Angle Converter
Convert any angle unit quickly and accurately. Whether you need to convert degrees to radians, minutes to seconds, or revolutions to gradians, our tool gives you instant results, clear explanations, and helpful tables – all in one place.
How to Use the Angle Converter
- Enter the value you want to convert.
- Select the original unit (From) and the target unit (To).
- See the result instantly, along with a human-readable explanation.
This tool supports all major angle units: degree, radian, gradian, minute, second, revolution, and more.
Popular Angle Conversions
| From | To | Formula |
|---|---|---|
| Degrees (°) | Radians (rad) | ° × π / 180 |
| Radians (rad) | Degrees (°) | rad × 180 / π |
| Degrees (°) | Gradians (grad) | ° × 1.11111 |
| Degrees (°) | Minutes (') | ° × 60 |
| Minutes (') | Seconds (") | ' × 60 |
| Revolutions (r) | Degrees (°) | r × 360 |
Angle Units Explained
What is a Degree?
The degree (°) is a unit of angle equal to 1/360 of a full rotation.
What is a Radian?
A radian (rad) is the SI unit of angle, defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
What is a Gradian?
A gradian (grad or gon) is a unit of angle where 100 gradians is a right angle, so a full circle is 400 gradians.
What are Minutes and Seconds?
Minutes (') and seconds (") are subdivisions of a degree. 1 degree = 60 minutes, 1 minute = 60 seconds.
What is a Revolution?
A revolution (r), circle, or turn is a complete rotation, equal to 360 degrees or 2π radians.
FAQ – Angle Conversion
- What is the use of radians in mathematics?
- Radians are commonly used in mathematics and physics because they provide a natural way to relate angles to arc lengths and are essential in trigonometric functions and calculus.
- How do I convert between degrees, minutes, and seconds?
- To convert degrees to minutes, multiply by 60. To convert minutes to seconds, multiply by 60. To convert back, divide accordingly.
- Why are there 360 degrees in a circle?
- The division of a circle into 360 degrees dates back to ancient Babylonian astronomy, likely because 360 is easily divisible by many numbers.
- What is a right angle and how is it measured?
- A right angle is an angle of 90 degrees, π/2 radians, or 100 gradians. It is the angle of a perfect corner in geometry.
- What is a sextant used for?
- A sextant is a navigational instrument used to measure the angle between two visible objects, commonly used in celestial navigation.
- What are practical applications of angle conversions?
- Angle conversions are used in navigation, engineering, astronomy, surveying, and many fields where precise measurement of rotation or direction is required.