GOEZLean angle is how far a motorcycle tilts from vertical in a corner. In a steady turn it follows tan θ = v² ÷ (g × r): speed squared divided by gravity times the corner radius. Double your speed in the same corner and the bike needs far more lean, which is why entry speed matters more than anything else.
Every corner you ride is a balance between two forces: gravity pulling the bike down and the sideways force that comes from changing direction. Lean angle is where those two meet. Once you understand the simple formula behind it, a lot of riding advice — slow in, look through the turn, don't rush a blind bend — suddenly makes sense.
What is motorcycle lean angle?
Lean angle is the angle between the motorcycle and a vertical line, measured while the bike is turning. Upright is 0°. Lying flat on the ground would be 90°. On the road, most riding happens at modest angles; deep lean is something you see in corners taken briskly or on a track.
Why does a bike lean at all? To turn, the tyres must push the bike sideways toward the inside of the corner. That sideways push tries to flip the bike outward. Leaning in lets gravity balance it out. The faster you go or the tighter the corner, the bigger the sideways force — and the more you have to lean to balance it.
The lean angle formula
For a steady corner on flat ground, the theoretical lean angle is:
tan θ = v² ÷ (g × r)
- θ — lean angle from vertical
- v — speed in metres per second (km/h ÷ 3.6, or mph × 0.447)
- g — gravity, about 9.81 m/s²
- r — corner radius in metres
Then θ = arctan(v² ÷ (g × r)). Any calculator with an "atan" or "tan⁻¹" button will do it.
Worked example
You ride a corner with a 50 m radius at 72 km/h.
- Convert speed: 72 ÷ 3.6 = 20 m/s.
- Square it: 20 × 20 = 400.
- Gravity × radius: 9.81 × 50 = 490.5.
- Divide: 400 ÷ 490.5 ≈ 0.82.
- arctan(0.82) ≈ 39°.
Same corner at 54 km/h (15 m/s)? 225 ÷ 490.5 ≈ 0.46, so about 25°. Dropping speed by a quarter cut the lean by more than a third. That's the squared term at work.
Lean angle calculator table
Theoretical lean for common speeds and corner radii, rounded to the nearest degree.
| Speed | r = 30 m | r = 50 m | r = 100 m | r = 200 m |
|---|---|---|---|---|
| 40 km/h (25 mph) | 23° | 14° | 7° | 4° |
| 60 km/h (37 mph) | 43° | 30° | 16° | 8° |
| 80 km/h (50 mph) | 59°* | 45° | 27° | 14° |
| 100 km/h (62 mph) | 69°* | 58°* | 38° | 21° |
| 120 km/h (75 mph) | 75°* | 66°* | 49° | 30° |
* Physically out of reach: no road motorcycle can corner at these angles. Read them as "this speed doesn't fit this corner".
Two patterns stand out. Doubling speed roughly quadruples the sideways force, so lean climbs fast. And halving the radius has the same effect as going about 40% faster. A tightening bend can turn a comfortable speed into a demanding one.
Why your real lean differs from the formula
The formula describes an ideal bike with razor-thin tyres and a rider sitting perfectly in line with it. Real riding adds a few twists:
- Tyre width. A wide tyre's contact patch moves toward its edge as you lean, so the bike has to lean a little more than the formula says to make the same turn.
- Body position. Shifting your body to the inside moves the combined centre of mass inward, so the bike itself can stay more upright at the same speed. Leaning your body out does the opposite.
- Road shape. Camber, crests and dips change the balance. A corner that slopes away from you needs more lean; a banked one needs less.
- Changing speed. Braking or accelerating mid-corner asks the tyres for grip in two directions at once, which leaves less for cornering.
What limits lean angle?
Two things decide how far you can lean: grip and ground clearance.
Grip depends on tyre type, tyre temperature and pressure, the road surface and the weather. Cold tyres, wet tar, gravel, diesel, painted lines and leaves all reduce it — sometimes suddenly. A lean that's comfortable on a warm, dry day can be too much on a cold morning.
Ground clearance is set by the bike. Footpegs, stands, exhausts and fairings touch down at different angles on different motorcycles. Cruisers usually scrape first; sport bikes are built to lean further. Lowered suspension or heavy luggage reduce clearance. Your owner's manual or dealer is the right source for your bike's figures.
The useful takeaway: lean angle is a budget. Every extra degree you use leaves less margin for a surprise — a bump, a patch of sand, a car on your side of the road.
How is lean angle measured?
There are three common ways, each with its own trade-off.
1. Phone GPS estimate
Your phone's GPS reports speed and heading. How fast the heading changes is the turn rate. Since speed ÷ radius equals turn rate, the formula can be rewritten as tan θ = v × ω ÷ g, where ω is the turn rate in radians per second. No mount and no extra hardware — the phone can stay in your pocket. The catch: it's an estimate. GPS can't see body position or tyre profile, and weak signal makes it noisy.
2. Gyro-based loggers
Dedicated data loggers and some phone apps read a gyroscope and accelerometer to track the bike's roll directly. They capture short, sharp corners better, but the device must be rigidly mounted to the bike and calibrated. A phone in a pocket moves with your body, not the bike, so gyro readings from a pocket don't work.
3. Built-in bike electronics
Many modern motorcycles have an inertial measurement unit (IMU) for cornering ABS and traction control, and some show lean on the dash. It's the most direct reading, but only if your bike has it.
How GOEZ estimates lean angle
GOEZ calculates lean from GPS speed and heading change — the first method above. A few rules keep the numbers honest:
- Speeds below about 14 km/h (4 m/s) are ignored, because GPS heading is unreliable when you're barely moving.
- Readings above 55° are treated as GPS noise and dropped.
- Your max lean is the 95th percentile of the ride, so one bad GPS fix can't set a record.
- Left and right are calculated separately.
GOEZ also counts corners: a corner counts when you keep turning the same way at 8° per second or more for at least 1.5 seconds. Corner count is free; lean angle comes with GOEZ PRO. Treat the number as a way to compare your own rides on similar roads, not as a measuring instrument.
How to build cornering confidence safely
Chasing a number on public roads is a bad idea. Building smooth, repeatable cornering is a good one. A few principles riders and instructors agree on:
- Set your speed before the corner. Do your braking upright, then roll in. Less speed means less lean — the table above shows how much.
- Look where you want to go. Turn your head and eyes toward the exit. The bike tends to follow your gaze.
- Be smooth. Gentle inputs on throttle, brakes and bars keep the tyres settled.
- Leave margin. On the road, ride corners well inside your limit. You can't see what's around a blind bend.
- Warm up. Cold tyres and a cold rider both need a few kilometres.
- Train properly. If you want to explore more lean, take a rider training course or a track day with instruction.
- Compare your own rides. Ride the same road a few times. Smoother lines and a steadier lean spread are better progress than one big peak.
Looking for good roads to practise smooth lines at a relaxed pace? Browse motorcycle routes with their corner counts, and record your rides to see how they compare. If you're new to tracking, start with how to track rides with your phone.