 153.810 | 72.162 |
| P10 | 1+080.000 | 27° 59' 56.481955" | 187.783 | 19.992 | 165.804 | 88.156 |
| PT | 1+093.969 | 30° 0' 0" | 200.000 | 13.967 | 173.205 | 100.000 |
Deflection angles are cumulative from the back tangent — the total at the PT equals Δ/2. "Chord (PC)" is the straight distance from the PC; "Sub-chord" is the chord from the previous peg (tape from peg to peg). Tangent X/offset Y support the offsets-from-tangent method. A study and field-planning aid — check against your design and standards before pegging.
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the deflection (intersection) angle Δ in DD, DMS or DDM, and the curve radius R.
- Set the peg / through-chainage interval and the reference chainage (measured at the PI or the PC), and pick whether the curve turns left or right.
- Read the elements and stationing, then work down the set-out table: occupy the PC, backsight the PI and turn each cumulative deflection angle, taping the sub-chord to each peg. Optionally add the PC coordinate and back-tangent bearing to get real E/N.
How it works
The curve elements come from the radius and deflection angle: tangent T = R·tan(Δ/2), curve length L = R·Δ(rad) and long chord C = 2R·sin(Δ/2). The PC (tangent point) chainage is the PI chainage minus T, and the PT chainage is the PC chainage plus L.
For a point a distance l along the curve from the PC, the deflection angle from the back tangent is δ = l / (2R) radians, and the straight chord from the PC is 2R·sin(δ). Pegs are placed at round through-chainages; the sub-chord is the chord from the previous peg. The cumulative deflection at the PT always equals Δ/2, which is the field check.
With a PC easting/northing and the back-tangent bearing, each peg's chord and deflection are turned into whole-circle bearings and reduced to real coordinates — so the same table drives both a theodolite/total-station set-out and a coordinate (stakeout) upload.
Worked example
Worked example. For Δ = 60°, R = 200 m and the PI at chainage 1000.000: T = 115.470 m, L = 209.440 m, so the PC is at 0+884.530 and the PT at 1+093.969. At the PT the cumulative deflection is exactly 30° (Δ/2) and the chord from the PC equals the long chord, 200.000 m — a quick check that the table is right.
Common mistakes
- Using a quadrant or half-angle for Δ — enter the full deflection (intersection) angle between the two straights.
- Setting the reference chainage at the PC when it was surveyed at the PI (or vice-versa) — toggle which point the chainage belongs to.
- Confusing the chord from the PC with the sub-chord: the theodolite turns the cumulative deflection but you tape the shorter peg-to-peg sub-chord.
Frequently asked questions
What is the deflection-angle method?
It is the standard way to set out a circular curve with a theodolite or total station: you occupy the PC (tangent point), backsight the PI, then turn a cumulative deflection angle for each peg and measure the chord to it. The deflection to any point is half the angle its arc subtends at the centre, so the total at the PT is Δ/2.
Does it give coordinates as well as angles?
Yes. Add the PC easting/northing and the back-tangent bearing and every peg is reduced to a real E/N coordinate, so you can either set out by angle-and-chord or upload the coordinates to a GNSS/robotic stakeout list. Leave the coordinates blank and you still get the full angle-and-chord table plus offsets from the tangent.
How is this different from the Circular Curve Elements Calculator?
The elements calculator gives only the single set of curve values (tangent, length, chord, mid-ordinate, external). This generator adds the PC/PT chainages and a full station-by-station set-out table with deflection angles, sub-chords, tangent offsets, coordinates and a plot.
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Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.