RealConversionTools
RealConversionTools
Angle Converter

Degree to Radian Converter

Convert Degree (°) to Radian (rad) instantly with our interactive tool, benchmark tables, and detailed unit information.

1 ° = 0.0175 rad
Editable
°
Input
Auto-Calculated
rad
Result
Angle conversion — instant results

Convert Degree to Radian

1 ° = 0.0175 rad
Degree (°) Radian (rad)
1 ° 0.017453 rad
5 ° 0.087266 rad
10 ° 0.174533 rad
25 ° 0.436332 rad
50 ° 0.872665 rad
100 ° 1.745329 rad
500 ° 8.726646 rad
1,000 ° 17.453293 rad

Convert Radian to Degree

1 rad = 57.2958 °
Radian (rad) Degree (°)
1 rad 57.29578 °
5 rad 286.478898 °
10 rad 572.957795 °
25 rad 1,432.394488 °
50 rad 2,864.788976 °
100 rad 5,729.577951 °
500 rad 28,647.889757 °
1,000 rad 57,295.779513 °

About Degree and Radian

Detailed information about both units of measurement.

ANGULAR UNIT

Degree

°
Definition
The most common angular unit. A full circle is divided into 360 equal parts called degrees.
SI / Standard Information
Not an SI unit but widely used. The 360-degree system originates from ancient Babylonian astronomy and their base-60 number system.
Approximate Comparison
One degree is about the width of a little finger held at arm's length.
Practical Applications
  • Navigation and GPS coordinates
  • Engineering and construction angles
  • Geometry and mathematics education
  • Compass and direction measurement
Real-World Examples
  • A right angle is 90 degrees
  • The Earth's axis is tilted at 23.5 degrees
  • A triangle's interior angles sum to 180 degrees
ANGULAR UNIT

Radian

rad
Definition
The SI unit of angle. One radian is the angle created when the arc length equals the radius.
SI / Standard Information
SI-derived unit (rad). A full circle equals 2π radians (~6.283 rad). Essential for calculus, trigonometry, and physics.
Approximate Comparison
One radian is about 57.3 degrees — roughly a 60-degree angle.
Practical Applications
  • Mathematics and calculus
  • Physics angular velocity calculations
  • Engineering and signal processing
  • Computer graphics rotation
Real-World Examples
  • A full circle is 2π radians
  • A right angle is π/2 radians (about 1.57 rad)
  • The Earth rotates at about 0.0000727 rad/s

About Converting Degree to Radian

Our Degree to Radian converter provides instant, accurate conversion between these two essential angle units. Whether you are working in engineering, construction, education, or everyday angle measurement, this tool delivers precise results with zero friction.

The Degree (°) is a angular unit of angle. The most common angular unit. A full circle is divided into 360 equal parts called degrees. One degree is about the width of a little finger held at arm's length.

The Radian (rad) is a angular unit of angle. The SI unit of angle. One radian is the angle created when the arc length equals the radius. One radian is about 57.3 degrees — roughly a 60-degree angle.

Conversion Formula & Worked Examples

The conversion between ° and rad uses the following mathematical relationship:

Radian = Degree × 0.017453

Degree = Radian × 57.295780

Whether you need to convert for navigation and gps coordinates or mathematics and calculus, our interactive converter provides instant, accurate results.

Example

1 °

=

0.0175 rad

Example

5 °

=

0.0873 rad

Example

10 °

=

0.1745 rad

Reverse Direction

Need to convert Radian back into Degree?

Switch conversion direction to view Radian → Degree tables, benchmarks, and detailed info.

Open Radian → Degree

Practical Use Cases & Applications

° Degree

  • Navigation and GPS coordinates
  • Engineering and construction angles
  • Geometry and mathematics education
  • Compass and direction measurement

rad Radian

  • Mathematics and calculus
  • Physics angular velocity calculations
  • Engineering and signal processing
  • Computer graphics rotation

Frequently Asked Questions

Common questions about this conversion and related measurement topics.

How do I convert Degree to Radian?
To convert Degree (°) to Radian (rad), multiply the degree value by the conversion factor. Our converter below handles this instantly — just enter the value in ° and the rad result appears in real time.
How many Radians are in one degree?
One degree (°) equals approximately 0.017453 radian (rad). This conversion factor is constant and can be used for any degree value.
What is the formula to convert ° to rad?
The conversion formula is: <strong>Radian = Degree × 0.017453</strong>. For example, 5 ° × 0.0175 = 0.0873 rad, and 10 ° × 0.0175 = 0.1745 rad.
Can I convert Radian back to Degree?
Yes! Use the reverse direction on our converter, or visit our dedicated <a href="/angle/radians-to-degrees/" class="text-accent-teal underline">Radian to Degree converter</a>. The reverse conversion factor is approximately 1 rad = 57.295780 °.
Where is Degree commonly used?
Navigation and GPS coordinates, Engineering and construction angles, Geometry and mathematics education. The most common angular unit. A full circle is divided into 360 equal parts called degrees.
What is the difference between Degree and Radian?
Degree (°) and Radian (rad) are both units of angle. Degree belongs to the angular system, while Radian belongs to the angular system. Understanding the conversion between them is essential for international work in angle measurement.
What are some real-world examples of degrees and radians?
Degree: A right angle is 90 degrees; The Earth's axis is tilted at 23.5 degrees Radian: A full circle is 2π radians; A right angle is π/2 radians (about 1.57 rad)

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About This Conversion ℹ

This Degree to Radian converter provides accurate, real-time conversions between these two angle units.

Both units are among the most commonly used angle measurements — rated 10/10 and 9/10 in popularity.

Bookmark this page for quick access to the Degree → Radian converter whenever you need precise unit conversion.

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