Calculate collar tie length from roof span and rise, with the tie at the upper-third line by default, or solve for rise, span or tie height in ft or m.
Collar Tie Formula
A collar tie is horizontal between opposing rafters near the ridge. For straight rafters in a symmetric gable, similar triangles determine its connection-to-connection span at a specified elevation. Roof span and rise alone cannot determine that span. The former hypotenuse formula measures common-rafter line length. Collar ties belong in the upper third of the roof height and resist uplift separation; this tool checks geometry only, excluding end overlap, cuts, member sizing and fastening. See the American Wood Council distinction.
- L = horizontal connection span, excluding end overlap
- R = ridge rise above the level wall plates
- S = full horizontal span between the wall plates
- H = tie elevation above the same wall-plate datum; 2R/3 ≤ H < R
Select the collar-tie dimension to solve and supply the other three dimensions; for the tie span, the default tie position is the upper-third line (⅔ of the rise). The inverse requires 0 < L < S and 0 < H < R; collar placement is restricted to the upper third. Select a separate rafter mode to use A = √(R² + (S/2)²), R = √(A² − (S/2)²), or S = 2√(A² − R²). A is the theoretical ridge-to-wall-plate line length, without overhang, ridge thickness or cuts; see Army TM 3-34.47, chapter 7. All dimensions are converted before computation.
Common Roof Geometry Values
The table gives horizontal connection spans at the specified elevations, using the same similar-triangle geometry. These are examples, not construction recommendations.
| Roof Span | Tie Elevation H | Roof Rise | Connection Span L |
|---|---|---|---|
| 16 ft | 3 ft | 4 ft | 4 ft |
| 20 ft | 4 ft | 5 ft | 4 ft |
| 24 ft | 4 ft | 6 ft | 8 ft |
| 30 ft | 5 ft | 7.5 ft | 10 ft |
These checks help avoid invalid inputs when solving for a missing value.
| Solve For | Required Inputs | Input Rule |
|---|---|---|
| Connection Span L | Rise, span and elevation | Positive R and S; 2R/3 ≤ H < R. |
| Rise | Connection span, roof span and elevation | 0 < L ≤ S/3; H > 0. |
| Span | Connection span, rise and elevation | L > 0; 2R/3 ≤ H < R. |
Examples
Example 1: Calculate collar tie connection span
For a 6 ft rise, 24 ft span and tie elevation of 4 ft above the wall plates:
The horizontal connection span is 8 ft, before any end overlap allowance.
Example 2: Calculate roof rise
For an 8 ft connection span, 24 ft roof span and tie elevation of 4 ft above the wall plates:
The roof rise is 6 ft.
FAQ
What does roof span mean in this calculator?
Roof span is the full horizontal distance between the wall-plate reference points. Half span is the run used only in the separate common-rafter right-triangle calculations.
Why is collar-tie elevation required?
Horizontal separation of opposing rafters changes with elevation. In this ideal symmetric gable, L/S = (R-H)/R. A tie in the upper third has 0 < L ≤ S/3. The former greater-than-half-span test belonged to a rafter hypotenuse, not a collar tie.
Is this the same as sizing a structural collar tie?
No. It gives ideal connection geometry using rise, span and elevation. Actual cut length requires overlap and connection details. Structural sizing, spacing, fastening and placement depend on applicable codes, loads and roof design, which this calculator does not verify.
