How do I convert degrees to radians?

To convert degrees to radians, multiply by π/180 (approximately 0.0174533). For example, 180° × π/180 = π radians = 3.1416 rad. 90° = π/2 rad, 360° = 2π rad.

What is the formula for degrees to radians?

radians = degrees × (π / 180). Since 180° = π radians, multiply degrees by π/180 to get radians. In code: Math.PI / 180. 1 radian ≈ 57.2958 degrees.

How many radians is 1 degree?

1° = 0.0174533 radians = π/180 rad. This is a very small angle. At a distance of 1 m, 1° spans about 1.75 cm. One degree is 1/360 of a full circle.

How many degrees is 1 radian?

1 radian = 57.2958° (approximately 57.3°). One radian is the angle where the arc length equals the radius. A full circle = 2π rad = 6.2832 rad = 360°.

> >Degrees to Radians Converter

Degrees to Radians Converter

Convert degrees (°) to radians (rad) with this easy-to-use angle converter.

Degrees

Related Tools

External Resources

Wikipedia: Degree (angle)Wikipedia: Radian NIST: Metric System

Frequently Asked Questions

How do I convert degrees to radians?: To convert degrees to radians, multiply by π/180 (approximately 0.0174533). For example, 180° × π/180 = π radians = 3.1416 rad. 90° = π/2 rad, 360° = 2π rad.
What is the formula for degrees to radians?: radians = degrees × (π / 180). Since 180° = π radians, multiply degrees by π/180 to get radians. In code: Math.PI / 180. 1 radian ≈ 57.2958 degrees.
How many radians is 1 degree?: 1° = 0.0174533 radians = π/180 rad. This is a very small angle. At a distance of 1 m, 1° spans about 1.75 cm. One degree is 1/360 of a full circle.
How many degrees is 1 radian?: 1 radian = 57.2958° (approximately 57.3°). One radian is the angle where the arc length equals the radius. A full circle = 2π rad = 6.2832 rad = 360°.
What is a radian?: A radian is the SI unit for measuring angles. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. There are 2π radians in a full circle. Radians are "natural" angular units in mathematics.
Why are radians used instead of degrees?: Radians simplify calculus and trigonometry formulas. Derivatives of sin(x) and cos(x) are clean only in radians. Arc length = rθ (θ in radians). Area of sector = ½r²θ. Most math libraries (JavaScript Math, Python math) use radians.
How do I convert degrees to radians in JavaScript?: Use: radians = degrees * Math.PI / 180. Example: Math.sin(90 * Math.PI / 180) = 1. To convert back: degrees = radians * 180 / Math.PI. JS Math functions all use radians.
What is the degrees to radians conversion for 90 degrees?: 90° = π/2 rad = 1.5708 rad. This is a right angle. Common in geometry: 90° rotation, perpendicular lines, square corners. The sine of 90° in radians: sin(π/2) = 1.
What is the degrees to radians conversion for 45 degrees?: 45° = π/4 rad = 0.7854 rad. This is half of a right angle. Used in isometric projections, 45° angles in geometry, and trigonometric values: sin(45°) = cos(45°) = √2/2 ≈ 0.7071.
How do I memorize common degree to radian conversions?: 0° = 0 rad, 30° = π/6 rad, 45° = π/4 rad, 60° = π/3 rad, 90° = π/2 rad, 120° = 2π/3 rad, 135° = 3π/4 rad, 150° = 5π/6 rad, 180° = π rad, 270° = 3π/2 rad, 360° = 2π rad. These cover the unit circle.
What is the degrees to radians conversion for 30 degrees?: 30° = π/6 rad = 0.5236 rad. Common angles: sin(30°) = 0.5, cos(30°) = √3/2 ≈ 0.8660. A 30-60-90 triangle has sides in ratio 1:√3:2.
How do I convert degrees to radians for GPS coordinates?: GPS coordinates are in degrees (±90° latitude, ±180° longitude). For distance calculations (haversine formula), convert to radians first. Earth radius ~6,371 km. 1° latitude ≈ 111 km.
What is the difference between degrees and radians?: Degrees: 360° in a circle, subdivision: minutes (') and seconds ("). Radians: 2π in a circle, no sub-units. Degrees are convenient for everyday use. Radians are essential for calculus, physics, and engineering.
What is the degrees to radians conversion for 180 degrees?: 180° = π rad = 3.1416 rad. This is a straight line angle (half circle). The famous identity: e^(iπ) + 1 = 0 (Euler's identity). sin(π) = 0, cos(π) = -1.
