Calculator Inputs
Formula Used
- Arc method: R = L / θ, where θ is in radians.
- Chord method: R = C / (2·sin(θ/2))
- Arc length: L = R·θ
- Chord length: C = 2·R·sin(θ/2)
- Sagitta: S = R·(1 − cos(θ/2))
- Tangent length: T = R·tan(θ/2)
- Speed-based minimum radius (optional): R = V²/(127·(e+f)) for km/h and meters, or R = V²/(15·(e+f)) for mph and feet.
How to Use This Calculator
- Select the unit system that matches your drawings.
- Choose a calculation method based on available measurements.
- Enter the required values for that method only.
- Optionally add ramp width for outer-edge checks.
- Optionally add speed, e, and f for a minimum-radius check.
- Press Calculate to view results above the form.
- Use the download buttons to export CSV or PDF.
Example Data Table
| Scenario | Method | Inputs | Key Output |
|---|---|---|---|
| Parking ramp quarter turn | Radius from chord + angle | Angle 90°, Chord 14.14 | Radius ≈ 10.00 |
| Service ramp bend | Radius from arc + angle | Angle 60°, Arc 12.57 | Radius ≈ 12.00 |
| Known radius layout | Curve elements from radius + angle | Radius 15.0, Angle 45° | Arc ≈ 11.78 |
| Measured stringline arc | Central angle from radius + arc | Radius 20.0, Arc 10.0 | Angle ≈ 28.65° |
| Measured endpoints | Central angle from radius + chord | Radius 25.0, Chord 20.0 | Angle ≈ 47.16° |
Curve radius and vehicle path control
Ramp curvature controls how quickly vehicles change heading, affecting comfort, lane encroachment, and barrier clearance. Tight service ramps may work at low speeds, but smaller radii increase steering demand and reduce inner-edge clearance. This calculator quantifies centerline radius from common drawing or field measurements. Pair results with your design vehicle to check swept path.
Choosing an input method during layout
Use Chord + Angle when endpoints and included angle come from control lines. Use Arc + Angle when the path length is specified by curb or striping. Use Radius + Angle to generate curve elements for setout and verification. Keep chord and arc referenced to the same centerline.
Interpreting sagitta and tangent length
Sagitta (middle ordinate) is the maximum offset between the curve and its chord. It helps check clearance to columns, walls, and parapets where the inside edge is constrained. Tangent length supports stationing and confirms approach tangents fit available straights. In the field, sagitta can be checked with a stringline.
Outer-edge checks using ramp width
With a defined width, the outer edge follows a larger radius. This calculator reports outer radius plus outer arc and chord to assess curb lengths, barrier alignment, and transitions. Small width changes can shift the outer chord and drive clashes near walls. Outer arc also supports curb length and barrier quantity takeoff.
| Example inputs | Computed highlights |
|---|---|
| Angle 90°, Inner radius 10, Width 3.5 | Inner arc ≈ 15.71, Outer radius ≈ 13.5, Outer arc ≈ 21.21 |
Screening minimum radius with speed, e, and f
The optional check estimates a minimum radius from design speed, superelevation, and side friction. Use it for early screening, then confirm with your governing standard and project vehicle criteria. If your radius is low, reduce speed assumptions, increase radius, or revisit crossfall and friction inputs. Enter e and f as decimals and apply conservative assumptions.
FAQs
1) Which method should I use first?
Start with the measurements you trust most. Chord+angle is best from control lines, arc+angle matches specified curb lengths, and radius+angle is ideal when the design radius is known.
2) Why does my chord-based radius differ from my arc-based radius?
Small differences usually come from rounding the angle, measuring along the wrong path, or mixing inner-edge and centerline lengths. Confirm the angle is the included central angle and that units are consistent.
3) What does sagitta tell me on a ramp?
Sagitta is the maximum “bulge” of the curve away from the chord. It helps estimate how far the curved path will intrude toward obstacles compared with a straight-line connection.
4) How should I use ramp width in the calculation?
Enter width when you need outer-edge checks. The tool adds width to the inner radius to report outer radius, arc, and chord, which are useful for curb lengths and barrier alignment.
5) Is the speed-based minimum radius check mandatory?
No. It is optional and simplified. Use it as a quick screening step and always confirm with your governing standard, signage, grades, visibility, and the project’s vehicle design criteria.
6) What ranges are reasonable for e and f?
Typical e values are small decimals (often a few percent). f varies with surface and speed. Use project criteria or published guidance, and keep inputs as decimals (e.g., 0.04 for 4%).
7) Can I export results for reporting?
Yes. After you calculate, use the CSV or PDF buttons shown in the results panel. Exports reflect the latest calculation stored in your session.