How do I convert radians to degrees?

Formula : degrees = radians × (180/π) = radians × 57.2958 Examples : 1 rad = 57.3° π/2 rad = 90° π rad = 180° 2π rad = 360° Radians to Degrees converter →

How many radians in 180 degrees?

180° = π radians ≈ 3.14159 radians This is the fundamental relationship between degrees and radians.

Why use radians instead of degrees?

Mathematical simplicity : d/dx[sin(x)] = cos(x) ONLY when x is in radians. Arc length = radius × angle (in radians). Taylor series formulas simpler with radians. Physics : Natural unit for rotational motion and oscillations.

Radian (rad) - Unit Information & Conversion

Symbol:rad

Plural:radians

Category:Angle

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What is a Radian?

The radian is the SI unit of angle, defined by the radius of a circle. Used in mathematics, physics, and engineering for trigonometry, calculus, and angular measurements.

History of the Radian

First used by Roger Cotes in 1714, formally named "radian" by James Thomson in 1873. Adopted as SI unit in 1960. Natural unit for mathematical analysis.

Quick Answer

What is a Radian? A radian (rad) is the SI unit of angle equal to the angle subtended by an arc length equal to the radius. π radians = 180°, 2π radians = 360° (full circle). Essential for calculus and physics. Use our angle converter to convert radians to degrees and other units instantly.

Quick Comparison Table

Radians	Degrees	Context	Convert Now
0	0°	Zero angle	rad to ° →
π/6 ≈ 0.524	30°	Common angle	rad to ° →
π/4 ≈ 0.785	45°	Diagonal	rad to ° →
π/3 ≈ 1.047	60°	Equilateral triangle	rad to ° →
π/2 ≈ 1.571	90°	Right angle	rad to ° →
π ≈ 3.142	180°	Straight angle	rad to ° →
2π ≈ 6.283	360°	Full circle	rad to ° →

Definition

A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. 1 radian ≈ 57.2958 degrees.

Key values:

π radians = 180°
2π radians = 360°
1 radian = 180/π ≈ 57.296°

Common Uses

Mathematics: Required unit for calculus (derivatives, integrals of trig functions).

Physics: Angular velocity (rad/s), rotational motion, oscillations.

Engineering: Computer graphics, robotics, signal processing.

Programming: Most programming languages use radians for trig functions.

Radian Conversion Formulas

To Degree:

1 rad = 57.29578 °

Example: 5 radians = 286.478898 degrees

To Gradian:

1 rad = 63.661977 grad

Example: 5 radians = 318.309886 gradians

To Arcminute:

1 rad = 3437.746771 ′

Example: 5 radians = 17188.733854 arcminutes

To Arcsecond:

1 rad = 206264.806247 ″

Example: 5 radians = 1031324.031235 arcseconds

To Turn:

1 rad = 0.159155 turn

Example: 5 radians = 0.795775 turns

To Revolution:

1 rad = 0.159155 rev

Example: 5 radians = 0.795775 revolutions

To Quadrant:

1 rad = 0.63662 quad

Example: 5 radians = 3.183099 quadrants

To Gon:

1 rad = 63.661977 gon

Example: 5 radians = 318.309886 gons

To Mil:

1 rad = 1018.591636 mil

Example: 5 radians = 5092.958179 mils

Frequently Asked Questions

Formula: degrees = radians × (180/π) = radians × 57.2958 Examples:

1 rad = 57.3°
π/2 rad = 90°
π rad = 180°
2π rad = 360° Radians to Degrees converter →

Convert Radian

Need to convert Radian to other angle units? Use our conversion tool.

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