What the Inverse Cosine Does
The arccosine function (arccos or cos⁻¹) is the inverse of the cosine function: given a cosine value, it returns the angle that produced it. Enter any number between −1 and 1 and this tool gives you the matching angle instantly.
cos(θ) = x then arccos(x) = θ, with x ∈ [−1, 1] and θ ∈ [0°, 180°].Domain and Range at a Glance
Domain [−1, 1]
Range [0°, 180°]
How to Calculate Arccos
Enter a Value in [−1, 1]
Type a cosine value between −1 and 1 into the input field. A number outside this range has no real arccosine.
Choose DEG or RAD
Select DEG to read the answer in degrees, or RAD for radians. The tool shows the other unit alongside it.
Read the Angle Instantly
The angle is computed automatically as you type — both the degree and radian values appear together, no button press needed.
Verify the Result
The calculator confirms the answer by feeding it back through cosine, so cos(result) matches your input.
Arccos Calculator Features
Inverse Cosine of Any Valid Value
Computes arccos for any input within the domain [−1, 1].
Degrees and Radians Together
Shows the resulting angle in both units at once, with radians formatted as π-fractions where they match a standard angle.
Domain Validation
Flags any value outside [−1, 1] so you never get an invalid result.
Built-In Verification
Displays the check cos(result) = input and recalculates in real time as you type.
Common Arccosine Values
| Input | arccos result | Radians |
|---|---|---|
| arccos(1) | 0° | 0 |
| arccos(√3/2) | 30° | π/6 |
| arccos(√2/2) | 45° | π/4 |
| arccos(0.5) | 60° | π/3 |
| arccos(0) | 90° | π/2 |
| arccos(−1) | 180° | π |
Frequently Asked Questions
What is the domain and range of arccos?
The input (domain) must be between −1 and 1. The output angle (range) is always between 0° and 180°, which is 0 to π in radians.
Why is the arccos range [0°, 180°] different from arcsin?
Each inverse trig function is restricted to one interval so it returns a single, unique angle. For arccos, [0°, 180°] covers every possible cosine value exactly once, whereas arcsin uses [−90°, 90°].
What is arccos(0) and arccos(−1)?
arccos(0) = 90° (π/2 radians), since cos(90°) = 0. arccos(−1) = 180° (π radians), the largest angle arccos returns.
Is cos⁻¹(x) the same as 1/cos(x)?
No. cos⁻¹(x) is the inverse function (arccos), which returns an angle. 1/cos(x) is the secant (sec). The superscript −1 here denotes the inverse, not a reciprocal.
Can I switch between degrees and radians?
Yes. Use the DEG / RAD toggle to pick the output unit. Either way, the calculator also shows the angle in the other unit, with radians written as a π-fraction for standard angles.
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