Angle Converter
Instantly convert between Degrees, Radians, Gradians, and Turns.
Essential for trigonometry, engineering, and game development.
Common Use Cases
Game Dev
Convert UI rotation inputs (Degrees) to engine logic (Radians) for Unity or Unreal Engine.
Surveying
Use Gradians (gons) to simplify right-angle calculations in civil engineering and land surveying.
Education
Visualize the relationship between π radians and 180 degrees for trigonometry homework.
Mechanics
Convert "Turns" or RPM to angular velocity (radians per second) for motor control.
Understanding Angle Units
Different fields use different units for measuring angles. This tool helps you bridge the gap.
- Degrees (°): The oldest and most common unit. 1 circle = 360°. Used in navigation, carpentry, and everyday geometry.
- Radians (rad): The standard SI unit. 1 circle = 2π rad. Used in calculus, physics, and computer programming.
- Gradians (grad/gon): metric angle unit. 1 circle = 400 grad. A right angle is exactly 100 grad. Used in surveying.
- Turns (tr): Represents a full cycle. 1 turn = 360°. Used in CSS animations (`rotate(0.5turn)`) and mechanical engineering.
Angle Conversion in Programming
Most programming languages use Radians for trigonometric functions (`sin`, `cos`), while humans prefer Degrees. Here is how to convert them in code.
function degToRad(degrees) {
return degrees * (Math.PI / 180);
}
function radToDeg(radians) {
return radians * (180 / Math.PI);
}
console.log(degToRad(180)); // 3.14159...import math
degrees = 90
radians = math.radians(degrees)
print(radians)
# Output: 1.57079... (pi/2)
back_to_deg = math.degrees(radians)#include <iostream>
#include <cmath>
// M_PI is often defined in cmath
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
double degToRad(double deg) {
return deg * M_PI / 180.0;
}using UnityEngine;
// Unity provides constants
float deg = 180f;
float rad = deg * Mathf.Deg2Rad;
Debug.Log(rad); // 3.141593Frequently Asked Questions
What is a Radian?
A radian is the standard unit of angular measure in mathematics. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius. A full circle is 2π radians (approx 6.283).
What is a Gradian (gon)?
The gradian (also known as gon or grad) divides a right angle into 100 parts, instead of 90. A full circle is 400 gradians. It is mostly used in surveying and mining.
How do I convert Degrees to Radians?
The formula is: Radians = Degrees × (π / 180). Conversely, Degrees = Radians × (180 / π).
What is an Arcminute?
An arcminute (or minute of arc) is 1/60th of a degree. It is used for precise measurements in astronomy and navigation (GPS coordinates).
Why define a full circle as 360 degrees?
Ancient Babylonians used a base-60 number system and roughly 360 days in a year. 360 is highly composite (divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, etc.), making division easy.
Are negative angles possible?
Yes. By convention, positive angles are measured counter-clockwise from the x-axis, while negative angles are measured clockwise.