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Angle conversion

°
Description

A tool for converting between common angle units such as degrees-minutes-seconds, decimal degrees, radians, and grads.

This calculator allows you to convert angles between different units used in geography, navigation, mathematics, and engineering. Input one value, and all others are automatically calculated.

Supported Units & Conversion Factors

Unit Full Name Relation to Degree (°)
Sexagesimal degree Degrees-Minutes-Seconds 1° = 60′, 1′ = 60″
Example: `90° 20′ 30″ = 90 + 20/60 + 30/3600 ≈ 90.3417°`
Sexagesimal degree (decimal) Decimal Degrees 1° = 1° (direct representation)
Radian Radian 1 rad = 180° / π ≈ 57.2958°
1° = π / 180 ≈ 0.017453 rad
Centesimal degree Grad (or Gon) 1 grad = 0.9°
1° = 100 centesimal minutes
1 grad = 100 centesimal seconds

Example Calculations

Example 1:
Input: `90° 20′ 30″`
Convert to decimal degrees:
`90 + 20/60 + 30/3600 = 90.3417°`

Example 2:
Input: `90.3417°`
Convert to radians:
`rad = 90.3417 × π / 180 ≈ 1.5768 rad`

Example 3:
Input: `π/2 rad ≈ 1.5708 rad`
Convert to grads:
First to degrees: `1.5708 × 180 / π ≈ 90°`
Then to grads: `90° × 100 / 90 = 100 grad`
So: `π/2 rad = 100 grad`

Example 4:
Input: `123.4 grad`
Convert to degrees: `123.4 × 0.9 = 111.06°`
Then to DMS:
- 111°
- 0.06 × 60 = 3.6′ → 3′ 36″
So: `123.4 grad ≈ 111° 3′ 36″`

Use Cases

  • Geographic Information Systems (GIS) and map coordinates
  • Navigation and aviation positioning
  • Mathematics education and trigonometric calculations
  • Robotics motion control
  • Astronomy and timekeeping
  • Engineering drawing and mechanical design

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