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Degree Conversion Table
This comprehensive degree conversion table shows how various units relate to degrees. Use this reference for quick conversions between degrees and other common angle units.
| Conversion | To Unit | Multiplier |
|---|---|---|
| Degrees to radians | Radians | π/180 ≈ 0.0174533 |
| Degrees to mils | Mils | 16/9 ≈ 1.77778 |
This degree conversion reference table provides accurate conversion factors for angle units. All values are based on internationally recognized standards for maximum precision in scientific and engineering applications.
What is a Degree?
The degree (symbol: °) is a unit of measurement for plane angles, representing 1/360 of a full rotation. Although not an SI unit (the radian is the SI derived unit for angle), the degree is widely used and accepted for use with the SI system. One degree is equivalent to π/180 radians.
The degree is used in many fields including mathematics, engineering, navigation, and everyday applications. Our degree conversion tool helps you easily convert between degrees and other units. For example, a right angle measures 90 degrees, and a straight angle measures 180 degrees.
Degree in the SI System
While the radian is the SI derived unit for measuring angles, the degree is accepted for use with the SI system. The relationship between degrees and radians is fixed: 360 degrees equals exactly 2π radians. This relationship makes conversions between these units straightforward.
Other common angle units and their relationships to degrees:
- Radian (rad) = 180/π ≈ 57.2958 degrees
- Grad (gon) = 0.9 degrees
- Mil = 0.05625 degrees (NATO standard)
What are Degrees Used For?
Degrees are used in a wide range of applications across various fields. As a widely accepted unit for measuring angles, degrees provide a familiar reference for many angle measurements:
Geometry & Mathematics
Measuring angles in triangles, circles, and polygons. For example, the sum of interior angles in a triangle is always 180 degrees, and a full circle measures 360 degrees.
Navigation & Geography
Latitude and longitude coordinates, compass directions, and map reading. For example, the equator is at 0 degrees latitude, and the North Pole is at 90 degrees north latitude.
Engineering & Construction
Designing structures, calculating slopes, and determining angles for cuts and joins. For example, a 45-degree angle is commonly used for miter cuts in woodworking.
Astronomy
Measuring positions of celestial objects and angular distances. For example, the angular diameter of the full moon is approximately 0.5 degrees.
Etymology and History
The word "degree" comes from Latin "gradus," meaning "step" or "grade." The choice of 360 degrees in a circle is believed to be related to the approximate number of days in a year and the ancient Babylonians' use of a base-60 (sexagesimal) number system. This system was convenient for calculations as 360 has many divisors (2, 3, 4, 5, 6, 8, 9, 10, 12, etc.).
The degree has been used for thousands of years and remains one of the most familiar units for measuring angles. In modern times, while the radian is preferred in scientific contexts due to its mathematical properties, the degree continues to be widely used in everyday applications and in fields like navigation and surveying.
Frequently Asked Questions
Why are there 360 degrees in a circle?
The choice of 360 degrees in a circle dates back to ancient civilizations, particularly the Babylonians who used a base-60 number system. The number 360 was chosen because it has many divisors, making it convenient for dividing the circle into equal parts. Additionally, it's close to the number of days in a year (365), which may have influenced this choice.
How accurate is the degree as a unit of measurement?
The degree is a defined unit with exact relationships to other angle units. Its relationship to the radian is precisely defined as 1 degree = π/180 radians. While not the SI unit for angles, it's accepted for use with the SI system and is precise for all practical applications. Our degree converter ensures accurate conversions to other units.
What's the difference between degrees and radians?
Degrees and radians are both units for measuring angles, but they're defined differently. A degree is 1/360 of a full rotation, while a radian is the angle subtended by an arc equal in length to the radius of the circle. The relationship is: 360 degrees = 2π radians. Radians are preferred in mathematics and science due to their natural relationship with circular measurements.
How do I convert degrees to other units?
Use our degree conversion calculators above, or multiply by the appropriate conversion factor. For example, to convert degrees to radians, multiply by π/180 (≈ 0.0174533). For detailed instructions on converting degrees to radians, visit our degree to radian converter.
What are common uses for degree conversion?
Degree conversion is essential in mathematics (geometry problems), navigation (compass bearings), engineering (structural design), astronomy (celestial coordinates), and surveying (land measurements). Whether calculating roof angles for construction or converting GPS coordinates, our degree converter tool simplifies these everyday tasks.
How does degree conversion differ from other angle units?
The degree is one of several units for measuring angles, with fixed relationships to others. Unlike radians which are based on the radius of a circle, degrees are an arbitrary division of a circle into 360 parts. This makes degrees more intuitive for many people, while radians are more mathematically natural. Our converter handles all common angle units with precision.
Can I convert very small or very large angle measurements in degrees?
Yes, our degree converter handles both extremely small and large measurements with precision. For very small angles, you can work with decimal degrees (like 0.0001 degrees). For multiple rotations, you can convert values greater than 360 degrees. Our smart rounding feature ensures readable results for all scales.
Is your degree conversion tool free to use?
Yes, our degree conversion calculator is completely free with no registration required. Simply enter your value, select your target unit, and get instant, accurate results. We believe precise measurement conversion should be accessible to everyone, from students learning geometry to professionals working on complex engineering projects.