Syntax
TAN(number)
| Parameter | Description |
|---|---|
| number | Parameter of the TAN function. |
Examples
Tangent of 45 degrees
Formula
=TAN(PI()/4)
Returns 1. The tangent of 45° is exactly 1, meaning a 45° slope rises 1 unit for every 1 unit of horizontal distance.
Height from angle
Formula
=100*TAN(RADIANS(35))
Returns ~70.02. Standing 100 meters from a building, looking up at 35°, the building is about 70 meters tall (height = distance × tan(angle)).
Roof pitch
Formula
=DEGREES(ATAN(6/12))
Returns ~26.57°. A 6:12 roof pitch (6 inches rise per 12 inches run) corresponds to about 26.6 degrees. (Uses ATAN, the inverse of TAN.)
Common Errors
#VALUE!
Non-numeric input returns #VALUE!.
#NUM!
TAN approaches infinity near π/2 (90°). While it won't error at exactly PI()/2 due to floating point, the result will be extremely large.
Tips
Slope = TAN(angle)
A line's slope equals the tangent of its angle with the horizontal. A 45° line has slope = TAN(45°) = 1.
Undefined at 90°
TAN is undefined at 90° (and 270°, etc.) because COS is zero there. Results near these angles will be extremely large numbers.
Surveying applications
Height = distance × TAN(elevation_angle). Distance = height / TAN(elevation_angle). These are the basic surveying formulas.
Try TAN in Viztab
Import your data and use TAN with 370+ other formulas. No signup required.
Open Viztab