Math
DEGREES function: convert radian outputs from ATAN, ASIN, and ACOS into degrees
Turn radian arc values and inverse-trigonometric results into readable degree angles using DEGREES.
Make inverse trigonometry human-readable
Inverse trigonometric functions such as ATAN, ASIN, and ACOS—as well as arc-length formulas angle = arc / radius—return angles in radians. DEGREES(angle) multiplies by 180 / PI() so a quarter-circle (PI()/2 ≈ 1.570796 rad) displays as 90 degrees.
For example, a ramp that rises 1 meter over a 1-meter horizontal run has ATAN(1/1) = 0.785398 radians; wrapping it in DEGREES(ATAN(1/1)) returns 45.
| Radian Input | Formula | Degrees |
|---|---|---|
| 0 | =DEGREES(0) | 0 |
| PI()/4 (0.785398) | =DEGREES(ATAN(1)) | 45 |
| PI()/2 (1.570796) | =DEGREES(PI()/2) | 90 |
| PI() (3.141593) | =DEGREES(PI()) | 180 |
| -PI()/6 (-0.523599) | =ROUND(DEGREES(-PI()/6), 4) | -30 |
Convert curved track arc angle to degrees
On a circular bend with radius B2 = 50 m and arc length A2 = 25 m, central angle in radians is A2 / B2 = 0.5 rad, which DEGREES converts to 28.6479°.
=ROUND(DEGREES(A2 / B2), 4)Guard zero radius and preserve negative angles
DEGREES preserves negative signs for counter-rotation (-28.6479°). When angle comes from a ratio A2 / B2, check B2<=0 before dividing so a zero radius returns a clear message instead of dividing by zero.
=IF(B2<=0, "Check radius", ROUND(DEGREES(A2 / B2), 4))Try the example
Use the original values or change them to test your understanding.