Arccosine Calculator

cos⁻¹(x) — find the angle whose cosine is x. Range [0°, 180°].

Inputs

Result

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General calculation reads

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How to use this calculator

  • Enter a value between -1 and 1.
  • Read the angle.

About this calculator

arccos (cos⁻¹) returns the angle whose cosine is the input. Domain [−1, 1]; principal range [0°, 180°] or [0, π]. Common values: arccos(1) = 0°, arccos(½) = 60°, arccos(0) = 90°, arccos(−½) = 120°, arccos(−1) = 180°.

Frequently asked

Why is the range 0° to 180°?+
arccos is the principal inverse of cosine, restricted to make the function single-valued. Cosine is one-to-one only on [0°, 180°].
How does arccos relate to arcsin?+
arccos(x) + arcsin(x) = 90° (or π/2 in radians) for any x in [−1, 1].
What if x is outside [-1, 1]?+
No real solution. Cosine only outputs values in [−1, 1], so its inverse only accepts those.
Common application?+
In the law of cosines: cos(C) = (a² + b² − c²)/(2ab), then C = arccos(...) gives the angle.
Why not just use arcsin and shift?+
You can — arccos(x) = 90° − arcsin(x). But arccos is convenient for problems where the cosine is naturally what you computed.

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