Math
COS function: calculate horizontal run from sloped distance and angle
Project sloped survey or rafter lengths onto the horizontal ground plane with COS(RADIANS(angle)), and round floating-point noise at 90 degrees.
Convert degrees to radians before calling COS
In right-triangle geometry, horizontal run equals sloped_length * cos(theta). Because COS(number) expects theta in radians, passing 60 directly evaluates 60 radians (-0.9524) instead of 60 degrees (0.5).
Pairing COS(RADIANS(B2)) converts degrees first: a 12-meter rafter pitched at 60° spans 12 * 0.5 = 6 meters horizontally.
| Sloped Length m (A) | Pitch Degrees (B) | COS(RADIANS(B)) | Horizontal Run m |
|---|---|---|---|
| 12 | 60 | 0.5 | 6 |
| 12 | 0 | 1 | 12 (flat) |
| 12 | 90 | 0 (rounded) | 0 (vertical) |
| 12 | 120 | -0.5 | -6 (opposite heading) |
Calculate horizontal run across pitch angles
Wrapping the projection in ROUND(..., 4) keeps plans clean while preserving sub-millimeter precision.
=ROUND(A2 * COS(RADIANS(B2)), 4)Why COS(RADIANS(90)) needs rounding
Because binary floating-point cannot represent pi/2 with infinite precision, raw COS(RADIANS(90)) returns roughly 6.12E-17 in spreadsheets rather than exact 0. Rounding to 6 decimal places yields clean 0.
=ROUND(COS(RADIANS(B3)), 6)Try the example
Use the original values or change them to test your understanding.