Rafter length from pitch angle and run calculator

Enter a positive run and a pitch angle measured in degrees from the horizontal. The calculator converts the angle to radians, evaluates its cosine, and divides the run by that ratio. The result stays in the same linear unit as the run, so feet produce feet, meters produce meters, and millimeters produce millimeters. It is a focused geometry result for planning and checking, not a substitute for structural design or field measurements.

Measure the horizontal run and pitch angle correctly

The horizontal run is the level distance covered by one rafter, not the sloped board length you are trying to find. On a simple symmetrical gable roof, it is commonly half the building span when measured from the outside wall plate to the ridge centerline, but roof details can change that reference. Measure or derive the run from the same endpoints that the intended rafter segment will connect. Enter that value in any consistent linear unit. The pitch angle is measured upward from a horizontal line, with zero degrees representing a flat member. Do not enter an angle measured from vertical, and do not enter a rise-over-twelve pitch number such as 6 unless you first convert it to degrees. A 6-in-12 pitch is about 26.565 degrees, not 6 degrees. This distinction matters because the cosine calculation expects an actual angular measure. The calculator accepts angles from zero up to, but not including, ninety degrees. A vertical line has no finite rafter length for a positive horizontal run under this model, so ninety degrees is rejected.

Understand the cosine calculation and result

A rafter, its horizontal run, and its vertical rise form a right triangle. Relative to the pitch angle, the run is the adjacent side and the rafter is the hypotenuse. The cosine ratio is adjacent divided by hypotenuse: cosine of the angle equals run divided by rafter length. Rearranging that relationship gives rafter length equals run divided by cosine of the pitch angle. The calculator converts degrees to radians because standard programming cosine functions use radians, calculates the cosine ratio, and performs that division. It returns the converted radian angle and cosine ratio alongside the final sloped length so the work is easy to audit. As the pitch angle increases, cosine decreases and the rafter becomes longer for the same run. At zero degrees, cosine is one, so the rafter length equals the run. Rounding is applied only to the returned fields at the requested precision; the core division uses the full floating-point values. Because the output unit is inherited from the input, label and record your chosen unit separately when using the number in plans.

Use the theoretical length in practical roof planning

The computed value is the geometric straight-line distance between the endpoints represented by your run and angle. That makes it useful for early material estimates, drawing checks, classroom problems, and comparing roof options. Real common rafters may require additional length or layout adjustments for an overhang, ridge-board thickness, birdsmouth seat, plumb cuts, fascia details, connectors, or the way dimensions are referenced on site. Those construction allowances are intentionally not guessed by this calculator. If an overhang has its own horizontal projection, include it in the run only when you want the returned sloped distance to cover that projection and the roof angle remains unchanged. Before cutting material, verify dimensions at the structure and follow the applicable drawings, building rules, and guidance from a qualified professional. For automation, send the run and pitch angle to the API for $0.002 per item; the same deterministic equation will return the same output for identical inputs. Choosing extra decimal places can help intermediate work, but it does not make a measured run or angle more accurate than the original measurement.