Angle Converter

Convert between degrees, radians, gradians, and other angle units instantly. Essential for mathematics, engineering, surveying, and scientific calculations.

How to Use

  1. Enter the angle value

    Type the angle value you want to convert.

  2. Select the units

    Choose the source unit and the target unit for conversion.

  3. 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°.

Frequently Asked Questions

What is the difference between degrees and radians?
A degree divides a circle into 360 parts, while a radian sets the angle at which the arc length equals the circle's radius (about 57.3 degrees) to 1. 180 degrees equals π radians.
What is a radian?
A radian is an angle unit that defines the central angle of an arc whose length equals the radius as 1 radian. A full circle is 2π radians (about 6.2832 rad), and it is the standard angle unit in mathematics and physics.
What is a gradian?
A gradian divides a right angle into 100 parts, so a full circle is 400 gradians. One gradian equals 0.9 degrees, and it is mainly used in surveying and civil engineering.
How do you convert between degrees and radians?
To convert degrees to radians, multiply by π/180; to convert radians to degrees, multiply by 180/π. For example, 180° = π rad (about 3.14159 rad), and 1 rad ≈ 57.2958°.
What kind of unit is a turn?
A turn counts one full revolution as 1. One turn = 360 degrees = 2π radians = 400 gradians, and it is intuitive when dealing with revolutions or cycles.
Why are radians the standard in mathematics?
Using radians makes the differentiation and integration of trigonometric functions the simplest. For example, the derivative of sin x is cos x only when x is in radians, so radians are the basis for calculus and physics formulas.
Which angle units are supported?
This converter supports degrees, radians, gradians, and turns, converting all values through degrees for interconversion. Results are shown to six decimal places.
How much are 90 and 180 degrees in radians?
90 degrees = π/2 ≈ 1.570796 rad, 180 degrees = π ≈ 3.141593 rad, 270 degrees = 3π/2 ≈ 4.712389 rad, and 360 degrees = 2π ≈ 6.283185 rad. It helps to memorize common angles like right and straight angles as fractions of π.
2026 international standards

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