How do I convert degrees to radians for trigonometric calculations?: Trig in radians: sin(x) ≈ x for small x (in radians). Period of sin/cos = 2π. sin(π/2) = 1, sin(π) = 0, sin(3π/2) = -1. Always check if your calculator or programming language expects degrees or radians.
What is the degrees to radians conversion for 60 degrees?: 60° = π/3 rad = 1.0472 rad. Common: sin(60°) = √3/2 ≈ 0.8660, cos(60°) = 0.5. An equilateral triangle has all angles 60°. A 30-60-90 triangle uses this angle.
How do I convert degrees to radians for rotation calculations?: In computer graphics: rotation = degrees × π/180. CSS transforms: rotate(45deg) vs JS Math functions using radians. Game engines (Unity, Unreal) use degrees for UI but convert internally to radians for physics.
What is the degrees to radians conversion for 360 degrees?: 360° = 2π rad = 6.2832 rad. Full circle. 2π is a fundamental constant appearing in physics: angular frequency ω = 2πf, wave number k = 2π/λ, etc.
How do I convert degrees to radians for physics problems?: Physics equations use radians: angular displacement θ (rad), angular velocity ω (rad/s), angular acceleration α (rad/s²). Centripetal acceleration: a = ω²r. Torque: τ = rF sin(θ). All in radians.
What is the degrees to radians conversion for 270 degrees?: 270° = 3π/2 rad = 4.7124 rad. Three-quarters of a circle. sin(270°) = -1, cos(270°) = 0. Used in 3D rotations and phasor diagrams.
How do I convert degrees to radians for navigation?: Navigation: bearings in degrees (0-360°, 0 = North). For great-circle calculations, convert to radians. Rhumb lines, Mercator projections use radians in formulas. Haversine: haversin(θ) = sin²(θ/2).
What is the history of the degree and radian?: Degrees (from Babylonians, base-60 system): 360° ≈ days in a year, 60 minutes per degree. Radians were introduced by Roger Cotes in the 1700s and popularized by Leonhard Euler for their mathematical naturalness.
What is the degrees to radians conversion for 120 degrees?: 120° = 2π/3 rad = 2.0944 rad. Used in equilateral triangle angles (each 60°, but 120° is the external angle). Also in hexagonal geometry and 3-phase electrical systems (120° phase shift).
How do I convert degrees to radians for Unity/Unreal?: Unity C#: Mathf.Deg2Rad constant. Mathf.Sin(angle * Mathf.Deg2Rad). Unreal Blueprints: "Degrees to Radians" node. Unreal C++: FMath::DegreesToRadians(). Both use radians internally for physics.
What is the degrees to radians conversion for 20 degrees?: 20° = π/9 rad = 0.3491 rad. Common in geometry: regular nonagon (9 sides, central angle 40°, exterior 20°). Also a typical camera field of view for telephoto lenses.
How do I convert angular degrees to radians for the sky?: Astronomy: angular size in degrees. Moon/Sun ≈ 0.5° = 0.00873 rad. 1° = 60 arcminutes, 1 arcminute = 60 arcseconds. Small-angle approximation: angular size (rad) ≈ actual size / distance.
What is the degrees to radians conversion for 15 degrees?: 15° = π/12 rad = 0.2618 rad. Common in geometry: 15° is 1/24 of a circle. Used in clock face angles: 1 hour = 30°, so 30 minutes = 15°. Also common in drafting and CAD.
How do I convert degrees to radians in Python?: Python: import math; radians = math.radians(degrees). Or manually: radians = degrees * math.pi / 180. NumPy: numpy.deg2rad(array). Math functions like math.sin() expect radians.
What is the degrees to radians conversion for 10 degrees?: 10° = π/18 rad = 0.1745 rad. Common in camera angles for wide-angle lenses (10-24 mm gives ~100-120° diagonal FOV). Also used in surveying for small angle measurements.
How do I use the degree to radian conversion for sine/cosine?: Example: sin(30°) = sin(π/6) = 0.5. In JS: Math.sin(30 * Math.PI / 180). In Python: math.sin(math.radians(30)). Most scientific calculators have a DEG/RAD mode switch.
What is the degrees to radians conversion for 75 degrees?: 75° = 5π/12 rad = 1.3090 rad. 75° is 15° less than 90. sin(75°) = (√6 + √2)/4 ≈ 0.9659. Not a standard unit circle angle but useful in surveying and navigation.