Free tool
Angle & bearing converter
Convert an angle between decimal degrees, DMS, gradians, NATO mils and radians, and between azimuths and quadrantal bearings — all computed in your browser.
Angle converter
| Unit | Value | Copy |
|---|---|---|
| Decimal degrees | 45 | |
| Degrees · minutes · seconds | 45° 0' 0.00" | |
| Gradians (gon) | 50 | |
| Mils (NATO) | 800 | |
| Radians | 0.78539816 |
Bearing ↔ azimuth
Azimuth is a whole-circle direction (0–360°) from north; a quadrantal bearing is measured 0–90° from the N–S axis (e.g. N30E).
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FAQ
- How do I convert between DMS and decimal degrees?
- One degree is 60 minutes and one minute is 60 seconds, so 30° 15′ 20″ = 30 + 15/60 + 20/3600 ≈ 30.2556°. Pick “Degrees · minutes · seconds” as the input unit and type the value (the converter accepts Arabic numerals and either ° ′ ″ symbols or plain spaces); the decimal degrees and the other units appear instantly.
- What are gradians (gon) and NATO mils?
- A gradian (gon) divides the circle into 400 units instead of 360, so a right angle is 100 gon; it is used in European surveying and some total stations. A NATO mil divides the circle into 6400 units and is used in artillery and the military because it approximates a milliradian (1 mil ≈ 1 metre at 1000 metres range).
- What is the difference between a bearing and an azimuth?
- An azimuth is a whole-circle direction measured 0–360° clockwise from north. A quadrantal bearing is measured 0–90° from the nearer end of the N–S axis with the quadrant named, e.g. N30E (30° east of north = azimuth 30°) or S45W (= azimuth 225°). The lower panel converts both ways and also accepts Arabic ش/ج/ق/غ letters.
- Why radians?
- The radian is the natural unit for computation: a full circle is 2π radians and a right angle is π/2. Trigonometric functions in code (JavaScript, Python) expect radians, not degrees, so we surface a copy-ready radian value for coordinate maths and instrument setup.
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