Angle Converter tool
Angle Unit Converter Tool
An Angle Unit Converter Tool is essential for converting between various units of angle measurement, such as degrees, radians, and gradians. This tool simplifies calculations, making it easier for engineers, scientists, and students to work with different angle units seamlessly. Whether you're working on a complex engineering project or a simple math problem, this converter ensures accuracy and efficiency.
In geometry, angle measurement units are used to quantify the size of an angle, which is the space between two intersecting lines or rays. The most common units of angular measurement are:
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Degrees (°):
- The degree is the most widely used unit for measuring angles. One complete revolution (a full circle) is divided into 360 degrees. Each degree can be further subdivided into 60 minutes (') and each minute into 60 seconds (").
- For example, an angle of 45° means the angle is 45 out of 360 parts of a circle.
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Radians (rad):
- The radian is the standard unit of angular measurement in mathematics and is used primarily in trigonometry and calculus. One radian is the angle created when the arc length of a circle equals the radius of the circle. There are 2π radians in a full circle, which is approximately 6.283 radians.
- A key conversion is that 180° equals π radians. So, 1 radian is approximately 57.3°.
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Gradians (gon or grad):
- The gradian, also known as a gon or grade, is less commonly used but divides a circle into 400 parts. In this system, a right angle is 100 gradians. This unit is sometimes used in surveying and engineering.
- One grad equals 0.9 degrees.
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Turns (or revolutions):
- A turn measures angles in terms of how many complete revolutions a point or line makes. One complete revolution is equal to 360 degrees or 2π radians.
- This unit is useful in certain applications such as mechanical engineering and robotics.
These units are used depending on the field and context, with degrees being most common in everyday use, radians in higher mathematics, and gradians in specific technical fields.
Conversion table for angles:
| Degrees (°) | Radians (rad) | Gradians (gon) | Turns (revolutions) |
|---|---|---|---|
| 0.1° | 0.00175 rad | 0.111 gon | 0.00028 turns |
| 1° | 0.01745 rad | 1 gon | 0.00278 turns |
| 5° | 0.08727 rad | 5 gon | 0.01389 turns |
| 10° | 0.17453 rad | 10 gon | 0.02778 turns |
| 15° | 0.26180 rad | 15 gon | 0.04167 turns |
| 30° | 0.52360 rad | 30 gon | 0.08333 turns |
| 45° | 0.78540 rad | 40 gon | 0.125 turns |
| 60° | 1.04720 rad | 50 gon | 0.16667 turns |
| 90° | 1.57080 rad | 100 gon | 0.250 turns |
| 120° | 2.09440 rad | 150 gon | 0.33333 turns |
| 180° | π rad ≈ 3.14159 rad | 200 gon | 0.500 turns |
| 270° | 4.71239 rad | 300 gon | 0.750 turns |
| 360° | 2π rad ≈ 6.28319 rad | 400 gon | 1 turn |
| 540° | 3π rad ≈ 9.42478 rad | 600 gon | 1.5 turns |
| 720° | 4π rad ≈ 12.56637 rad | 800 gon | 2 turns |
Key Conversion Formulas:
- Degrees to Radians: radians = degrees × (π / 180)
- Radians to Degrees: degrees = radians × (180 / π)
- Degrees to Gradians: gradians = degrees × (10 / 9)
- Gradians to Degrees: degrees = gradians × (9 / 10)
- Degrees to Turns: turns = degrees × (1 / 360)
- Turns to Degrees: degrees = turns × 360
This table covers a range of angles for each unit and should be helpful for various calculations and conversions.