Convert Degrees to Radians
Instantly convert Degrees (°) to Radians (rad) with our free online calculator.
Formula: ° to rad — multiply by 0.0174533
Reference Table
| Degrees (°) | Radians (rad) |
|---|---|
| 1 | 0.0174533 |
| 5 | 0.0872665 |
| 10 | 0.174533 |
| 25 | 0.436332 |
| 50 | 0.872665 |
| 100 | 1.74533 |
How to Convert Degrees to Radians
Formula
To convert Degrees (°) to Radians (rad): multiply by 0.0174533
Step-by-Step
- Start with your value in Degrees (°).
- Multiply by 0.0174533 to perform the conversion.
- The result is your value expressed in Radians (rad).
Conversion Factor
1 ° = 0.0174533 rad
Reverse Factor
1 rad = 57.2958 °
Worked Example
Convert 25 Degrees to Radians: 25 ° = 0.436332 rad
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.
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.
Quick Facts
- 1 Degree equals 0.0174533 Radians
- 1 Radian equals 57.2958 Degrees
- Degree is a unit of angle
- Radian is a unit of angle
- This conversion is commonly used in surveying, navigation, trigonometry, and mechanical design
Common Degree to Radian Conversions
| Degrees (°) | Radians (rad) |
|---|---|
| 0.01 | 0.000174533 |
| 0.1 | 0.00174533 |
| 0.25 | 0.00436332 |
| 0.5 | 0.00872665 |
| 1 | 0.0174533 |
| 2 | 0.0349066 |
| 3 | 0.0523599 |
| 5 | 0.0872665 |
| 10 | 0.174533 |
| 15 | 0.261799 |
| 20 | 0.349066 |
| 25 | 0.436332 |
| 50 | 0.872665 |
| 75 | 1.309 |
| 100 | 1.74533 |
| 250 | 4.36332 |
| 500 | 8.72665 |
| 1000 | 17.4533 |
| 5000 | 87.2665 |
| 10000 | 174.533 |
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.
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.
Why Convert Degrees to Radians?
Converting between Degrees and Radians 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 Degrees to Radians?
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... To convert Degrees to Radians, multiply by 0.0174533. For example, 25 ° equals 0.436332 rad.
How many Radians are in 1 Degree?
There are 0.0174533 Radians in 1 Degree.
How many Degrees are in 1 Radian?
There are 57.2958 Degrees in 1 Radian.
What is the formula for Degree to Radian conversion?
The formula is: multiply by 0.0174533. This means 1 ° = 0.0174533 rad.
Is a Degree bigger than a Radian?
Yes. One Degree is larger than one Radian because 1 ° equals 0.0174533 rad, which is less than 1.
When do you need to convert between Degrees and Radians?
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. Degree and Radian 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.