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Half angle calculator

Calculate the sine, cosine and tangent of half your angle in degrees.

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Answer

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Calculate the sine, cosine and tangent of half your angle in degrees.

More results
Precision and calculation record
Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.
Saved scenario
Save the current answer, then change an input to compare. This clears when you leave.
Formula and assumptions
The sign comes from the actual half-angle quadrant, not an always-positive square root. Tangent is undefined at half-angles of 90° plus whole half-turns.
Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.
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Updated 
Using Half angle calculator
Calculate the sine, cosine and tangent of half your angle in degrees.
The sign comes from the actual half-angle quadrant, not an always-positive square root. Tangent is undefined at half-angles of 90° plus whole half-turns.
Next: Scientific calculator
A worked example
Example inputs: angle θ (degrees) = 180. sin(θ/2) = 1.
Before you use the result
The sign comes from the actual half-angle quadrant, not an always-positive square root. Tangent is undefined at half-angles of 90° plus whole half-turns.
Example results for angle θ (degrees)
These examples use the formula above. They are reference calculations, not recommended settings.
Angle θ (degrees)sin(θ/2)
900.707106781187
1801
3601.22464679915e-16
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ToolOctopus. “Half angle calculator.” Updated 2026-09-26. https://tooloctopus.com/half-angle-calculator.
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