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Angle Converter
Input Format
Formula Reference
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DD ↔ DMS (Degrees Minutes Seconds)
DD to DMS
d = ⌊DD⌋   m = ⌊(DD − d) × 60⌋   s = ((DD − d) × 60 − m) × 60
Extract integer degrees, convert the fractional degree to minutes, then the fractional minute to seconds.
DMS to DD
DD = d + m / 60 + s / 3600
Sum degrees, minutes converted to fractions of a degree, and seconds as a fraction.
DD ↔ Compact DMS
Compact DMS format
value = DD.MMSS    e.g. 45.4530 = 45° 45′ 30″
The integer part is degrees. The first two decimal digits are minutes. The next two are seconds. Both digit pairs must be 00–59.
Compact to DD
d = trunc(value)   m = trunc(frac × 100)   s = (frac × 10000) mod 100
Isolate the minute and second digit pairs by scaling the fractional part. Then apply DD = d + m/60 + s/3600.
DD to Compact
compact = d + pad(m) / 100 + pad(s) / 10000
Compute DMS from DD, then reassemble with zero-padded two-digit m and s (e.g. 45° 5' 3" → 45.0503).
DD ↔ Radians
Degrees to Radians
rad = DD × (π / 180)
Multiply decimal degrees by π/180. One full rotation = 2π ≈ 6.2832 radians.
Radians to Degrees
DD = rad × (180 / π)
Inverse of the above. Multiply radians by 180/π.
Key radian values
0° = 0   90° ≈ 1.5708   180° = π   270° ≈ 4.7124   360° = 2π
Common reference angles in radians.
DD ↔ Grads / Gon
Degrees to Grads
grad = DD × (400 / 360) = DD × 10 / 9
There are 400 grads in a full circle. Used in European surveying and engineering.
Grads to Degrees
DD = grad × (360 / 400) = grad × 0.9
Inverse. Multiply grads by 0.9 to get decimal degrees.
Key grad values
0° = 0   90° = 100   180° = 200   270° = 300   360° = 400 grad
Quarter-circle = 100 grad — the defining property of the grad system.
Quadrant Bearing ↔ Azimuth (DD)
Azimuth to Bearing — NE quadrant (0°–90°)
N [Az]° E
Azimuth equals the bearing angle measured from North toward East.
Azimuth to Bearing — SE quadrant (90°–180°)
S [180 − Az]° E
Bearing angle = 180° minus the azimuth.
Azimuth to Bearing — SW quadrant (180°–270°)
S [Az − 180°]° W
Bearing angle = azimuth minus 180°.
Azimuth to Bearing — NW quadrant (270°–360°)
N [360 − Az]° W
Bearing angle = 360° minus the azimuth.
Bearing to Azimuth
NθE → Az=θ   SθE → Az=180−θ   SθW → Az=180+θ   NθW → Az=360−θ
θ is always positive and 0–90°. Cardinals: N=0°, E=90°, S=180°, W=270°.