rad = deg * π / 180
deg = rad * 180 / π
grad = deg * 200 / 180
deg = Sexagesimal degree
rad = Radian
grad = Centesimal degree
π = 3.1415926535
Convert between degrees-minutes-seconds (DMS), decimal degrees, radians, and grads. Ideal for GIS, navigation, mathematics, engineering, and astronomy. Supports real-time bidirectional conversion with high precision.
| Unit | Full Name | Relation to Degree (°) |
|---|---|---|
| DMS | Degrees-Minutes-Seconds | 1° = 60′, 1′ = 60″ Example: `90° 20′ 30″ = 90 + 20/60 + 30/3600 ≈ 90.3417°` |
| Decimal Degree | Decimal Degrees | 1° = 1° (direct representation) |
| Rad | Radian | 1 rad = 180° / π ≈ 57.2958° 1° = π / 180 ≈ 0.017453 rad |
| Grad | Grad (or Gon) | 1 grad = 0.9° 1° = 100 centesimal minutes 1 grad = 100 centesimal seconds Example: `100 grad = 90°` |
DMS → Decimal Degrees:
Decimal° = Degrees + Minutes/60 + Seconds/3600
Decimal Degrees → Radians:
rad = ° × π / 180
Radians → Decimal Degrees:
° = rad × 180 / π
Decimal Degrees → Grads:
grad = ° × 100 / 90 = ° × 1.111...
Grads → Decimal Degrees:
° = grad × 0.9
Input: `90° 20′ 30″`
Calculation:
90 + 20/60 + 30/3600 = 90 + 0.3333 + 0.008333 ≈ 90.3417°
Input: `90.3417°`
Calculation:
90.3417 × π / 180 ≈ 1.5768 rad
Input: `π/2 rad ≈ 1.5708 rad`
Step 1: Convert to degrees: 1.5708 × 180 / π ≈ 90°
Step 2: Convert to grads: 90° × 100 / 90 = 100 grad
So: `π/2 rad = 100 grad`
Input: `123.4 grad`
Step 1: Convert to degrees: 123.4 × 0.9 = 111.06°
Step 2: Convert to DMS:
- Degrees: 111°
- Minutes: 0.06 × 60 = 3.6′ → 3′ 36″
Result: 111° 3′ 36″
| Degrees | Radians | Grads |
|---|---|---|
| 0° | 0 | 0 |
| 15° | π/12 | 16.66 |
| 30° | π/6 | 33.33 |
| 45° | π/4 | 50 |
| 60° | π/3 | 66.66 |
| 90° | π/2 | 100 |
| 180° | π | 200 |
| 360° | 2π | 400 |
Geographic Information Systems (GIS) and map coordinates — converting latitude/longitude from DMS to decimal
Navigation and aviation positioning — GPS data often uses decimal degrees
Mathematics education and trigonometric calculations — teaching students how to convert between systems
Robotics motion control — angular position sensors may output in radians or degrees
Astronomy and timekeeping — celestial coordinates use DMS format
Engineering drawing and mechanical design — CAD software may require specific angle formats
ISO 19111: Geographic information — Spatial reference systems
WGS84: World Geodetic System 1984 (used by GPS)
IEC 60050: International Electrotechnical Vocabulary
Textbooks: "Calculus" by James Stewart, "Surveying Principles and Applications" by Charles D. Ghilani
Every unit pair works both ways using mathematically inverse formulas, and results update instantly as you type — no calculate button or page reload is needed.
Free online converter for four angle formats: DMS, decimal degrees, radians and grads, with real-time bidirectional conversion and high precision.
One full circle is:
360° in degrees
2π radians ≈ 6.2832 rad
400 grads
So:
1 rad = 180° / π ≈ 57.2958°
1° = π / 180 ≈ 0.017453 rad
Key values: 90° = π/2 rad, 180° = π rad.
Use radians in formulas and programming, degrees in daily work — the tool converts both instantly.
Login
