Inputs
Choose what you want to solve for. Enter values, then calculate. Add friction to estimate a safe speed range.
Results
Angles are shown in degrees and radians. Speeds and radii are shown in your chosen units and SI units.
Enter inputs and press Calculate to see results.
How to use this calculator
- Select what you want to solve for: angle, speed, or radius.
- Enter the required inputs. Use the unit dropdowns.
- Choose a gravity preset, or enter a custom gravity value.
- Optionally enter μ to estimate minimum and maximum speeds.
- Click Calculate to view the results instantly.
- Use Download CSV or Download PDF to export.
Example data table
Example angles use ideal banking. When μ is provided, vmin and vmax show an estimated speed band for the same θ and radius.
| Speed |
Radius |
μ |
Gravity |
Ideal angle θ (deg) |
vmin (same unit) |
vmax (same unit) |
| 60 km/h | 100 m | 0.15 | Earth | 15.82° | 40.31 | 75.83 |
| 80 km/h | 200 m | 0.20 | Earth | 14.13° | 35.40 | 109.97 |
| 45 mph | 300 ft | 0.25 | Earth | 24.29° | 28.49 | 59.56 |
| 55 mph | 600 ft | 0.12 | Earth | 18.63° | 43.27 | 65.38 |
| 120 km/h | 250 m | 0.00 | Earth | 24.38° | — | — |
| 25 m/s | 80 m | 0.20 | Mars | 64.59° | 19.95 | 34.38 |
| 70 ft/s | 900 ft | 0.18 | Moon | 45.69° | 58.40 | 84.04 |
Tip: If you already know θ and μ, use the Speed mode to estimate a safe speed band.
Tip: If you already know θ and μ, use the Speed mode to estimate a safe speed band.
Angle of banking article
1) Banking angle in one idea
A banked curve tilts the surface so part of the normal force points toward the curve center. That inward component supplies centripetal acceleration, reducing lateral tire demand near the design speed.
2) Inputs and realistic ranges
Road design speeds often sit around 40–120 km/h, while curve radii commonly range from 50–600 m. Above 90 km/h, small radius changes can noticeably shift θ and comfort. Gravity defaults to Earth’s 9.80665 m/s², but you can test other values for simulations and teaching.
3) Ideal banking example
The core relationship is tan(θ)=v²/(r·g). With v=80 km/h (22.22 m/s) and r=200 m on Earth, v²/(r·g)≈0.252, so θ≈14.1°. If speed rises to 100 km/h on the same radius, θ increases to about 21.7°.
4) How friction changes the picture
Tire friction widens the usable speed range around the ideal point. Using μ=0.20 with θ fixed at 14.1° and r=200 m, the estimated band is roughly vmin≈52 km/h and vmax≈111 km/h. Lower μ (wet) shrinks this band.
5) Reading the outputs
The tool reports θ in degrees and radians, plus speed and radius in your chosen units and in SI. When μ is entered, vmin and vmax are computed for the same θ and r, helping you judge operating tolerance.
6) Common checks for design
If θ looks high, increase radius or reduce speed, and confirm units and gravity. Treat μ as an estimate, add safety margin, and respect construction and comfort limits for real curves. Great for classrooms and project planning.
7) Documenting results
Export CSV to compare scenarios and export PDF for a compact report. Saving runs with different radii, speeds, and μ values makes assumptions visible and decisions easier.
FAQs
1) What is the angle of banking?
It is the tilt of a curve relative to level ground. The tilt helps create inward centripetal force, reducing the sideways friction needed to follow the curve at a given speed.
2) Which inputs affect θ the most?
Speed has the strongest effect because θ depends on v². Radius also matters: tighter curves require larger θ. Gravity changes the result linearly, so a smaller g requires a larger θ for the same speed and radius.
3) Do I need friction μ for the main angle?
No. The ideal banking angle uses only speed, radius, and gravity. μ is optional and is used to estimate a minimum and maximum speed range around the same θ and radius.
4) Why is my vmax missing or marked unstable?
For some θ and μ combinations, the denominator (cosθ − μ·sinθ) can approach zero or become negative. In that case, the standard vmax formula is not valid for the chosen inputs.
5) Is this suitable for roads, tracks, and rail?
Yes for quick physics estimates and comparisons. Real design must also consider superelevation limits, drainage, comfort, vehicle dynamics, and local standards. Use the calculator as a starting point, not a final specification.
6) What units should I use for best accuracy?
Any supported units are fine because the tool converts internally to SI. Just keep speed and radius consistent with their unit selectors, and avoid mixing values without updating the dropdowns.