A degree is pi/180 radians.
Degrees to Circles Converter — deg to circle
Convert Degree (deg) to Circle (circle) using the exact conversion factor (1 degree = 0.0027777778 circle). See the formula, worked examples, conversion table, history, and common uses.
Degrees to Circles 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.
One complete circle.
Result = input x 0.01745329252 / 6.283185307.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Degrees to Circles
Degree and Circle 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. Degree is most often used for navigation and cartography (latitude/longitude).
Formula
circles = degrees × 0.00277777777778
This factor comes from each unit's defined relationship to the category's base unit: 1 degree equals 0.0174532925199 base units, and 1 circle equals 6.28318530718 base units, so dividing one by the other gives the direct degree-to-circle factor of 0.00277777777778.
Simple example
1 deg × 0.002777777778 = 0.0027777778 circle
1 degree = 0.0027777778 circles.
Real-world example
90 deg × 0.002777777778 = 0.25 circle
90 degrees = 0.25 circles.
Conversion table
| Degree (deg) | Circle (circle) |
|---|---|
| 0 deg | 0 circle |
| 30 deg | 0.0833333333 circle |
| 45 deg | 0.125 circle |
| 90 deg | 0.25 circle |
| 180 deg | 0.5 circle |
| 360 deg | 1 circle |
Reverse conversion: Circle to Degree
0.0027777778 circle × 360 = 1.000000008 deg
0.0027777778 circles = 1.000000008 degrees.
degrees = circles × 360
For a page dedicated to this direction, see Circle to Degree.
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.
Understanding the Circle (circle)
One complete circle.
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 circles are in 1 degree?
1 degree equals 0.0027777778 circles, using the exact defined conversion factor rather than an estimate.
How do I convert degree to circle?
Multiply the degree value by 0.002777777778. The converter above does this instantly to whatever precision you set.
How do I convert circle back to degree?
Use the reverse factor: 1 circle equals 360 degrees. You can also use the swap control in the converter above to flip the direction instantly.
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.
What is a circle?
Circle (circle) is a unit of angle.
Is the degree to circle conversion exact?
Yes. Both degree and circle are defined by fixed standards rather than physical artifacts, so the factor of 0.002777777778 used above is exact to as many digits as you choose to display.
Where is the degree still used today?
Used worldwide for navigation, geography, and everyday angle measurement.