Convert Radians to Degrees
Instantly convert Radians (rad) to Degrees (°) with our free online calculator.
Formula: rad to ° — multiply by 57.2958
Reference Table
| Radians (rad) | Degrees (°) |
|---|---|
| 1 | 57.2958 |
| 5 | 286.479 |
| 10 | 572.958 |
| 25 | 1432.39 |
| 50 | 2864.79 |
| 100 | 5729.58 |
How to Convert Radians to Degrees
Formula
To convert Radians (rad) to Degrees (°): multiply by 57.2958
Step-by-Step
- Start with your value in Radians (rad).
- Multiply by 57.2958 to perform the conversion.
- The result is your value expressed in Degrees (°).
Conversion Factor
1 rad = 57.2958 °
Reverse Factor
1 ° = 0.0174533 rad
Worked Example
Convert 25 Radians to Degrees: 25 rad = 1432.39 °
About Radian (rad)
The SI unit of plane angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One full revolution is 2π radians ≈ 6.283 rad. Radians are the native unit for calculus — derivatives of trigonometric functions (d/dx sin x = cos x) only hold when x is in radians — and for every physics and engineering formula involving rotational motion, wave phase, or angular frequency.
About Degree (°)
A unit of angle equal to 1/360 of a full rotation, inherited from Babylonian astronomy's base-60 number system about 4,000 years ago. Degrees are the universal everyday angle unit — compass bearings, latitude/longitude, machine-tool protractors, GIS data, and architectural drawings. A right angle is 90°, a straight line 180°, a full turn 360°. Trigonometry education worldwide introduces sine and cosine in degrees before moving students to radians.
Quick Facts
- 1 Radian equals 57.2958 Degrees
- 1 Degree equals 0.0174533 Radians
- Radian is a unit of angle
- Degree is a unit of angle
- This conversion is commonly used in surveying, navigation, trigonometry, and mechanical design
Common Radian to Degree Conversions
| Radians (rad) | Degrees (°) |
|---|---|
| 0.01 | 0.572958 |
| 0.1 | 5.72958 |
| 0.25 | 14.3239 |
| 0.5 | 28.6479 |
| 1 | 57.2958 |
| 2 | 114.592 |
| 3 | 171.887 |
| 5 | 286.479 |
| 10 | 572.958 |
| 15 | 859.437 |
| 20 | 1145.92 |
| 25 | 1432.39 |
| 50 | 2864.79 |
| 75 | 4297.18 |
| 100 | 5729.58 |
| 250 | 14323.9 |
| 500 | 28647.9 |
| 1000 | 57295.8 |
| 5000 | 286479 |
| 10000 | 572958 |
Understanding Radians
The Radian (symbol: rad) is a unit of angle. The SI unit of plane angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One full revolution is 2π radians ≈ 6.283 rad. Radians are the native unit for calculus — derivatives of trigonometric functions (d/dx sin x = cos x) only hold when x is in radians — and for every physics and engineering formula involving rotational motion, wave phase, or angular frequency.
Radians are commonly used in surveying, navigation, trigonometry, and mechanical design.
Understanding Degrees
The Degree (symbol: °) is a unit of angle. A unit of angle equal to 1/360 of a full rotation, inherited from Babylonian astronomy's base-60 number system about 4,000 years ago. Degrees are the universal everyday angle unit — compass bearings, latitude/longitude, machine-tool protractors, GIS data, and architectural drawings. A right angle is 90°, a straight line 180°, a full turn 360°. Trigonometry education worldwide introduces sine and cosine in degrees before moving students to radians.
Degrees are commonly used in surveying, navigation, trigonometry, and mechanical design.
Why Convert Radians to Degrees?
Converting between Radians and Degrees is a frequent requirement for engineers, scientists, and students working with angle values. Different industries and regions favour different unit systems, so having a dependable conversion tool saves time and prevents errors in technical calculations. Whether you are verifying a specification sheet, cross-checking simulation results, or preparing a report for an international audience, accurate angle conversion is essential.
Frequently Asked Questions
How do I convert Radians to Degrees?
The SI unit of plane angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. To convert Radians to Degrees, multiply by 57.2958. For example, 25 rad equals 1432.39 °.
How many Degrees are in 1 Radian?
There are 57.2958 Degrees in 1 Radian.
How many Radians are in 1 Degree?
There are 0.0174533 Radians in 1 Degree.
What is the formula for Radian to Degree conversion?
The formula is: multiply by 57.2958. This means 1 rad = 57.2958 °.
Is a Radian bigger than a Degree?
No. One Radian is smaller than one Degree because 1 rad equals 57.2958 °, which is greater than 1.
When do you need to convert between Radians and Degrees?
A unit of angle equal to 1/360 of a full rotation, inherited from Babylonian astronomy's base-60 number system about 4,000 years ago. Radian and Degree are both angle units, so conversion comes up whenever one source of information uses one unit and another uses the other — a classic cross-reference challenge in engineering, trade, travel, and everyday life.