Machining
Online angle converter
Convert angles between decimal format and DMS (degrees °, minutes ′, seconds ″) — handy for CNC programming and checking part geometry.
Angle calculator
Convert DMS, decimal degrees and radians. Result is shown to 4 decimal places.
Decimal degrees (DD.DDDD°)
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📊 Mathematical basis
An angle in decimal degrees (DD), minutes (MM) and seconds (SS) follows the DMS standard. A radian (rad) is the angle whose arc length equals the circle radius. The result is rounded to 4 decimal places.
Conversion formulas
- DMS → decimal degrees
DD = D + MM / 60 + SS / 3600
Constraints: 0 ≤ MM < 60, 0 ≤ SS < 60
- Decimal degrees → radians
rad = DD × π / 180
- Radians → decimal degrees
DD = rad × 180 / π
Reference values
| Quantity | Value |
|---|---|
| π (pi) | 3.1415926535… |
| 1° in radians | π / 180 ≈ 0.0174533 rad |
| 1 rad in degrees | 180 / π ≈ 57.2958° |
Example: 48° 30′ 15″ → 48 + 30/60 + 15/3600 = 48.5042° → 48.5042 × π/180 ≈ 0.8466 rad.
Frequently asked questions
What is DMS angle format?
DMS (Degrees, Minutes, Seconds) writes an angle as degrees, minutes and seconds, e.g. 45°30′15″. It is common on drawings and when entering angles into CNC posts by hand.
Why convert angles for CNC?
Coordinate systems and CAM tools prefer decimal degrees, while drawings may use DMS. The converter helps verify values before programming.