Fork trail calculator: trail, offset and axle-to-crown
Fork trail comes from three numbers: head angle, fork offset and the radius of the wheel with its tyre. The formula is trail = (Rw · cos α − offset) / sin α, with the head angle α measured from the horizontal. The calculator below works it out as you type, and also converts between fork length L (parallel to the head tube) and axle-to-crown AC.
Bike trail and offset calculator
The starting values are only an example so the calculator shows a result; they are not a recommendation. Everything is calculated in your browser and nothing is sent anywhere.
What fork trail is
Trail is the horizontal distance on the ground between the front wheel's contact point and the point where the steering axis meets the ground. It is positive when the contact point sits behind that point. That is the definition in Wikipedia's article on bicycle and motorcycle geometry.
Three inputs are involved:
- Head angle (α): on bicycles it is measured from the horizontal.
- Offset (R): the perpendicular distance from the steering axis to the centre of the front wheel. On bicycles it is also called rake.
- Wheel radius with tyre (Rw): from the axle centre to the ground.
The same source lists the ways offset is built into a fork: curving the blades, adding a perpendicular tab at their lower ends, placing the crown's blade sockets ahead of the steerer, or mounting the blades into the crown at an angle to the steerer.
The fork trail formula
The geometric formula for bicycles, as Wikipedia gives it:
trail = (Rw · cos α − R) / sin α
The numerator, Rw · cos α − R, is the mechanical trail: the perpendicular distance from the contact point to the steering axis. Dividing by sin α turns it into the horizontal distance on the ground.
Worked example with the calculator's starting values: 622 rim, 40 mm tyre, 72° head angle, 45 mm offset.
- Rw = 622 / 2 + 40 = 351 mm.
- Rw · cos 72° = 351 · 0.3090 = 108.5 mm.
- Mechanical trail = 108.5 − 45 = 63.5 mm.
- Trail = 63.5 / sin 72° = 63.5 / 0.9511 = 66.7 mm.
Wheel radius: rim BSD plus tyre height
The calculator uses Rw = BSD / 2 + tyre height, and takes the nominal tyre width as the height. That is an approximation: a mounted tyre's height need not match its width, and the marked width is not always the real one. Sheldon Brown notes that nominal width is what is marked on the tyre, that actual width can be measured once the tyre is mounted, and that marked widths are often inaccurate.
For an exact figure, measure the real radius of the inflated wheel, from the axle centre to the ground, and use that in the formula.
BSD (bead seat diameter) is the second number in the ISO tyre designation, as in 40-622. That designation is defined by ISO 5775 and was formerly known as the E.T.R.T.O. system.
| ISO BSD (mm) | Common name | BSD / 2 (mm) |
|---|---|---|
| 622 | 700C / 29" | 311 |
| 584 | 650B / 27.5" | 292 |
| 559 | 26" | 279.5 |
| 630 | 27" | 315 |
How offset, head angle and wheel size change trail
Wikipedia puts it this way: "Trail is often cited as an important determinant of bicycle handling characteristics." The formula shows how it moves, and the same source sums it up:
- More trail with a larger wheel, a slacker (smaller) head angle or less offset.
- Less trail with a steeper (larger) head angle, more offset or a smaller wheel.
The formula describes the bike upright with the steering straight. Wikipedia notes that trail varies as the bike leans or steers.
How to calculate fork offset for a target trail
If you start from the trail you want, solve the same formula for offset:
R = Rw · cos α − trail · sin α
With the example above: 351 · 0.3090 − 66.7 · 0.9511 = 45 mm, the starting offset. You can also adjust the offset in the calculator until it shows the trail you are after.
Offset, length L and axle-to-crown (AC)
Fork length is given in two ways. L is measured parallel to the head tube, from the crown race seat down to the level of the axle. AC is the direct axle-to-crown: the straight-line distance from the crown race seat to the axle centre. Because the axle sits R away from the steering axis, the three form a right triangle:
L = √(AC² − R²) and, the other way round, AC = √(L² + R²)
So with the same AC, changing the offset changes L, and with it the height of the front end. In ForkCAD these are "Length parallel to steerer" and "Axle-to-crown (direct)", next to "Offset", in the "Length and offset" group; you work with one or the other. How to measure them and why they differ is covered in fork axle-to-crown length.
Axle-to-crown from L and offset
L from axle-to-crown and offset
With length and offset settled, the rest of the design is covered in unicrown fork design and fork tyre and fender clearance.
FAQ
Are fork offset and rake the same thing?
Yes. On bicycles, fork offset is also called rake: the perpendicular distance from the steering axis to the wheel centre.
Which wheel radius goes into the trail formula?
The radius of the wheel with its tyre mounted. Half the BSD plus the nominal tyre width is an approximation; for an exact value, measure from the axle centre to the ground with the tyre inflated.
Is head angle measured from the horizontal or the vertical?
On bicycles, from the horizontal. Motorcycles use the angle from the vertical, with a different form of the formula; with the angle from the horizontal, the one on this page applies.
Does trail change when the bike leans or the bar is turned?
Yes. The formula gives trail with the bike upright and the steering straight; Wikipedia notes that it varies as the bike leans or steers.
Sources
- Wikipedia: Bicycle and motorcycle geometry (definition of trail and offset, trail formula, head angle from the horizontal, how trail varies).
- Wikipedia: Bicycle tire (ISO 5775 tyre designation, also known as ETRTO).
- Sheldon Brown: Tire Sizing Systems (BSD 622, 584, 559 and 630; nominal versus actual width).