Math
ACOS function: find roof or vector angles from adjacent-over-hypotenuse ratios
Calculate arccosine angles in [0, 180] degrees using DEGREES(ACOS(ratio)), and guard ratios outside [-1, 1].
Recover an unknown pitch angle from horizontal run and rafter length
When you know a rafter's horizontal run (adjacent) and sloped length (hypotenuse), their ratio run / length equals cos(theta). ACOS(number) computes the inverse cosine in radians from 0 to pi (0° to 180°).
Wrapping ACOS in DEGREES converts the output directly into degrees: a 6-meter run under a 12-meter rafter has ratio 0.5 and angle DEGREES(ACOS(6/12)) = 60°.
| Cosine Ratio | ACOS (Radians) | DEGREES(ACOS(Ratio)) |
|---|---|---|
| 1 (run = length) | 0 | 0° (flat) |
| 0.5 | 1.047198 | 60° |
| 0 | 1.570796 | 90° (perpendicular) |
| -0.5 | 2.094395 | 120° (obtuse vector angle) |
Convert ACOS output to degrees
Unlike ASIN (which returns [-90°, +90°]) and ATAN (strictly between those endpoints for finite inputs), ACOS spans [0°, 180°], making it the standard choice for computing the angle between two vectors via their dot product.
=ROUND(DEGREES(ACOS(A2 / B2)), 2)Guard ratios outside [-1, 1]
No real triangle has a horizontal run longer than its hypotenuse, so |ratio| > 1 is geometrically invalid. Checking ABS(A2/B2) > 1 catches data-entry swaps before calling ACOS.
These examples assume a strictly positive measured length. Validate that length is greater than zero before dividing; a zero length makes the ratio undefined.
=IF(ABS(A2 / B2) > 1, "Invalid ratio", ROUND(DEGREES(ACOS(A2 / B2)), 2))Try the example
Use the original values or change them to test your understanding.