Curve radius calculator form
Choose a method based on the measurements you already have. The calculator solves the radius and returns related curve geometry instantly.
Formula used
This calculator assumes a simple circular curve, common in construction layout, curb setting, roadway checks, and horizontal alignment planning.
1) Radius from arc length and angle
R = L / θ(rad)
2) Radius from chord and sagitta
R = (C² / 8s) + (s / 2)
3) Radius from chord and angle
R = C / [2 sin(θ / 2)]
4) Radius from tangent and angle
R = T / tan(θ / 2)
5) Radius from external distance and angle
R = E / [sec(θ / 2) - 1]
Related curve values
Chord = 2R sin(θ / 2)
Arc Length = Rθ(rad)
Sagitta = R[1 - cos(θ / 2)]
Tangent = R tan(θ / 2)
How to use this calculator
- Choose the measurement method that matches your field data.
- Select the length unit you want to keep throughout the calculation.
- Enter the required known values, such as chord, angle, or sagitta.
- Set the decimal precision for the final output.
- Press Calculate Curve Radius to solve the curve geometry.
- Review the result section above the form for radius and related values.
- Use the graph to verify the curve shape visually.
- Download the summary as CSV or PDF for site records or reporting.
Example data table
These examples show typical ways to solve radius from different construction geometry measurements.
| Method | Input 1 | Input 2 | Calculated Radius |
|---|---|---|---|
| Arc Length + Angle | Arc Length = 62.832 m | Angle = 60° | 60.000 m |
| Chord + Sagitta | Chord = 40 m | Sagitta = 5 m | 42.500 m |
| Chord + Angle | Chord = 30 m | Angle = 45° | 39.197 m |
| Tangent + Angle | Tangent = 25 m | Angle = 50° | 53.613 m |
| External Distance + Angle | External = 4 m | Angle = 40° | 62.327 m |
Frequently asked questions
1) What does this curve radius calculator solve?
It finds the radius of a simple circular curve from common field measurements such as chord, sagitta, arc length, tangent length, external distance, and central angle. It also returns related geometry used in construction layout and checking.
2) Which method is best for site work?
Use the method that matches the measurements you can trust most onsite. Chord and sagitta work well for direct physical checks, while tangent and angle are common when layout points come from drawings or alignment data.
3) Is sagitta the same as middle ordinate?
Yes. In this context, sagitta and middle ordinate describe the same vertical offset from the midpoint of the chord to the curve. Many construction and roadway references use the terms interchangeably.
4) Why must the angle stay below 180 degrees?
The calculator is designed for simple circular construction curves, where the included angle is greater than zero and less than 180 degrees. That keeps the geometry practical for common layout, alignment, and formwork checks.
5) Can I use feet, meters, millimeters, or centimeters?
Yes. The selected unit is carried through the calculation consistently. Just enter every length in the same unit system, and the solved radius, chord, tangent, and related outputs will stay in that unit.
6) Why am I seeing an invalid geometry message?
That usually means the inputs cannot form a valid simple circular curve. Examples include a zero value, an angle outside the allowed range, or a chord that is too large for the solved circle geometry.
7) How does the graph help me?
The graph gives a quick visual check of the solved curve, its chord, and the center point. It helps you confirm whether the curvature looks reasonable before using the values for marking or review.
8) Is this useful for roads, curbs, and pipelines?
Yes. It is useful anywhere simple circular geometry is used, including roads, curbs, paths, retaining wall alignments, pipe runs, and general construction layout where radius and offset checks are required.