One complete circle.
Circles to Degrees Converter — circle to deg
Convert Circle (circle) to Degree (deg) using the exact conversion factor (1 circle = 360 degree). See the formula, worked examples, conversion table, history, and common uses.
Circles to Degrees 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.
A degree is pi/180 radians.
Result = input x 6.283185307 / 0.01745329252.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Circles to Degrees
Circle and Degree 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. Specifically: One complete circle, and a degree is pi/180 radians.
Formula
degrees = circles × 360
This factor comes from each unit's defined relationship to the category's base unit: 1 circle equals 6.28318530718 base units, and 1 degree equals 0.0174532925199 base units, so dividing one by the other gives the direct circle-to-degree factor of 360.
Simple example
1 circle × 360 = 360 deg
1 circle = 360 degrees.
Real-world example
90 circle × 360 = 32,400 deg
90 circles = 32,400 degrees.
Conversion table
| Circle (circle) | Degree (deg) |
|---|---|
| 0 circle | 0 deg |
| 30 circle | 10,800 deg |
| 45 circle | 16,200 deg |
| 90 circle | 32,400 deg |
| 180 circle | 64,800 deg |
| 360 circle | 129,600 deg |
Reverse conversion: Degree to Circle
360 deg × 0.002777777778 = 1 circle
360 degrees = 1 circle.
circles = degrees × 0.00277777777778
For a page dedicated to this direction, see Degree to Circle.
Understanding the Circle (circle)
One complete circle.
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.
Degree — sources
- NIST Special Publication 811 — Lists the degree among non-SI units accepted for use with SI.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many degrees are in 1 circle?
1 circle equals 360 degrees, using the exact defined conversion factor rather than an estimate.
How do I convert circle to degree?
Multiply the circle value by 360. The converter above does this instantly to whatever precision you set.
How do I convert degree back to circle?
Use the reverse factor: 1 degree equals 0.0027777778 circles. You can also use the swap control in the converter above to flip the direction instantly.
What is a circle?
Circle (circle) is a unit of angle.
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.
Is the circle to degree conversion exact?
Yes. Both circle and degree are defined by fixed standards rather than physical artifacts, so the factor of 360 used above is exact to as many digits as you choose to display.