The radian is the SI angle unit.
Radians to Degrees Converter — rad to deg
Convert Radian (rad) to Degree (deg) using the exact conversion factor (1 radian = 57.29577951 degree). See the formula, worked examples, conversion table, unit comparison, history, and common uses.
Radians to Degrees converter
Converter
Angle Converter
Convert radians, degrees, gradians, turns, arcminutes, arcseconds, and milliradians.
Context values
Some unit families need one extra value for a physically accurate result.
A degree is pi/180 radians.
Result = input x 1 / 0.01745329252.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Radians to Degrees
Radian and Degree are the two standard ways to measure angles — degrees for everyday and navigational use, radians for calculus and physics — so converting between them comes up constantly in math, engineering, and programming. Radian is typically associated with standard angle unit in mathematics, physics, and engineering worldwide., while Degree is typically associated with used worldwide for navigation, geography, and everyday angle measurement..
Formula
degrees = radians × 57.2957795131
This factor comes from each unit's defined relationship to the category's base unit: 1 radian equals 1 base unit, and 1 degree equals 0.0174532925199 base units, so dividing one by the other gives the direct radian-to-degree factor of 57.2957795131.
Simple example
1 rad × 57.29577951 = 57.29577951 deg
1 radian = 57.29577951 degrees.
Real-world example
90 rad × 57.29577951 = 5,156.620156 deg
90 radians = 5,156.620156 degrees.
Conversion table
| Radian (rad) | Degree (deg) |
|---|---|
| 0 rad | 0 deg |
| 30 rad | 1,718.873385 deg |
| 45 rad | 2,578.310078 deg |
| 90 rad | 5,156.620156 deg |
| 180 rad | 10,313.24031 deg |
| 360 rad | 20,626.48062 deg |
Reverse conversion: Degree to Radian
57.29577951 deg × 0.01745329252 = 0.9999999999 rad
57.29577951 degrees = 0.9999999999 radians.
radians = degrees × 0.0174532925199
For a page dedicated to this direction, see Degree to Radian.
Radian vs. Degree
| Aspect | Radian | Degree |
|---|---|---|
| Family | SI derived unit | Non-SI unit accepted for use with SI |
| Typical use | Calculus and trigonometry (derivatives of trig functions are simplest in radians) | Navigation and cartography (latitude/longitude) |
| Where it's used | Standard angle unit in mathematics, physics, and engineering worldwide. | Used worldwide for navigation, geography, and everyday angle measurement. |
Understanding the Radian
Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.
Where it's used: Standard angle unit in mathematics, physics, and engineering worldwide.
Uses of the Radian today
- Calculus and trigonometry (derivatives of trig functions are simplest in radians)
- Physics and engineering (angular velocity, rotational mechanics)
- Computer graphics and robotics
History of the Radian
The radian was developed in the 1870s, with the term itself coined by James Thomson (brother of Lord Kelvin) around 1873, formalizing a ratio-based angle measure that mathematicians had used implicitly for calculus since Newton and Leibniz.
It was adopted as the SI derived unit of angle because it makes many physics and calculus formulas simpler than using degrees.
Historical origin. Radian was not the invention of a single named person; it developed through the process described above.
Understanding the Degree
Degree (deg) measures angle. A degree is 1/360 of a full rotation, a division dating to Babylonian base-60 astronomy. It is classified as a Non-SI unit accepted for use with SI.
Where it's used: Used worldwide for navigation, geography, and everyday angle measurement.
Uses of the Degree today
- Navigation and cartography (latitude/longitude)
- Construction and surveying
- Everyday angle measurement (protractors, sports)
History of the Degree
The 360-degree circle traces to ancient Babylonian astronomy, whose base-60 (sexagesimal) number system made 360 — divisible by many small numbers — a practical choice for dividing a circle. The convention passed through Greek astronomy (Hipparchus, Ptolemy) into common use.
Historical origin. Degree was not the invention of a single named person; it developed through the process described above.
Radian — sources
- BIPM SI Brochure — Coherent derived units — Defines the radian as the SI unit of plane angle.
Degree — sources
- NIST Special Publication 811 — Lists the degree among non-SI units accepted for use with SI.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many degrees are in 1 radian?
1 radian equals 57.29577951 degrees, using the exact defined conversion factor rather than an estimate.
How do I convert radian to degree?
Multiply the radian value by 57.29577951. The converter above does this instantly to whatever precision you set.
How do I convert degree back to radian?
Use the reverse factor: 1 degree equals 0.0174532925 radians. You can also use the swap control in the converter above to flip the direction instantly.
What is a radian?
Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.
What is a degree?
Degree (deg) measures angle. A degree is 1/360 of a full rotation, a division dating to Babylonian base-60 astronomy. It is classified as a Non-SI unit accepted for use with SI.
Is the radian to degree conversion exact?
Yes. Both radian and degree are defined by fixed standards rather than physical artifacts, so the factor of 57.29577951 used above is exact to as many digits as you choose to display.
Where is the radian still used today?
Standard angle unit in mathematics, physics, and engineering worldwide.