Free tool · Survey calculations
Horizontal Curve Calculator: Tangent Length, Chainages and Setting Out
Type a curve's radius, deflection angle and the chainage of the intersection point, and get every curve element and a setting-out table of deflection angles and chords.
Free · no sign-up · works in your browser, on phone and computer
Example · A 300 m radius bend on a site road
- Curve
- R 300 m · Δ 35°24'30" · IP at 1+245.600 · pegs every 20 m
- Tangent · curve length
- T 95.766 m · L 185.398 m
- TC → CT
- 1+149.834 → 1+335.231
- First peg
- 1+160.000: deflection 0°58'14.9", chord 10.166 m
What it does
Every element
Tangent length, curve length, long chord, external distance and mid-ordinate, worked out together.
TC and CT chainages
From the intersection point's chainage, with CT carried along the arc as it should be, not along the tangents.
Setting-out table
A peg on every whole chainage: deflection angle from TC, the chord from the last peg and from TC, and offsets from the tangent as a check.
Copy to Excel
Copy the whole table in one go and paste it into a spreadsheet or your field book template.
How to use it
- 1
Press Use the tool.
- 2
Type the radius, the deflection angle Δ and the chainage of the intersection point, and pick the peg interval.
- 3
Read the curve elements, then copy the setting-out table.
Who it's for
- Surveyors setting out a road or track curve with a total station or theodolite
- Site engineers checking a curve on a drawing before pegging it
- Civil engineering students learning simple circular curves
The curve elements
- Tangent length T = R·tan(Δ/2): from the intersection point (IP) back to the start of the curve (TC) and on to its end (CT).
- Curve length L = π·R·Δ/180: the length along the arc, so CT = TC + L (not IP + T).
- Long chord C = 2R·sin(Δ/2): straight from TC to CT.
- External E = R·(sec(Δ/2) − 1) and mid-ordinate M = R·(1 − cos(Δ/2)): from IP and from the long chord to the middle of the curve.
Setting out by deflection angles
Each peg's deflection from the tangent is half the angle the arc to it makes at the centre: δ = arc ÷ 2R, in radians. Set up on TC, sight IP, turn δ for each peg and measure the chord from the previous peg. The first and last chords are shorter because the pegs sit on whole chainages. If a peg is hidden, the offsets from the tangent let you set it from the tangent line instead.
For a whole road with its curves, edges, signs and markings, RoadPro draws it in AutoCAD from the centre line, with the TC / CT chainages and curve data labelled on the plan.
Questions
What is the deflection angle Δ?
The angle between the two straights at their intersection point: how much the road turns. It is also the angle the curve makes at its centre. Type it in degrees, minutes and seconds or in decimal degrees.
Why is CT not IP plus the tangent length?
Chainage runs along the road, and the road follows the arc. So CT = TC + curve length. The tangent from IP is shorter than the way round on the curve.
Which definition of the curve does it use?
The radius (arc) definition used by most road design today. If a drawing gives a degree of curve instead, work out the radius from it first.
Does it work for transition (spiral) curves?
No, only simple circular curves. Transitions need their own length and offsets.
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Got a whole sheet of points?
Open the web app in your browser, or install the Windows app to work offline. Both are free, with no point limit.