Calculate roof collar tie length, rise, or span for roof framing by entering any two values and choose ft, m, in, or cm with unit conversion.
Collar Tie Formula
The calculator uses a right-triangle model. The roof rise is one leg of the triangle, half of the roof span is the other leg, and the collar tie length is treated as the sloped length between those two points.
CollarTie = sqrt(Rise^2 + (Span/2)^2)
Rise = sqrt(CollarTie^2 - (Span/2)^2)
Span = 2*sqrt(CollarTie^2 - Rise^2)
- CollarTie = collar tie length
- Rise = vertical rise of the roof
- Span = full horizontal roof span
- Span/2 = half span, also called the roof run in this triangle
If you enter the rise and span, the calculator solves for the collar tie length. If you enter the collar tie length and span, it solves for the rise. If you enter the collar tie length and rise, it solves for the span. Inputs can be entered in feet, meters, inches, or centimeters, and the calculator converts the values before applying the formula.
Common Roof Geometry Values
The table below shows example collar tie lengths for common roof spans and rises using the same formula as the calculator.
| Roof Span | Half Span | Roof Rise | Collar Tie Length |
|---|---|---|---|
| 16 ft | 8 ft | 4 ft | 8.944 ft |
| 20 ft | 10 ft | 5 ft | 11.180 ft |
| 24 ft | 12 ft | 6 ft | 13.416 ft |
| 30 ft | 15 ft | 7.5 ft | 16.771 ft |
These checks help avoid invalid inputs when solving for a missing value.
| Missing Value | Required Inputs | Input Rule |
|---|---|---|
| Collar Tie Length | Rise and span | Both values must be positive. |
| Rise | Collar tie length and span | Collar tie length must be greater than half the span. |
| Span | Collar tie length and rise | Collar tie length must be greater than the rise. |
Examples
Example 1: Calculate collar tie length
You have a roof rise of 6 ft and a roof span of 24 ft.
CollarTie = sqrt(6^2 + (24/2)^2)
CollarTie = sqrt(36 + 144) = sqrt(180) = 13.4164 ft
The collar tie length is 13.4164 ft.
Example 2: Calculate roof rise
You have a collar tie length of 10 ft and a roof span of 16 ft.
Rise = sqrt(10^2 - (16/2)^2)
Rise = sqrt(100 - 64) = sqrt(36) = 6 ft
The roof rise is 6 ft.
FAQ
What does roof span mean in this calculator?
Roof span means the full horizontal distance across the roof section. The formula uses half of that span because the triangle is measured from the center ridge line to one side of the roof.
Why does the collar tie length need to be greater than half the span?
When solving for rise, the formula subtracts half-span squared from collar tie length squared. If the collar tie length is equal to or less than half the span, the triangle cannot have a positive vertical rise, so the input is not valid.
Is this the same as sizing a structural collar tie?
No. This calculator gives a geometric length based on rise and span. Structural collar tie sizing, spacing, fastening, and placement depend on building code requirements, roof loads, rafter size, and the actual roof design.
