The geometry, set out
Put the bottom bracket centre at the origin, with forward positive and up positive. The seat post rises along the seat tube, so a point at distance d up the post axis sits at minus d times the cosine of the seat angle horizontally, and d times the sine vertically. That is the whole of a straight post with the saddle clamped on its axis.
Three things move the saddle top off that axis. Post setback pushes the rail clamp backwards square to the post. The rail position slides the saddle fore or aft along its rails, which run close enough to horizontal to treat as horizontal. And the saddle shell lifts its own top surface above the rails by a fixed vertical amount.
Those three form a constant offset vector added to whatever point on the post axis the clamp reaches. Since you know the saddle height rather than the post extension, the calculation solves for the extension that puts the saddle top exactly that straight-line distance from the bottom bracket, which is a quadratic with one physically sensible root. Set post setback, rail offset and shell height all to zero and it collapses to the obvious answer: setback equals saddle height times the cosine of the seat angle.
Effective seat angle is the number that actually describes the position
The seat tube angle on a geometry chart describes a tube. What matters for where you sit is the angle of the line from the bottom bracket to the saddle top, and that is a different number as soon as anything moves the saddle off the post axis.
A 20 mm setback post on a 73.5 degree seat tube pulls the effective angle down to a little under 73, which is roughly what a frame half a degree slacker would give with a straight post. This is why comparing two frames on seat tube angle alone is unreliable: a steep frame with a layback post and a slack frame with an inline post can put the saddle in almost the same place.
Manufacturers who quote an effective seat angle for a frame with a bent or forward-offset seat tube are quoting it at one specific saddle height, usually the top of the head tube or a stated stack. Above or below that height the number changes, which is a fact about the frame rather than an error in the chart.
Height and setback are the same adjustment
| Seat angle | Setback added per 10 mm of extra height |
|---|---|
| 71 degrees | about 3.3 mm |
| 73 degrees | about 2.9 mm |
| 75 degrees | about 2.6 mm |
| 78 degrees | about 2.1 mm |
Raising the post moves the saddle along the seat tube, not straight up, so every height change carries a fore-aft change with it. Ten millimetres up on a typical road angle is nearly three millimetres back. That is small in isolation and not small at all when someone raises a saddle 15 mm after a shoe or cleat change and then wonders why the reach to the bars grew.
It also means the two adjustments cannot be made independently on the rails alone. Sliding the saddle forward to recover the setback puts the nose in a different place relative to the rails, which changes the effective height slightly because the saddle top is not level. The interactions are small but they are real, and they are the reason changes get made one at a time.
What this page will not do
It will not tell you where your saddle should be. There is no shortage of rules of thumb — knee over pedal spindle, a fraction of inseam, a target effective angle for a discipline — and every one of them is a starting point that a real fitting session revises. Bodies differ in femur length, in hip and ankle mobility, in injury history and in what they are being asked to do on the bike, and none of that is visible to arithmetic.
So the honest scope is measurement. Given a frame chart and the parts on the bike, this tells you where the saddle is, how much of that comes from each component, and how much the position moves when you change one thing. If the goal is a position rather than a number, a bike fitter watches you pedal, which no calculator can. If riding produces pain, numbness or anything that persists after you get off, that belongs with a clinician before it belongs with a geometry chart.
Questions people ask
How is saddle setback calculated?
Horizontally, from the bottom bracket centre back to the saddle top. With a straight post and the saddle centred it is simply the saddle height multiplied by the cosine of the seat tube angle. Post setback, rail position and the height of the saddle shell above the rails each shift the saddle top off the post axis and are added to that base figure.
What is effective seat tube angle?
The angle from horizontal of the line between the bottom bracket and the saddle top, as opposed to the angle of the tube itself. They are only the same when the saddle sits directly on the post axis. A setback post makes the effective angle slacker than the tube, and because the offset is fixed while the height varies, the effective angle changes as the post goes up or down.
Does raising my saddle move it backwards?
Yes, along the seat tube. At a 73 degree seat angle roughly 2.9 mm of setback comes with every 10 mm of height. It is why a saddle raised after a shoe change also lengthens the reach to the bars, and why height and fore-aft position are best treated as one adjustment made in small steps rather than two independent ones.
Is a setback post the same as a slacker frame?
For where the saddle ends up, close to it. A 20 mm setback post on a 73.5 degree seat tube puts the saddle at roughly the effective angle a frame half a degree slacker would give with a straight post. What it does not replicate is everything else about the frame, and it does move the saddle further behind the post clamp, which changes how the post is loaded.
What setback should I use?
That is not a question this page answers, and it should not be. Where a saddle belongs depends on your proportions, your mobility, your history and what you are riding, and the common rules of thumb are starting points that a fitting session revises. Use this to measure and compare positions; use a fitter to choose one, and a clinician if anything on the bike hurts.