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 (ISO 80000-3 §3-5, BIPM SI Brochure), defined as the plane angle subtended at the center of a circle by a circular arc equal in length to the radius. One full revolution is exactly 2π radians ≈ 6.2832 rad; one degree = π/180 radians ≈ 0.01745 rad. Radians are the native unit for calculus — derivative identities (d/dx sin x = cos x; d/dx cos x = −sin x) only hold when x is in radians, not degrees, because the small-angle limit lim x→0 sin(x)/x = 1 only equals 1 in radians — and for every physics and engineering formula involving rotational dynamics, wave-phase calculations (Fourier series, signal processing), angular frequency ω = 2πf in oscillation analysis, complex-number arguments (Argand-plane angle = radians by convention), and gyroscope output. Reference values: 30° = π/6 rad, 45° = π/4 rad, 60° = π/3 rad, 90° = π/2 rad, 180° = π rad, 360° = 2π rad. The radian is technically a dimensionless ratio (arc length / radius), but is treated as a unit by SI convention.
About Degree (°)
A unit of plane angle equal to exactly 1/360 of a full rotation (= π/180 radians), inherited from ancient Babylonian astronomy's sexagesimal (base-60) number system circa 2000 BCE — the 360-degree convention reflects the ~360-day Babylonian solar year. Degrees are the universal everyday angle unit in non-scientific contexts: compass bearings and ship/aircraft heading per ICAO and IMO conventions (0° = magnetic north, 90° = east), latitude / longitude geographic coordinates per WGS84 (the GPS datum), machine-tool protractors and CNC G-code, GIS data (Esri ArcGIS, QGIS), CAD-software 2D-sketch dimensions (Autodesk Inventor, SolidWorks, Fusion 360, CATIA), and architectural drawings. Reference values: a right angle is exactly 90°, a straight line 180°, a full turn 360°, an equilateral triangle has 60° interior angles, a regular pentagon 108°, a regular hexagon 120°. Trigonometry education worldwide introduces sine and cosine in degrees before transitioning students to radians for calculus. Convert degrees to radians by multiplying by π/180 ≈ 0.01745.
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 (ISO 80000-3 §3-5, BIPM SI Brochure), defined as the plane angle subtended at the center of a circle by a circular arc equal in length to the radius. One full revolution is exactly 2π radians ≈ 6.2832 rad; one degree = π/180 radians ≈ 0.01745 rad. Radians are the native unit for calculus — derivative identities (d/dx sin x = cos x; d/dx cos x = −sin x) only hold when x is in radians, not degrees, because the small-angle limit lim x→0 sin(x)/x = 1 only equals 1 in radians — and for every physics and engineering formula involving rotational dynamics, wave-phase calculations (Fourier series, signal processing), angular frequency ω = 2πf in oscillation analysis, complex-number arguments (Argand-plane angle = radians by convention), and gyroscope output. Reference values: 30° = π/6 rad, 45° = π/4 rad, 60° = π/3 rad, 90° = π/2 rad, 180° = π rad, 360° = 2π rad. The radian is technically a dimensionless ratio (arc length / radius), but is treated as a unit by SI convention.
Radians are commonly used in surveying, navigation, trigonometry, and mechanical design.
Understanding Degrees
The Degree (symbol: °) is a unit of angle. A unit of plane angle equal to exactly 1/360 of a full rotation (= π/180 radians), inherited from ancient Babylonian astronomy's sexagesimal (base-60) number system circa 2000 BCE — the 360-degree convention reflects the ~360-day Babylonian solar year. Degrees are the universal everyday angle unit in non-scientific contexts: compass bearings and ship/aircraft heading per ICAO and IMO conventions (0° = magnetic north, 90° = east), latitude / longitude geographic coordinates per WGS84 (the GPS datum), machine-tool protractors and CNC G-code, GIS data (Esri ArcGIS, QGIS), CAD-software 2D-sketch dimensions (Autodesk Inventor, SolidWorks, Fusion 360, CATIA), and architectural drawings. Reference values: a right angle is exactly 90°, a straight line 180°, a full turn 360°, an equilateral triangle has 60° interior angles, a regular pentagon 108°, a regular hexagon 120°. Trigonometry education worldwide introduces sine and cosine in degrees before transitioning students to radians for calculus. Convert degrees to radians by multiplying by π/180 ≈ 0.01745.
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 (ISO 80000-3 §3-5, BIPM SI Brochure), defined as the plane angle subtended at the center of a circle by a circular 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 plane angle equal to exactly 1/360 of a full rotation (= π/180 radians), inherited from ancient Babylonian astronomy's sexagesimal (base-60) number system circa 2000 BCE — the 360-degree convention reflects the... 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.