Arccos Calculator

Enter a value between −1 and 1 to find the angle (in degrees or radians) whose cosine equals it.

How to Use the Arccos Calculator

Enter a value between −1 and 1 — the cosine ratio itself, not an angle — and pick degrees or radians for the output. The result updates as the value changes.

Arccos undoes cosine directly: if cos(θ) equals x, then arccos(x) returns θ. The catch is that cosine isn't one-to-one — cos(60°) and cos(300°) both equal 0.5, along with infinitely many other angles sharing that same value — so a function can't just hand back "all of them." By convention, arccos always returns exactly one answer, the principal value, somewhere between 0° and 180° (0 and π radians). Feed it 0.5 and it always comes back with 60°, never 300°, even though both are technically correct answers to "what angle has a cosine of 0.5."

Why the Input Domain Stops at −1 and 1

The −1-to-1 restriction on arccos's input isn't a limitation added on top of the math — it falls straight out of what cosine already does. Cosine, for any real angle, never produces a value outside that range in the first place, so there's no angle out there whose cosine could ever land at 1.5 or −2. Asking arccos for one is asking it to reverse-engineer something that was never produced to begin with, which is exactly why this calculator rejects anything outside that band instead of guessing rather than returning something that merely looks like a number.