Converting Angle
Convert between degrees, radians, gradians, and other angle units.
Table of Contents
Angle Converter
Angle Conversion Charts
Degrees to Radians
Conversion factor: 1° = 0.0174533 radians
| Degrees (°) | Radians (rad) |
|---|---|
| 1 | 0.01745 |
| 5 | 0.08727 |
| 10 | 0.17453 |
| 45 | 0.78540 |
| 90 | 1.57080 |
| 180 | 3.14159 |
Example: 45° × 0.0174533 ≈ 0.7854 rad
Degrees to Gradians (Gons)
Conversion factor: 1° ≈ 1.11111 gradians. For instance 90° × 1.11111 ≈ 100 gon
| Degrees (°) | Gradians (gon) |
|---|---|
| 1 | 1.11111 |
| 5 | 5.55556 |
| 10 | 11.11111 |
| 45 | 50 |
| 90 | 100 |
| 180 | 200 |
Degrees to Arcminutes
Conversion factor: 1° = 60 arcminutes. Example: 10° × 60 = 600'
| Degrees (°) | Arcminutes (') |
|---|---|
| 1 | 60 |
| 5 | 300 |
| 10 | 600 |
| 45 | 2700 |
| 90 | 5400 |
| 180 | 10800 |
Degrees to Arcseconds
Conversion factor: 1° = 3600 arcseconds. Example: 5° × 3600 = 18000"
| Degrees (°) | Arcseconds (") |
|---|---|
| 1 | 3600 |
| 5 | 18000 |
| 10 | 36000 |
| 45 | 162000 |
| 90 | 324000 |
| 180 | 648000 |
Degrees to Mil
Using a full circle divided into 6400 mils, 1° ≈ 17.7778 mil. Example: 10° × 17.7778 ≈ 177.78 mil
| Degrees (°) | Mil (mil) |
|---|---|
| 1 | 17.78 |
| 5 | 88.89 |
| 10 | 177.78 |
| 45 | 800 |
| 90 | 1600 |
| 180 | 3200 |
Additional Informations
Angular Units
- Degree (°):This is the fundamental unit for angular measurement. All other units are defined relative to one degree.
- Radian:Defined as π/180 radians per degree, 1° is approximately 0.017453292519943 radians. Radians are extensively used in mathematics, physics, trigonometry, and calculus.
- Grad (Gradian) / Gon:Since a full circle is 400 gradians, 1° is roughly 1.1111111111111 gradians. This unit is popular in engineering and surveying.
- Minute (Arcminute):One degree is divided into 60 arcminutes, providing a finer subdivision for precise measurements.
- Second (Arcsecond):Each arcminute contains 60 arcseconds, so 1° equals 3600 arcseconds.
- Sign:In astrology, the zodiac is divided into 12 signs of 30° each, meaning 1° is equivalent to 1/30 (≈0.033333333333333) of a sign.
- Mil:Often used in military and engineering applications, where a full circle is divided into 6400 mils, 1° is approximately 17.777777777778 mils.
- Revolution / Circle / Turn: A complete rotation is 360°, so 1° equals 1/360 (≈0.0027777777778) of a revolution.
- Quadrant / Right Angle: A quadrant (or right angle) measures 90°, making 1° equal to 1/90 (≈0.0111111111111) of a quadrant.
- Sextant: Defined such that 1 sextant equals 60°, 1° represents about 1/60 (≈0.0166666666667) of a sextant.
Practical Applications and Usefulness
Angle conversion tool is essential across various fields:
- Engineering & Navigation: Precise radian and mil conversions are critical in design, construction, and military applications.
- Astronomy & Surveying: Conversions involving gradians, arcminutes, and arcseconds support accurate positional measurements.
- Education & Research: By demonstrating how each unit relates to a degree, our tool serves as an excellent resource for understanding angular measurements.
- Everyday Calculations: Whether adjusting angles in computer graphics or construction projects, our conversion factors ensure reliable results.