SmartKitio

Angle Converter

Convert angles between degrees, radians, gradians, and full turns. Negative angles are allowed because they describe rotation in the opposite direction.

Formula: multiply the source value by 0.01745329

Quick Conversions

About this tool

Plane angles convert through the radian. A full turn is 2π rad, 360°, or 400 gon.

How to use it

Enter an angle, choose units, and read the converted value. Negative angles are allowed.

value_to = value_from × (from_in_radians / to_in_radians)

Examples

  • 180° to radians

    180 × π / 180 = π rad ≈ 3.1416 rad.

  • 90 ° to rad

    90 × 0.0174533 = 1.5708 rad.

  • 1 rad to °

    1 × 57.2958 = 57.2958 °.

Every unit expressed in radians

UnitEqual to (rad)
1 radian (rad)1
1 degree (°)0.0174532925
1 gradian (gon)0.0157079633
1 turn (turn)6.283185307

FAQ

What is a gradian?
A gon. A right angle is 100 gon, so a full circle is 400 gon.
Are negative angles allowed?
Yes. Direction matters in geometry and navigation.
How many degrees is one radian?
180/π, about 57.2958°. A full circle is 2π radians, 360 degrees, or 400 gradians.