ArcCos Calculator
Find the angle whose cosine equals a given value, with principal value in degrees or radians.
About ArcCos Calculator
The inverse cosine (arccos) returns the angle whose cosine equals x. The principal value is in [0°, 180°] or [0, π]. The domain is [−1, 1].
Formula
Inverse cosine
θ = arccos(x), where −1 ≤ x ≤ 1
- x
- The cosine value
- θ
- The resulting angle in [0°, 180°]
Worked example
With the default values below, ArcCos Calculator returns arccos(x) of 60.00000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Value (x)accepts -1–1
- 0.5
- Angle unitone of Degrees, Radians
- Degrees
Results
- arccos(x)
- 60.00000000
- Result (degrees)
- 60.000000 °
- Result (radians)
- 1.04719755
Step by step
- 1Input value= 0.5
- 2Compute arccos= 60° = 1.04719755 rad
- 3Principal range= [0°, 180°]
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is arccos(0.5)?
arccos(0.5) = 60°, because cos(60°) = 0.5.
What is arccos(−1)?
arccos(−1) = 180°, the largest value in the principal range.