Find the Quadrant of an Angle - Trigonometry Calculator

Find the Quadrant of an Angle with Step-by-Step Solutions

Determine the quadrant (or axis) of any angle in standard position. Complete step-by-step explanation shown for every calculation.
What is an Angle in Standard Position?

An angle in standard position has its vertex at the origin and its initial side along the positive x-axis. The terminal side determines the quadrant.

Quadrant Rules:

• Quadrant I: \(0° < \theta < 90°\) or \(0 < \theta < \frac{\pi}{2}\)

• Quadrant II: \(90° < \theta < 180°\) or \(\frac{\pi}{2} < \theta < \pi\)

• Quadrant III: \(180° < \theta < 270°\) or \(\pi < \theta < \frac{3\pi}{2}\)

• Quadrant IV: \(270° < \theta < 360°\) or \(\frac{3\pi}{2} < \theta < 2\pi\)

• Quadrantal angles: \(0°, 90°, 180°, 270°, 360°\) (or \(0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi\)) lie on the axes.

📐 Degrees

Quadrant / Axis
📐 Step-by-step solution will appear here.

Radians (as fraction of π)

/ π
Example: 27π/5 = 27/5 π
Quadrant / Axis
Step-by-step solution will appear here.

Quick Reference

Quadrant I: 0° to 90° (0 to π/2) | Quadrant II: 90° to 180° (π/2 to π)
Quadrant III: 180° to 270° (π to 3π/2) | Quadrant IV: 270° to 360° (3π/2 to 2π)
Axes: 0°, 90°, 180°, 270°, 360° (0, π/2, π, 3π/2, 2π)


More References and Links

  • Questions on Angles in Standard Position
  • Angle in Standard Position
  • Math Calculators and Solvers