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How to Use
- Enter the angle value
Type the angle value you want to convert.
- Select the units
Choose the source unit and the target unit for conversion.
- View the result
Click Convert to see the converted angle value.
What are angle units?
An angle describes how far two lines or planes spread apart at a single point, and several angle units express the same amount of rotation using different references. The most familiar one, the degree (°), divides a full circle into 360 parts, while the radian defines the central angle of an arc whose length equals the radius as 1, making a full turn 2π.
The gradian is a surveying unit that splits a right angle into 100 parts, and the turn counts one full revolution as 1. Which unit is used to express the same rotation depends on the field.
- Radians are the standard in trigonometry and calculus in math and physics
- Degrees are intuitive for everyday use, drafting, and CAD
- Gradians are convenient for calculations in civil engineering and surveying
Calculation Formula
This is a two-step method that first converts every angle into the base unit, the degree, and then divides by the target unit.
result = value × (degree factor of the source unit) / (degree factor of the target unit)
Key conversion factors: degree=1, radian=180/π≈57.29578, gradian=0.9, turn=360
Example) 90 degrees to radians: 90 × 1 / 57.29578 = 1.570796 rad (≈ π/2). Conversely, converting 1 rad to degrees gives 1 × 57.29578 / 1 = 57.29578°.