How this calculation works
Compare the supplied angle with the defining boundaries. An angle strictly below 90° and above zero is acute; exactly 90° is right; the interval up to 180° is obtuse; exactly 180° is straight. Values above 180° and below 360° are reflex, while 360° is a full turn. The SVG uses the same counterclockwise convention as the numeric input.
Radians = degrees × π / 180; classify at 0°, 90°, 180° and 360° boundariesA worked example
45° is acute, π/4 radians and one eighth of a full turn. 90° is right rather than acute, and 180° is straight rather than obtuse. Zero is handled as its own type.
Good to know
One nonnegative angle through 360° only. This does not normalize negative or multi-turn inputs or infer an angle from an image. The classification uses the entered value without an arbitrary closeness tolerance; radian and full-turn decimal displays are approximate.
Reference: OpenStax Prealgebra: geometry and measurement (opens in a new tab) ↗
A full turn and a zero angle can point the same way
After a complete 360-degree turn, the ending ray points in the same direction as the starting ray. The amount turned is nevertheless different from zero. This classifier reports zero and full turn separately rather than reducing both to the same orientation.
The exact boundaries matter: 90 degrees is right, not acute or obtuse; 180 degrees is straight, not obtuse or reflex. Values between those boundaries belong to open intervals. A value very close to a boundary is classified from the value entered, without an unstated snapping tolerance.
A full turn is 2π radians, so 45 degrees is π/4 radians and one eighth of a turn. The clock angle calculator finds an angle from a different model: the moving positions of clock hands. This page begins with an angle already supplied in degrees.
Direction conventions make the arc readable
The illustration starts at the positive horizontal ray and sweeps counterclockwise. That is the stated mathematical convention for this diagram. A compass bearing uses a different reference direction and usually turns clockwise; the compass bearing calculator handles that context.
The displayed arc shows the full supplied angle rather than always choosing the smaller angle between two rays. For a 270-degree input, a reflex arc is therefore appropriate even though the smaller angle between the ending rays is ninety degrees.
Inputs below zero or above a full turn belong to a normalization problem and are rejected here. This keeps the classroom classification from silently discarding complete turns that may be meaningful in a rotation description.
A few questions, answered
Is 180 degrees obtuse?
No. It is a straight angle. Obtuse angles are strictly between 90 and 180 degrees.
Why is 270 degrees reflex when its rays also enclose 90 degrees?
The input specifies the counterclockwise sweep of 270 degrees, rather than the smaller angle between rays.
Are zero and 360 degrees treated as the same type?
No. They have the same ending orientation but different amounts of turn.