Angle Measurement
Calculate angle ∠ABC between two rays meeting at a common vertex point.
Trigonometric Angle Principles
Vertex B is the anchor point where the two rays originate. Dragging Vertex B moves the pivot without altering ray angles relative to the origin.
Every two intersecting lines form an interior angle (≤ 180°) and a reflex angle (≥ 180°) whose sum is always exactly 360°.
Useful for physical therapy joint angle analysis, carpentry miter cuts, mechanical engineering drafting, and physics ray tracing.
Looking for a circular drafting instrument? Open our Online Protractor, measure physical lengths with the Online Ruler, or check distances with the Distance Measurement Tool.
Frequently Asked Questions About 3-Point Angle Measurement
Common questions regarding vertex geometry, vector math, and goniometry.
How is an angle measured between three points?▼
The angle is defined by two rays meeting at a common vertex: Ray BA and Ray BC. The angle is calculated using vector dot product and arc tangent trigonometry: θ = arccos((vBA · vBC) / (|vBA| × |vBC|)), giving exact decimal degrees and radian values.
What is the difference between interior and reflex angles?▼
The interior angle is the smaller opening between the two rays (0° to 180°). The reflex angle is the outer sweep (180° to 360°), which together with the interior angle totals 360°.
What are the common angle classifications?▼
Acute angles are strictly less than 90°. Right angles equal exactly 90°. Obtuse angles are between 90° and 180°. Straight angles equal 180°. Reflex angles are between 180° and 360°.