Half Angle Calculator

Enter an angle to calculate sin, cos, and tan of half that angle.

How to Use the Half Angle Calculator

Enter an angle. The calculator returns sin, cos, and tan of half that angle, derived from the half angle identities rather than by simply dividing the angle in two and re-measuring.

sin(θ ÷ 2) = ±√((1 − cos θ) ÷ 2)
cos(θ ÷ 2) = ±√((1 + cos θ) ÷ 2)
tan(θ ÷ 2) = sin θ ÷ (1 + cos θ)

The ± in the sine and cosine formulas isn't a computational error — it reflects that knowing cos(θ) alone doesn't say which quadrant θ÷2 lands in, so the correct sign has to come from context. This calculator resolves it automatically by checking which quadrant the half angle actually falls in. Tangent sidesteps the issue entirely: dividing sine by one-plus-cosine cancels the ambiguity, which is why it's the one identity here with no ± in front of it.