Reference Angle Calculator

∡ Reference Angle Calculator

Find the acute angle formed with the nearest X-axis.

Enter an Angle ($\theta$)

Units

Q I

Q II

Q III

Q IV

Angle $\theta$ (Blue) | Reference Angle $\theta_R$ (Orange)

Reference Angle ($\theta_R$)

–° — rad

Location

—

Principal Angle: –°

Q I ($0^\circ < \theta < 90^\circ$)

$$\theta_R = \theta$$

Q II ($90^\circ < \theta < 180^\circ$)

$$\theta_R = 180^\circ – \theta$$

Q III ($180^\circ < \theta < 270^\circ$)

$$\theta_R = \theta – 180^\circ$$

Q IV ($270^\circ < \theta < 360^\circ$)

$$\theta_R = 360^\circ – \theta$$

**Disclaimer:** The calculator first determines the Coterminal Angle between 0° and 360° before applying the Reference Angle rules.