Angle Converter
Convert angles between degrees, radians, gradians, and DMS (degrees-minutes-seconds). Includes trigonometric values, unit circle diagram, reference angles, arc length, and compass bearing converter.
Quick Calculator Get a fast estimate
Degrees
90°
Radians
1.57079633 rad
Gradians
100 grad
DMS (Degrees Min Sec)
90° 0' 0.00"
sin
1
cos
0
tan
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How to Use the Angle Converter
Select your input unit (degrees, radians, or gradians), enter the angle, and all equivalent values are shown. Trigonometric values (sin, cos, tan) are also displayed.
The Extended Calculator adds a unit circle SVG and full trig function table. The Professional Calculator covers reference angles, arc length, and compass bearings.
Need more detail?
Extended Calculator More options, charts, and scenario comparison
Conversions
45°
Radians
0.785398 rad
Gradians
50 grad
DMS
45° 0' 0"
In π radians
0.25π
Normalised (0–360)
45°
Supplementary angle
135°
Angle Conversion Formulas
Degrees to radians: rad = deg × π / 180
Radians to degrees: deg = rad × 180 / π
Degrees to gradians: grad = deg × 10 / 9
Gradians to degrees: deg = grad × 9 / 10
DMS to decimal: deg = D + M/60 + S/3600
Decimal to DMS: D=floor(deg), M=floor((deg-D)×60), S=((deg-D)×60-M)×60
Common Angle Conversions
| Degrees | Radians | Gradians | sin | cos |
|---|---|---|---|---|
| 0° | 0 | 0 | 0 | 1 |
| 30° | π/6 | 33.33 | 0.5 | √3/2 |
| 45° | π/4 | 50 | √2/2 | √2/2 |
| 60° | π/3 | 66.67 | √3/2 | 0.5 |
| 90° | π/2 | 100 | 1 | 0 |
| 180° | π | 200 | 0 | -1 |
| 270° | 3π/2 | 300 | -1 | 0 |
| 360° | 2π | 400 | 0 | 1 |
Need full precision?
Professional Calculator Complete parameters, sensitivity analysis, and detailed breakdown
Reference Angle
30°
Quadrant
II (90°–180°)
Normalised angle
150°
Co-terminal +360°
510°
Co-terminal −360°
-210°
sin (from ref)
0.5
cos (from ref)
-0.866025
Frequently Asked Questions
Multiply by π/180 (≈0.01745). Key values: 30°=π/6, 45°=π/4, 60°=π/3, 90°=π/2, 180°=π, 360°=2π. Radians are the natural unit — arc length = radius × angle in radians.
Gradians (grads/gons) divide a right angle into 100 equal parts. A full turn = 400 grad. Used in surveying and some European countries. 1 grad = 0.9° = π/200 rad.
The acute angle (<90°) between the terminal ray and the x-axis. For 150° (Q2): reference = 180°−150°=30°. For 210° (Q3): reference=210°−180°=30°. Trig functions equal those of the reference angle (with sign from quadrant).
Add degrees + minutes÷60 + seconds÷3600. Example: 52° 14' 36" = 52 + 14/60 + 36/3600 = 52.2433°. Used in GPS coordinates (latitude/longitude).
Compass bearing: 0°=North, increases clockwise. Math angle: 0°=East (right), increases anticlockwise. Convert: math = 90° − bearing. North bearing 0° = math angle 90°.