Calculate bicycle saddle setback from saddle height and seat-tube angle (73° typical), or solve saddle height or angle, in mm, cm or inches.
Saddle Setback Formula
The saddle setback calculation uses simple right-triangle geometry. Height is the distance along an inclined reference line through the bottom-bracket reference. Total setback adds a separately measured horizontal rail or clamp offset; positive setback is rearward. This coordinate model does not select a bike fit.
- SS = total horizontal setback (rearward positive, forward negative)
- O = signed horizontal offset: rearward positive, forward negative; blank means zero
- SH = positive height along the inclined reference line, before the horizontal offset
- STA = reference-line angle from horizontal, from 0° to 90°
- cos = cosine of the seat tube angle
- arccos = inverse cosine, used to solve for the angle
If you enter saddle height and seat tube angle, the calculator finds saddle setback.
If you enter saddle setback and seat tube angle, it finds saddle height.
If you enter saddle height and saddle setback, it finds the seat tube angle. For this mode, setback minus the signed offset must be between zero and the reference-line height.
The calculator converts lengths to millimeters before calculating, then converts lengths to the selected result unit. Changing an input unit converts its current quantity. The following examples and angle table use zero additional offset.
Seat Tube Angle Reference Values
These values show how much horizontal setback is produced for each 100 mm of saddle height along the seat tube line.
| Seat Tube Angle | cos(angle) | Setback per 100 mm Saddle Height |
|---|---|---|
| 70° | 0.342 | 34.2 mm |
| 72° | 0.309 | 30.9 mm |
| 73° | 0.292 | 29.2 mm |
| 74° | 0.276 | 27.6 mm |
| 76° | 0.242 | 24.2 mm |
A steeper seat tube angle gives less calculated setback for the same saddle height. A slacker seat tube angle gives more calculated setback.
Length Unit Conversions
| Conversion | Value |
|---|---|
| 1 inch to millimeters | 25.4 mm |
| 1 millimeter to inches | 0.0393701 in |
| 10 mm to inches | 0.3937 in |
| 1 inch to centimeters | 2.54 cm |
Example Problems
Example 1: Calculate saddle setback
You have a saddle height of 720 mm and a seat tube angle of 73°.
The saddle setback is about 210.5 mm.
Example 2: Calculate seat tube angle
You have a saddle height of 700 mm and a saddle setback of 200 mm.
The seat tube angle is about 73.4°.
FAQ
What is saddle setback?
Saddle setback is a horizontal coordinate relative to a bottom-bracket reference. This calculator projects a reference-line height and adds an optional horizontal offset. Use consistent measurement points and do not count an offset twice. Frame seat-tube angles may use different effective reference points; saddle shape, rider position and fit suitability are not determined.
What happens at the angle limits?
The model accepts 0° through 90° as mathematical limits. At 90°, the geometric setback is zero and total setback equals the signed offset; height cannot be determined uniquely from those inputs. At 0°, the vertical coordinate is zero. These endpoints are not fit recommendations; scenarios outside the angle range are omitted.
Which setbacks allow an angle solution?
When solving for angle, the calculator uses (SS − O) / SH inside inverse cosine. The ratio must be between 0 and 1. It is the setback after removing the signed offset that must fit the reference-line height, rather than the total setback alone.
