Angle Calculator
Convert angles and explore related properties.
Angle conversions
Table of Contents
How to Use
- Enter the angle you want to convert.
- Choose the unit the value is currently expressed in.
- Select Calculate to generate all conversions.
- Review normalized values, quadrant, and complementary or supplementary angles.
Angle Units Explained
Angles measure how much one ray rotates around a vertex to coincide with another ray. The same rotation can be described using multiple units.
Most common units
- Degrees (°): A full rotation is 360°.
- Radians (rad): Based on arc length, a full rotation is 2π rad.
- Gradians (gon): A full rotation is 400 gon, popular in surveying.
- Turns (rev): A full rotation is 1 turn.
Complementary and Supplementary Angles
Complementary angles sum to 90° and only exist for acute angles. Supplementary angles sum to 180° and work for angles up to a straight line.
Our calculator automatically checks whether the complement or supplement exists and reports the missing amount.
Quadrant Analysis
Angles in standard position fall into four quadrants or lie on axes. Knowing the quadrant helps when evaluating trigonometric signs.
Trigonometric signs by quadrant
- Quadrant I: sin, cos, tan positive.
- Quadrant II: sin positive; cos, tan negative.
- Quadrant III: tan positive; sin, cos negative.
- Quadrant IV: cos positive; sin, tan negative.
Frequently Asked Questions
- How do I convert an angle larger than 360°?
- Enter the value and the calculator will normalize it into the 0°–360° range while still showing the raw conversions in every unit.
- Why does the complementary angle sometimes say "Not defined"?
- Complements only make sense for acute angles (0°–90°). If the normalized angle exceeds that range there is no valid complement.
- What is a turn and when should I use it?
- A turn (or revolution) measures rotation relative to a full circle. It is convenient in engineering, robotics, and animation where multiple full spins occur.