CalcaTools

Inverse Cos Calculator

Calculates inverse cosine using θ = cos⁻¹(x), defined for −1 ≤ x ≤ 1, live in your browser.

Last updated: July 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

What the Inverse Cos Calculator does

Every result on this page comes from a real formula — θ = cos⁻¹(x), defined for −1 ≤ x ≤ 1; result ranges from 0° to 180° — computed live in your browser the moment you press the button.

For context, the sections beneath the calculator include typical values, a worked example you can recompute by hand, and an FAQ covering the practical details of inverse cosine calculator.

Quick reference

xarccos(x)
10°
0.86630°
0.70745°
0.560°
090°
−0.5120°
−1180°

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

OutputMeaning
DegreesThe angle whose cosine equals x, between 0° and 180°.
RadiansThe same angle in radians (0 to π).
Domainx must be between −1 and 1; outside that, arccos is undefined.

Formula & methodology

Formula: θ = cos⁻¹(x), defined for −1 ≤ x ≤ 1; result ranges from 0° to 180°

The inverse cosine (arccos or cos⁻¹) returns the angle whose cosine is the value you enter. It is the inverse of the cosine function on the range 0°–180°.

  1. Enter a value x between −1 and 1.
  2. The calculator computes θ = cos⁻¹(x) in radians.
  3. It converts radians to degrees (× 180 ÷ π).
  4. Read the angle in both degrees and radians below the result.

Worked example: cos⁻¹(0.5) = 60° = 1.0472 radians.

Frequently asked questions

What is the inverse cosine of a number?
It is the angle whose cosine equals that number. For example, cos⁻¹(0.5) = 60°, because cos(60°) = 0.5.
What is the domain of arccos?
Arccos is only defined for inputs between −1 and 1. Values outside that range have no real inverse cosine.
What range does arccos return?
The principal value of arccos always lies between 0° and 180° (0 to π radians).
Is cos⁻¹ the same as 1/cos?
No. cos⁻¹ is the inverse function (arccos), not the reciprocal. The reciprocal of cosine is secant (sec = 1/cos).
Is it free and private to use?
Yes — it is 100% free, needs no sign-up, and every calculation runs in your browser, so your inputs are never uploaded or stored.
What do cos⁻¹, arccos, and acos mean — are they different?
They're three notations for the same inverse cosine function. cos⁻¹(0.5) = 60° whichever way it's written. The trap is reading cos⁻¹ as 1/cos — that reciprocal is the secant, a different function entirely. On most calculators you reach it with SHIFT/2nd + COS.
Why does inverse cosine say 'math error' for my number?
Arccos only accepts inputs from −1 to 1, because cosine never leaves that range. If you're solving a triangle and get cos θ = 1.15, the triangle as specified is impossible — usually a sides mix-up in the law of cosines. Also check the mode: arccos(0.5) is 60 in degrees but 1.047 in radians.