Calxsolver
Trigonometry

Angle Converter

Enter an angle in degrees or radians. The converter gives the equivalent in the other unit, the coterminal angle in the range 0°–360°, the quadrant it lands in, and the reference angle used to relate it to first-quadrant trig values.

Angle Converter

Convert degrees and radians, with reference angle.

Try:
Answer210° = 3.66519 rad · reference angle 30°
  1. To radians210° × π/180 = 3.66519 rad
  2. Coterminal angle210° ≡ 210° (mod 360°)
  3. QuadrantQuadrant 3
  4. Reference angle30°
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Worked examples

Convert 180° to radians Convert degrees to radians and find the reference angle and quadrant. Convert π/3 rad to degrees Convert a radian measure to degrees and report the reference angle.

Key terms

Radian The natural unit of angle: a full turn is 2π radians.

Frequently asked questions

How do degrees and radians relate?

A full turn is 360° or 2π radians, so 1° = π/180 radians.

What is a reference angle?

It is the acute angle between the terminal side and the x-axis — always between 0° and 90°.

What is a coterminal angle?

An angle that shares the same terminal side, differing by a whole number of full turns (multiples of 360°).

Related solvers

Right Triangle Solver Solve a right triangle from its two legs. Trig Function Evaluator Evaluate sin, cos, tan, csc, sec or cot of an angle. Pythagorean Theorem Find the missing side of a right triangle. Law of Cosines Solve a triangle from two sides and the included angle. Law of Sines Solve a triangle from two angles and a side. Trig Equation Solver Solve sin(x) = c, cos(x) = c, tan(x) = c (and reciprocals) with general solution. Trig Identity Verifier Check whether LHS = RHS as an identity by numeric sampling. Cartesian to Polar Coordinates Convert (x, y) to (r, θ), reporting θ in both degrees and radians. Polar to Cartesian Coordinates Convert (r, θ) to (x, y), accepting θ in degrees or radians.