Horizontal Curve Calculator: Tangent, Arc Length, Chord, External Distance and Chainages of a Circular Curve
Setting-out numbers for a simple circular curve.
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How this calculator works
Enter the radius and the deflection angle.
Enter the chainage of the intersection point.
The calculator gives the curve elements and the chainages.
Formulas used
- T = R\tan\frac{\Delta}{2}
- L = R\Delta
- C = 2R\sin\frac{\Delta}{2}
- E = R\left(\sec\frac{\Delta}{2} - 1\right)
Worked example
With the default numbers in the calculator above:
- Tangent length: 109.191 m
- Length of the curve: 209.44 m
- Long chord: 205.212 m
- External distance (from the intersection point to the curve): 19.253 m
- Middle ordinate (from the chord to the curve): 18.092 m
- Chainage of the start of the curve (PC): 1140.809 m
- Chainage of the end of the curve (PT): 1350.248 m
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What is the tangent length of a curve?
The distance from the intersection point of the two straights back to the start of the curve, or forward to the end.
How do I find the chainage of the end of the curve?
Add the curve length to the chainage of the start. The start is the chainage of the intersection point less the tangent length.
Does this include a transition curve?
No. This is a simple circular curve only.
Related calculators
Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any surveying or road design text (simple circular curves). Use the design standard for minimum radius and superelevation.
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