Degrees to Radians

Analytical Trigonometry & Radians Standards

A Radian (rad) is the SI unit of angular measure, defined as the angle subtended at the center of a circle by an arc equal in length to the circle's radius.

Primary Unit Circle Angle Equivalents

• 0^: = 0 rad

• 30^: = (π) / (6) rad ≈ 0.5236 rad

• 45^: = (π) / (4) rad ≈ 0.7854 rad

• 60^: = (π) / (3) rad ≈ 1.0472 rad

• 90^: = (π) / (2) rad ≈ 1.5708 rad

• 180^: = π rad ≈ 3.14159 rad

• 270^: = (3π) / (2) rad ≈ 4.7124 rad

• 360^: = 2π rad ≈ 6.28318 rad

• 1 Radian: = (180^) / (π) ≈ 57.29578^

How to Use This Calculator

Enter your Angle Value to Convert (e.g. 45.0) and Conversion Direction — choose from Degrees to Radians (° → rad / multiply by π/180), Radians to Degrees (rad → ° / multiply by 180/π). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Formula Reference: Degrees to Radians

Input variables:

angleValue — Angle Value to Convert

conversionDirectionSelect — Conversion Direction

Computed outputs:

convertedAngle — Converted Angle

equivalentRadians — Angle in Radians (rad)

piFractionRepresentation — Exact π Multiple

equivalentDegrees — Angle in Degrees (°)

equivalentGradians — Angle in Gradians (grad)

Mathematical relationships extracted from calculation logic:

rad = (val * Math.PI) / 180.0

deg = (val * 180.0) / Math.PI

grad = deg * (10.0 / 9.0)

mrad = rad * 1000.0

num = Math.round(degrees * 10000)

den = 180 * 10000

rNum = num / g

rDen = den / g

Standard: NIST Handbook 44 and BIPM SI unit definitions

Worked Example

A 45-degree angle corresponds to exactly π/4 radians (0.7854 rad) in unit circle geometry, representing a diagonal bisector in the first Cartesian quadrant.

Understanding Your Result

Unit conversion precision: round to the same number of significant figures as your original measurement. Converting 6 feet to meters gives 1.8288 m — but if your measurement was approximate (±1 inch), expressing more than 2 decimal places is false precision. For international trade and technical specifications, SI units (meters, kilograms, liters) are the standard. US customary units (feet, pounds, gallons) differ from Imperial UK units: 1 US gallon = 3.785 L vs. 1 UK gallon = 4.546 L.