Full Angle — Definition, Formula & Examples

A full angle is an angle that measures exactly 360 degrees. It occurs when a ray rotates all the way around and returns to its starting position.

A full angle is an angle whose measure equals $360°$ (or $2\pi$ radians), formed by one complete revolution of a ray about its endpoint, so that the terminal side coincides with the initial side.

Key Formula

1 \text{ full angle} = 360° = 2\pi \text{ radians}

Where:

$360°$ = The degree measure of one complete rotation
$2\pi$ = The radian measure of one complete rotation

How It Works

Imagine a ray anchored at a point. If you spin that ray in one direction until it lands exactly where it started, you have swept out a full angle. A full angle covers twice the rotation of a straight angle (

180°

) and four times the rotation of a right angle (

90°

). On a protractor or in a diagram, a full angle looks like a complete circle drawn around the vertex.

Worked Example

Problem: A spinner makes one full rotation plus an additional 90°. What is the total angle it has turned through?

Step 1: One full rotation equals a full angle.

1 \text{ full rotation} = 360°

Step 2: Add the extra rotation.

360° + 90° = 450°

Answer: The spinner has turned through a total of

450°

Why It Matters

Full angles appear whenever you work with complete rotations — clock hands, wheels, compass bearings, and circular motion in physics all rely on the idea that one full turn is

360°

. Understanding this also helps when measuring angles greater than

360°

in trigonometry and navigation.

Common Mistakes

Mistake: Confusing a full angle (360°) with a straight angle (180°).

Correction: A straight angle is half a rotation and forms a straight line. A full angle is a complete rotation where the ray returns to its starting position.