Lean angle in roundabouts and hairpins
Small bends give big-looking numbers, but the speed is low. A roundabout is often ridden at around 20 to 25 km/h and needs roughly 12 to 26° of lean; a hairpin taken calmly needs less still. Below are the numbers for your radius and speed, and the point where the pedal first becomes the topic.
About the numbers. Every angle and speed below is a model value from the same formula as the calculator (g = 9.81 m/s²). Real corners differ, so use the numbers to build a feel for them. The radii are example radii for the bike’s own line, chosen to show how lean grows as the bend tightens. Krengo shows your lean angle in a corner.
Why small bends feel dramatic but are often calm
The lean angle for a steady corner is θ = atan(v² / (g · r)), with speed v in m/s, radius r in metres and g = 9.81 m/s². Speed enters squared: halve the speed and the lean needed falls to about a quarter in the small-angle range. That is why a tight bend at walking-to-jogging pace can ask for less lean than a long bend at 40 km/h. Try your own numbers in the lean angle calculator.
Roundabouts
The FHWA guide Roundabouts: An Informational Guide gives a feel for the size of a single-lane roundabout: an inscribed circle diameter of at least about 30 m (Exhibit 6-19, page 146), so an outer radius of at least about 15 m. For entry speed it suggests about 25 km/h for mini and compact urban roundabouts, 35 km/h for urban single-lane and 40 km/h for urban double-lane and rural single-lane (Exhibit 6-4, page 133).1 Those are design figures for the car lane. A bike rides inside the outer edge, so the table uses 10 to 20 m as example radii for the bike’s own line; that range is our assumption, not a figure from the guide.
| Radius | 15 km/h | 20 km/h | 25 km/h | 30 km/h | 35 km/h |
|---|---|---|---|---|---|
| 10 m | ≈ 10.0° | ≈ 17.5° | ≈ 26.2° | ≈ 35.3° | ≈ 43.9° |
| 12 m | ≈ 8.4° | ≈ 14.7° | ≈ 22.3° | ≈ 30.5° | ≈ 38.8° |
| 15 m | ≈ 6.7° | ≈ 11.8° | ≈ 18.1° | ≈ 25.3° | ≈ 32.7° |
| 20 m | ≈ 5.1° | ≈ 8.9° | ≈ 13.8° | ≈ 19.5° | ≈ 25.7° |
The rows are the radius of the line, the columns the speed, and the cells the model lean angle: atan((v / 3.6)² / (9.81 · r)), rounded to 0.1°. For example, a 12 m line at 25 km/h takes about 22.3° of lean, and a 15 m line at 20 km/h about 11.8°. Ridden calmly through the middle of the range, a roundabout is a modest lean. The same 12 m line at 35 km/h takes about 38.8°, which is why a calm speed suits a small radius.
Hairpins
Hairpin radii vary a great deal from road to road, and we have no source for a typical value, so the table shows example radii of 6, 8, 10 and 12 m rather than a claim about any road. The speeds are the low ones of a climb or a careful descent.
| Radius | 10 km/h | 15 km/h | 20 km/h | 25 km/h |
|---|---|---|---|---|
| 6 m | ≈ 7.5° | ≈ 16.4° | ≈ 27.7° | ≈ 39.3° |
| 8 m | ≈ 5.6° | ≈ 12.5° | ≈ 21.5° | ≈ 31.6° |
| 10 m | ≈ 4.5° | ≈ 10.0° | ≈ 17.5° | ≈ 26.2° |
| 12 m | ≈ 3.8° | ≈ 8.4° | ≈ 14.7° | ≈ 22.3° |
The pattern is the point. Uphill, the speed is so low that the lean stays small: an 8 m bend at 15 km/h takes about 12.5°, and at 10 km/h about 5.6°. On a gentle downhill the same bend grows quickly with speed, to about 31.6° at 25 km/h. The same formula covers both; only the speed changes.
Where the pedal comes in
With the Krengo defaults the pedal warning level is about 33.2° and touch-down about 36.2° (see pedal touch-down angle). In a small radius that is the angle you reach first, so the pedal is the figure to know. The table gives the speed that produces each lean.
| Radius | 10° | 20° | 30° | 33.2° |
|---|---|---|---|---|
| 8 m | ≈ 13.4 km/h | ≈ 19.2 km/h | ≈ 24.2 km/h | ≈ 25.8 km/h |
| 10 m | ≈ 15.0 km/h | ≈ 21.5 km/h | ≈ 27.1 km/h | ≈ 28.8 km/h |
| 12 m | ≈ 16.4 km/h | ≈ 23.6 km/h | ≈ 29.7 km/h | ≈ 31.6 km/h |
| 15 m | ≈ 18.3 km/h | ≈ 26.3 km/h | ≈ 33.2 km/h | ≈ 35.3 km/h |
On a 10 m line, 33.2° comes at about 28.8 km/h. Geometry helps you here: with the inside pedal up and the outside pedal down you get the most clearance, and the cornering technique page covers the position. On a longer, steadier descent the radius is larger and the numbers are lower; see descending technique.
Reading it on a ride
Krengo shows your lean angle in a corner. Take a roundabout or a hairpin you ride often, note the lean you see and compare it with the row for your radius and speed. It is a quick way to build a feel for what small radii ask for, and to see how little lean a calm speed needs. The lean angle glossary explains the terms, and how far can a road bike lean has more radii.
Try it yourself
Put your own speed and radius into the lean angle calculator and compare the answer with the tables. Learn new speeds on a closed or quiet road with permission to ride there.
Frequently asked questions
How much lean does a roundabout need?
With a 10 to 15 m line at 20 to 25 km/h the model gives about 11.8 to 26.2° of lean (the roundabout table above).
How much lean in a hairpin?
The hairpin table gives, for example, about 12.5° for an 8 m bend at 15 km/h.
At what speed does the pedal become the limit in a roundabout?
On a 10 m line the pedal warning level of 33.2° (the Krengo default) comes at about 28.8 km/h.
Sources
- FHWA, Roundabouts: An Informational Guide, chapter 6 Geometric Design. Used for the inscribed circle diameter (Exhibit 6-19, page 146) and recommended entry speeds (Exhibit 6-4, page 133). Read on 5 October 2026.
The lean formula is a standard textbook model and is not taken from the source. The angles and speeds are Krengo’s own model values from site/calc.js, rounded to 0.1°. The radii of the bike’s line and of the hairpins are example values; the pedal angles are the Krengo defaults on the linked page.