How Many Degrees in a Circle
360 degrees in a circle - Learn why and master angle conversions
⚡Quick Answer
A circle has 360 degrees (360°). Quarter circle = 90° (right angle). Half circle = 180° (straight line). 360° = 2π radians. The 360° convention comes from Babylonian astronomy and base-60 math.
Step-by-Step Guide
Quick Answer
A circle has 360 degrees (360°). This is the complete rotation around a point. One degree (1°) is 1/360th of a full circle.
Common Circle Divisions
Quarter circle (90°) = right angle | Half circle (180°) = straight line | Three-quarters (270°) | Full circle (360°) = complete rotation
Degrees to Radians
360° = 2π radians | 180° = π radians | 90° = π/2 radians | 1 radian = 57.3°
Why 360 Degrees?
Ancient Babylonians used base-60 math and noticed ~360 days per year. 360 is divisible by many numbers (1,2,3,4,5,6,8,9,10,12,15,etc), making it practical for subdivisions.
Frequently Asked Questions
Why did we choose 360 degrees for a circle?
The Babylonians used a base-60 number system and observed roughly 360 days in a year. 360 is highly divisible (24 factors!), making it practical for geometry, astronomy, and navigation. The convention stuck for over 4,000 years.
How many degrees in a right angle?
A right angle = 90° (quarter of a circle). Two right angles = 180° (straight line). Four right angles = 360° (full circle).
What is a radian vs a degree?
Radians are an alternative angle measurement based on the radius. 1 radian = angle where arc length equals radius. 2π radians = 360°. Radians are preferred in higher mathematics and physics.
How many degrees does a clock's minute hand move per minute?
The minute hand moves 360° in 60 minutes, so 6° per minute. The hour hand moves 360° in 12 hours (720 min), so 0.5° per minute.
Can a circle have more or less than 360 degrees?
Mathematically, you can use any division (gradians use 400, turns use 1). But by universal convention, a circle always has 360° - it's a definition, not a measurement.