Lean Angle & Cornering Calculator
Enter a corner radius and speed to see the lean angle the physics requires — or switch it around to find the maximum speed a given lean angle can hold.
The geometry of a corner
When you round a bend, the corner pushes the bike toward its centre while gravity pulls straight down. The motorcycle leans until those two effects line up through the tyres, and that balance angle depends only on how fast you are going and how tight the corner is — double the speed and you need roughly four times the sideways effect, because it scales with the square of speed.
The result is pure physics, not a grip limit: what actually holds you up is the rubber on the road. Good tyres, quality gloves and boots, and abrasion-resistant gear are what turn confidence in a corner into a margin for the moment it doesn’t go to plan.
Frequently Asked Questions
What is the lean angle formula?
On a steady, flat corner the geometric lean angle is θ = atan(v² / (r · g)), where v is speed in metres per second, r is the corner radius in metres, and g is gravitational acceleration (about 9.81 m/s²). Rearranged, the maximum speed for a chosen angle is v = √(r · g · tan θ). The calculator does both directions for you.
Does this tell me how fast I can safely corner?
No — it gives the geometric angle for a balanced turn, not a grip limit. Available grip depends on tyres, temperature, road surface, and camber, and it runs out well before the geometry becomes impossible. Treat the number as physics for understanding, not a licence to carry that speed into a real corner.
Why do racers hang off the bike?
Moving body weight to the inside shifts the combined centre of mass inward, so the motorcycle itself needs less lean to hold the same line. That keeps more of the tyre's grip in reserve and the bike more upright than the geometric angle suggests. The formula gives the angle of the combined system; hanging off changes how that angle is shared between rider and machine.
What lean angles are realistic on the road?
Sane road riding rarely exceeds 30 to 40 degrees, and most street tyres and ground-clearance limits sit around 45 to 50 degrees. MotoGP riders reach 60-plus degrees on purpose-built tyres and surfaces. If the calculator returns a very high angle for your speed and radius, that is the physics telling you the corner needs to be taken slower.
Educational estimate of the geometric lean angle only. It is not a grip or safety limit — real traction depends on tyres, surface, and conditions, and runs out first. Ride within your limits.