Calculate the lean angle of a motorcycle from speed and turn radius, or solve for the maximum cornering speed or minimum radius at any lean angle.
Motorcycle Lean Angle Formula
LA = atan( V^2 / (g * R) )
- LA is the lean angle from vertical (degrees, after converting from radians)
- V is the forward speed (m/s)
- R is the radius of the turn (m)
- g is the acceleration of gravity (9.80665 m/s²)
The same relationship can be rearranged to solve for the other two variables, which is what the maximum speed and minimum radius modes of the calculator do:
Vmax = sqrt( g * R * tan(LA) )
Rmin = V^2 / (g * tan(LA))
The lateral g-force mode uses the fact that the tangent of the lean angle equals the lateral acceleration in g, so LA = atan(G). This same tangent also equals the friction coefficient the tires must supply, which is why the calculator reports required grip alongside every result.
The advanced option estimates the real lean of the frame, which is larger than the ideal value because wide tires move the contact patch off the centerline:
ADD = asin( t * sin(LA) / (h - t) )
- ADD is the extra lean added to LA (degrees)
- t is half the rear tire width
- h is the height of the combined bike and rider center of mass
Lean Angles at Common Speeds and Turn Radii
The table below shows the ideal lean angle for typical street speeds and turn radii. Values over about 50 degrees demand more grip than street tires provide on public roads.
| Speed | 100 ft radius | 200 ft radius | 300 ft radius | 500 ft radius |
|---|---|---|---|---|
| 30 mph | 31.0° | 16.7° | 11.3° | 6.9° |
| 45 mph | 53.5° | 34.1° | 24.3° | 15.2° |
| 60 mph | 67.4° | 50.3° | 38.7° | 25.7° |
| 75 mph | 75.1° | 62.0° | 51.4° | 36.9° |
Because the tangent of the lean angle equals both the lateral g-force and the friction coefficient the tires must deliver, every lean angle maps directly to a grip requirement. This table interprets common lean angle limits in those terms.
| Riding situation | Typical lean limit | Lateral g / grip needed |
|---|---|---|
| Cruiser (floorboards touch down) | 28–32° | 0.53–0.62 |
| Traction control rain mode (BMW S1000RR) | 38° | 0.78 |
| Sport mode / brisk street riding | 45° | 1.00 |
| Race mode on sport tires | 48° | 1.11 |
| Slick mode on race tires | 53° | 1.33 |
| MotoGP maximum | 60–64° | 1.73–2.05 |
Motorcycle Lean Angle Example Problems
Example 1: You take a turn with a 200 ft (60.96 m) radius at 45 mph (20.12 m/s). First square the speed: 20.12² = 404.8. Then multiply gravity by the radius: 9.80665 * 60.96 = 597.8. Divide: 404.8 / 597.8 = 0.677. The lean angle is atan(0.677) = 34.1 degrees, and the tires must supply a friction coefficient of about 0.68.
Example 2: You want the maximum speed through a 100 m radius sweeper without leaning past 40 degrees. tan(40°) = 0.839. Vmax = sqrt(9.80665 * 100 * 0.839) = sqrt(822.9) = 28.7 m/s, which is 103.3 km/h or about 64.2 mph.
FAQ
Why does my bike lean more than the calculator predicts?
The basic formula treats the motorcycle as a line with zero-width tires. Real tires are wide, so the contact patch moves toward the inside of the turn as you lean, and the frame must tip further to keep the balance of forces. The advanced option quantifies this: a 6 inch wide rear tire with a 26 inch center of mass height adds about 3.2 degrees to a 25 degree ideal lean. Sitting bolt upright or leaning your body out (counterleaning) also forces the bike itself to lean more, while hanging off toward the inside lets the bike stay more upright for the same corner.
Does the weight of the bike or rider change the lean angle?
No. Mass appears on both sides of the force balance and cancels out, so a 900 lb touring bike and a 250 lb dirt bike need the same lean angle for the same speed and radius. What weight placement does change is the center of mass height, which slightly alters the tire width correction, and heavier bikes work their tires harder in absolute terms.
What is the maximum lean angle a motorcycle can hold?
The physical limit is grip: the tangent of the lean angle equals the friction coefficient the tires must produce, so a tire that grips at mu = 1.0 supports at most a 45 degree lean on clean dry pavement. Good sport tires reach roughly 48 to 53 degrees, wet pavement drops the limit to around 40 degrees or less, and many bikes touch pegs, floorboards, or exhaust before running out of tire. MotoGP machines on slicks exceed 60 degrees.
