Arccos Calculator
Enter a number x between -1 and 1 to get arccos(x) = cos⁻¹(x), the inverse cosine, as an angle in degrees and in radians — plus the degrees-minutes-seconds form and the general periodic solution — all computed in this browser tab.
Principal value and its negative: ±θ° + k×360°.
Principal value and its negative: ±θ rad + k×2π.
Enter a value for x, then press Calculate. Results appear here.
How it works: arccos(x) = cos⁻¹(x) is the inverse cosine: if cos(60°) = 0.5 then arccos(0.5) = 60°. The principal value is defined only for -1 ≤ x ≤ 1, from 0° to 180° (0 to π rad); the full solution repeats as ±θ + k×360°. Results are shown in degrees, radians, degrees-minutes-seconds and π-radians, with degrees/radians rounded to 8 decimals. All math happens in this browser tab — nothing is uploaded, stored, or shared.
Enter x
Type any number from -1 to 1 (decimals and scientific notation are fine, e.g. 0.5 or -0.7071068). Anything outside this range has no real arccos, and the calculator says so instead of inventing a number.
Press Calculate
The principal angle is computed with the standard inverse-cosine function: degrees and radians rounded to 8 decimals, seconds to 3, and the π-radians coefficient to 6.
Read every form
You get degrees and radians as ±θ pairs, a degrees-minutes-seconds breakdown, and the general solution ±θ + k×360° (or ±θ + k×2π) that lists every angle sharing the same cosine.
Common arccos values
| x | arccos(x) — degrees | arccos(x) — radians |
|---|---|---|
| -1 | 180° | π |
| -0.8660254 | 150° | 5π/6 |
| -0.7071068 | 135° | 3π/4 |
| -0.5 | 120° | 2π/3 |
| 0 | 90° | π/2 |
| 0.5 | 60° | π/3 |
| 0.7071068 | 45° | π/4 |
| 0.8660254 | 30° | π/6 |
| 1 | 0° | 0 |
Arccos definition
The arccosine function is the inverse function of cos(x) — arccos(x) = cos⁻¹(x). For example, if the cosine of 60° is 0.5 (cos 60° = 0.5), then the arccos of 0.5 is 60°: arccos(0.5) = cos⁻¹(0.5) = 60°.
How this calculator works
- Why must x be between -1 and 1?
- Cosine only ever outputs values from -1 to 1, so no real angle has a cosine outside that interval. Values like 2 or -1.0000001 are rejected with a clear message instead of a made-up angle.
- What is the principal value?
- Every valid x has infinitely many matching angles. The calculator first reports the principal value — the unique angle from 0° to 180° (0 to π rad) whose cosine is x — and the result fields show it together with its negative.
- What do the ±θ + k×360° lines mean?
- They are the general solution: if θ is one angle with cos θ = x, then every angle ±θ + k×360° (equivalently ±θ + k×2π, or the shown π-radians coefficient) has the same cosine, for any integer k.
- How precise are the results?
- Degrees and radians are rounded to 8 decimals, DMS seconds to 3, and the π-radians coefficient to 6. Type a rounded table value like 0.7071068 and you get 44.99999848°, not a fudged 45° — the math tracks your exact input.
Privacy: this calculator runs entirely in your browser tab. Your input and results are never uploaded, stored, or shared.