Angle Converter
Convert between degrees, radians and grads, and between decimal degrees and DMS (degrees-minutes-seconds).
Input Data
Results
At a glance:Base is degrees: π rad = 180°, 1 rad = 180/π ≈ 57.29578°; 1 grad = 0.9° (400 grad = 360°). DMS: 1° = 60′, 1′ = 60″; decimal degree d = D + M/60 + S/3600, and reverse by taking the integer part as degrees, the remainder×60 integer as minutes, and the rest×60 as seconds.
Formula
rad = deg × π/180; grad = deg / 0.9.
DMS → deg: deg = D + M/60 + S/3600.
How to Use
- Simple mode: enter a value and pick from/to units.
- DMS mode: enter decimal degrees to get a DMS string (or enter DMS parts to get decimal degrees).
Case Studies
180° → rad
180 × π/180 = π ≈ 3.141593 rad.
45.5° → DMS
45° + 0.5×60 = 30′ → 45°30′0″.
FAQ
Why use radians?
Trigonometry and calculus use radians; for example the derivative of sin(x) is cos(x) only in radians.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.