Example 1
- x: 0.5
- Degrees
60°
Because cos 60° = 0.5.
Arccos calculator
Type x from −1 to 1 and pick degrees or radians. Arccos, inverse cosine, rebuilds the angle whose cosine is x. arccos(0.5) = 60°. arccos(0) = 90°. arccos(1) = 0°.
arccos only works for x in [−1, 1]. The result lies between 0° and 180° (0 to π).
Result
Enter x between −1 and 1.
How it works
Inverse cosine undoes cosine: from a number x you recover an angle α such that cos α = x. arccos(0.5) = 60°. arccos(0) = 90°. arccos(1) = 0°. arccos(−1) = 180°. The result lies between 0° and 180° (0 to π).
x must sit in [−1, 1], because cosine never leaves that interval. 1.2 the calculator rejects. 0.8 from a 3-4-5 triangle (4/5) gives the angle whose cosine is 0.8, about 36.87°.
Fields: Value x (cosine) and Show result in degrees or radians. Type 0.5, leave degrees, click Calculate. A comma and a period both parse. In radians 60° is π/3, about 1.047.
Bare cosine of 60° lives on cosine. Sine is not inverted here: sine needs a different inverse. This calculator stays with cosine and an angle in [0°, 180°].
Without an x in range, nothing computes. 0.5 still gives 60° no matter the header units.
arccos(√2/2) = 45°. arccos(√3/2) = 30°. arccos(−0.5) = 120°. Check 0.5 and 0 on the page.
Formula
α = arccos(x), where −1 ≤ x ≤ 1
How to use
- Type x in Value x (cosine), from −1 to 1, for example 0.5.
- Pick Show result in: Degrees (°) or Radians.
- Click Calculate. 0.5 gives 60°. 0 gives 90°. 1 gives 0°. −1 gives 180°.
- x outside [−1, 1] does not run. 1.2 is not a real cosine.
- Bare cosine of 60° lives on cosine. Here you go from a value to an angle.
arccos(0.5) = 60°
Arccos rebuilds the angle whose cosine is x. arccos(0.5) = 60°. arccos(0) = 90°. arccos(1) = 0°. x only from −1 to 1.
- arccos
- Inverse cosine in this calculator. Input only from −1 to 1. arccos(0.5) = 60°, arccos(−1) in radians is π.
- x
- The cosine value. 0.5, 0, 1 or −1. 1.2 does not run, because it is not a real cosine.
Examples
Example 2
- x: 0
90°
cos 90° = 0.
Example 3
- x: 1
0°
cos 0° = 1.
Example 4
- x: −1
- Radians
π ≈ 3.1416
That is 180°.
Example 5
- Value x (cosine): -0.5
- Show result in: deg
120 deg
What is arccos(−0.5) in degrees? 120°.
Example 6
- Value x (cosine): 0.866
- Show result in: deg
30 deg
What is arccos(0.866) in degrees? About 30°.
Example 7
- Value x (cosine): 0.707
- Show result in: deg
45 deg
What is arccos(0.707) in degrees? About 45°.
Example 8
- Value x (cosine): -0.5
- Show result in: rad
2.094 rad
What is arccos(−0.5) in radians? About 2.094.
Related calculators
Frequently asked questions
What is arccos(0.5)?
The angle is 60°, because cos 60° = 0.5. In radians about 1.047, which is π/3. First clean example on the page.
What is arccos(0)?
The angle is 90°. cos 90° = 0. In radians π/2, about 1.5708. The middle of the range from 0° to 180°.
What are arccos(1) and arccos(−1)?
arccos(1) = 0°, arccos(−1) = 180°. Those are the ends of the domain and of the range. Past that there is no real angle.
Why does 1.2 fail?
Cosine in the reals only runs from −1 to 1. 1.2 sits outside that interval, so there is no angle here.
What angle comes from 0.8 (4/5)?
About 36.87°. That is the cosine of adjacent 4 over hypotenuse 5 in a 3-4-5 triangle. The calculator computes the angle, not the sides.
What is arccos(−0.5)?
The angle is 120°. A negative cosine lands in the second quadrant and still stays from 0° to 180°.
Can the result be 270°?
No. The principal value of arccos runs from 0° to 180°. 270° would share cosine with 90°; the calculator picks 90° from zero.
How do I get radians?
Set Show result in: Radians. 60° becomes π/3, about 1.047. 180° becomes π.
How is this different from cosine?
Cosine of 60° gives 0.5. Here 0.5 returns 60°. The same two numbers, the inverse path and another field.
Does arccos invert sine?
No. Sine has its own inverse. Here x is a cosine value, not a sine. Another function, another field.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.