Arccos Calculator — Inverse Cosine (cos⁻¹)
The arccosine function (arccos or cos⁻¹) finds the angle whose cosine equals a given value. Enter x in [−1, 1] to see the result in degrees, radians, and as a fraction of π — plus arcsin(x) as a complement.
Angle whose cosine equals x, in the range 0° to 180°
- 1
Apply inverse cosine
arccos(0,5) = 1,047198 radReturns the principal value in [0, π] radians. - 2
Convert radians to degrees
1,047198 × (180 ÷ π) = 60
Comment fonctionne cette calculatrice ?
arccos(x) = cos⁻¹(x) returns the angle in [0°, 180°] whose cosine is x. Input x must be in [−1, 1]. Common values: arccos(0) = 90°, arccos(1) = 0°, arccos(−1) = 180°, arccos(0.5) = 60°. Multiply radians by 180/π to convert to degrees.
Formule
How this is calculated
The cosine function maps any angle θ to a value cos(θ) in the interval [−1, 1]. Its inverse — the arccosine — reverses this: given a value x, arccos(x) returns the unique angle θ in [0, π] (i.e. 0° to 180°) whose cosine equals x. The restriction to a single half-period [0, π] is necessary because cosine is not one-to-one over all angles; without it there would be infinitely many solutions.
The relationship between the six inverse trig functions is useful: arccos(x) and arcsin(x) are complementary — they always sum to π/2 (90°). This means arcsin(x) = π/2 − arccos(x). Similarly, arctan(x) = arcsin(x) / arccos(x) (via the identity). Most programming languages provide `Math.acos()` for arccos in radians; divide by π/180 to convert to degrees, or multiply by 180/π.
Common exact values: arccos(0) = 90°, arccos(1) = 0°, arccos(−1) = 180°, arccos(√2/2) = 45°, arccos(1/2) = 60°, arccos(√3/2) = 30°. The plot above shows the full arccos curve from −1 to 1, with your chosen point highlighted — notice that arccos is strictly decreasing: higher x gives a smaller angle.
Questions fréquentes
Cosine repeats every 360°, so many angles have the same cosine value (e.g., cos(60°) = cos(300°) = 0.5). To make arccos a well-defined function, its output is restricted to the principal value range [0°, 180°], also written [0, π] radians. If you need an angle outside this range, you'll need context-specific reasoning (e.g., the quadrant of your original problem).
The real-valued arccos function is only defined for x ∈ [−1, 1] because cosine never exceeds 1 or falls below −1. Inputs outside this range produce NaN (Not a Number) in most calculators and programming languages. In complex analysis, arccos can accept other inputs, but that requires complex numbers.
Degrees = radians × (180/π). Radians = degrees × (π/180). Gradians (grads) = degrees × (10/9) or radians × (200/π). The result is always in [0°, 180°] or equivalently [0, π] rad or [0, 200] grad.
Aussi appelé
TG we-Calculate Editorial Team. (2026). Arccos Calculator — Inverse Cosine (cos⁻¹) [Online calculator]. TG we-Calculate. https://we-calculate.com/fr/calculator/arccos-calculator
TG we-Calculate Editorial Team. "Arccos Calculator — Inverse Cosine (cos⁻¹)." TG we-Calculate. 2026. https://we-calculate.com/fr/calculator/arccos-calculator.
TG we-Calculate Editorial Team, "Arccos Calculator — Inverse Cosine (cos⁻¹)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/fr/calculator/arccos-calculator
@misc{wecalculate_arccos_calculator, title = {Arccos Calculator — Inverse Cosine (cos⁻¹)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/fr/calculator/arccos-calculator}}, year = {2026}, note = {TG we-Calculate} }
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