Half-Angle Calculator

The half-angle calculator finds trigonometric values for half of a given angle. It is useful for algebra, calculus, exact trig values, geometry, signal analysis, and checking work that uses trigonometric identities.

How to use this calculator

Enter an Angle in degrees from -360 through 360. The calculator divides it by 2 and returns sin(x/2) as the main result, plus cos(x/2), tan(x/2), and the sine, cosine, and tangent of the original angle.

Formula

The calculator uses the original angle to compute half-angle values and selects signs from the quadrant of the half angle.

$\sin\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 - \cos x}{2}}$

$\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 + \cos x}{2}}$

$\tan\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 - \cos x}{1 + \cos x}}$

For example, entering 60° gives a half angle of 30°. The results are sin 30° = 0.5, cos 30° ≈ 0.8660, and tan 30° ≈ 0.5774.

Quadrant tips

Always determine the quadrant after halving the angle, not before. Tangent may be undefined when cosine of the half angle is zero. Related tools include the angle converter, slope calculator, and scientific notation calculator.