A degree is pi/180 radians.
Degrees to Radians Converter — deg to rad
Convert Degree (deg) to Radian (rad) using the exact conversion factor (1 degree = 0.0174532925 radian). See the formula, worked examples, conversion table, unit comparison, history, and common uses.
Degrees to Radians 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.
The radian is the SI angle unit.
Result = input x 0.01745329252 / 1.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Degrees to Radians
Degree and Radian 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. Degree is typically associated with used worldwide for navigation, geography, and everyday angle measurement., while Radian is typically associated with standard angle unit in mathematics, physics, and engineering worldwide..
Formula
radians = degrees × 0.0174532925199
This factor comes from each unit's defined relationship to the category's base unit: 1 degree equals 0.0174532925199 base units, and 1 radian equals 1 base unit, so dividing one by the other gives the direct degree-to-radian factor of 0.0174532925199.
Simple example
1 deg × 0.01745329252 = 0.0174532925 rad
1 degree = 0.0174532925 radians.
Real-world example
90 deg × 0.01745329252 = 1.570796327 rad
90 degrees = 1.570796327 radians.
Conversion table
| Degree (deg) | Radian (rad) |
|---|---|
| 0 deg | 0 rad |
| 30 deg | 0.5235987756 rad |
| 45 deg | 0.7853981634 rad |
| 90 deg | 1.570796327 rad |
| 180 deg | 3.141592654 rad |
| 360 deg | 6.283185307 rad |
Reverse conversion: Radian to Degree
0.0174532925 rad × 57.29577951 = 0.9999999989 deg
0.0174532925 radians = 0.9999999989 degrees.
degrees = radians × 57.2957795131
For a page dedicated to this direction, see Radian to Degree.
Degree vs. Radian
| Aspect | Degree | Radian |
|---|---|---|
| Family | Non-SI unit accepted for use with SI | SI derived unit |
| Typical use | Navigation and cartography (latitude/longitude) | Calculus and trigonometry (derivatives of trig functions are simplest in radians) |
| Where it's used | Used worldwide for navigation, geography, and everyday angle measurement. | Standard angle unit in mathematics, physics, and engineering worldwide. |
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.
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.
Degree — sources
- NIST Special Publication 811 — Lists the degree among non-SI units accepted for use with SI.
Radian — sources
- BIPM SI Brochure — Coherent derived units — Defines the radian as the SI unit of plane angle.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many radians are in 1 degree?
1 degree equals 0.0174532925 radians, using the exact defined conversion factor rather than an estimate.
How do I convert degree to radian?
Multiply the degree value by 0.01745329252. The converter above does this instantly to whatever precision you set.
How do I convert radian back to degree?
Use the reverse factor: 1 radian equals 57.29577951 degrees. You can also use the swap control in the converter above to flip the direction instantly.
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.
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.
Is the degree to radian conversion exact?
Yes. Both degree and radian are defined by fixed standards rather than physical artifacts, so the factor of 0.01745329252 used above is exact to as many digits as you choose to display.
Where is the degree still used today?
Used worldwide for navigation, geography, and everyday angle measurement.