Inverse Cosine Calculator — arccos(x)
Enter a cosine value between −1 and 1 and get the angle (in degrees, radians or gradians) whose cosine equals that value. The result is the principal value of arccos.
Output unit
Principal value: the angle whose cosine equals the input
- 1
arccos(x) in radians
arccos(0.5) = 1.04719755Principal value — the unique angle θ in [0, π] whose cosine equals x. - 2
Convert to degrees
1.04719755 × 180 ÷ π = 60
How does this calculator work?
arccos(x) returns the angle θ in [0°, 180°] whose cosine equals x (where x must be between −1 and 1). Enter the cosine value and choose degrees, radians or gradians; the calculator also shows the supplement angle and exact equivalents across all units.
Formula
How this is calculated
The inverse cosine function, written arccos(x) or cos⁻¹(x), answers the question: "which angle has this cosine?" Because cosine is periodic, infinitely many angles share the same cosine value. To give a unique answer, arccos is restricted to the principal-value branch, returning an angle in the range [0°, 180°] (equivalently [0, π] radians). If you need the full set of solutions, the general formula is θ = ±arccos(x) + 360°·n for any integer n.
The domain of arccos is [−1, 1], exactly the output range of the cosine function. Inputs outside this interval have no real solution. Common exact values include arccos(1) = 0°, arccos(0) = 90°, arccos(−1) = 180°, arccos(0.5) = 60° and arccos(√2/2) ≈ 45°.
Conversions: 1 radian = 180°/π ≈ 57.296°; 1 gradian (grad) = 0.9°, and a full circle is 400 grad. The supplement of an arccos result is 180° − arccos(x) = arccos(−x), which is useful in triangle calculations.
Frequently asked questions
Arccos is defined as the inverse of cosine restricted to [0°, 180°], making it a true function (one output per input). Outside this range cosine is not one-to-one, so a unique inverse is impossible without restriction.
No real angle has a cosine outside [−1, 1]. The calculator shows a warning. In complex arithmetic arccos can accept values outside this range, but for real-world geometry inputs must stay within the domain.
For any x in [−1, 1]: arccos(x) + arcsin(x) = 90° (π/2 radians). So once you know arccos(x) you can immediately find arcsin(x) = 90° − arccos(x).
Also known as
TG we-Calculate Editorial Team. (2026). Inverse Cosine Calculator — arccos(x) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/inverse-cosine-calculator
TG we-Calculate Editorial Team. "Inverse Cosine Calculator — arccos(x)." TG we-Calculate. 2026. https://we-calculate.com/calculator/inverse-cosine-calculator.
TG we-Calculate Editorial Team, "Inverse Cosine Calculator — arccos(x)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/inverse-cosine-calculator
@misc{wecalculate_inverse_cosine_calculator, title = {Inverse Cosine Calculator — arccos(x)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/inverse-cosine-calculator}}, year = {2026}, note = {TG we-Calculate} }
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