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Inverse Cos Calculator | Compute arccos for inputs -1 to 1

Convert a cosine ratio to its angle with arccos, in degrees or radians, including the supplementary solution. Shows the principal range and the unit-circle reasoning — ideal for right-triangle trigonometry and physics problems.

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°

info Inverse Cos Calculator

Free math calculator — enter your numbers and get an instant, accurate result.

info Private by design

Everything runs locally in your browser. No uploads, no accounts, no tracking.

info Works everywhere

Fully responsive and mobile-friendly — calculate on any device, any time.

info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

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.

lightbulb Worked example

Let's say you are using the Inverse Cos Calculator. Calculates inverse cosine using θ = cos⁻¹(x), defined for −1 ≤ x ≤ 1, live in your browser. Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula θ = cos⁻¹(x), defined for −1 ≤ x ≤ 1; result ranges from 0° to 180° and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

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

The Inverse Cos Calculator is built on a well-established calculation method. It uses the formula θ = cos⁻¹(x), defined for −1 ≤ x ≤ 1; result ranges from 0° to 180° to turn your inputs into a reliable result. Calculates inverse cosine using θ = cos⁻¹(x), defined for −1 ≤ x ≤ 1, live in your browser. The steps are shown on the page so you can follow the reasoning from input to output.

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.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is the inverse cosine of a number?
The Inverse Cos Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Calculates inverse cosine using θ = cos⁻¹(x), defined for −1 ≤ x ≤ 1, live in your browser. There is no limit on usage, and it works on any device.
What is the domain of arccos?
The Inverse Cos Calculator is a free online tool that calculates inverse cosine using θ = cos⁻¹(x), defined for −1 ≤ x ≤ 1, live in your browser. You enter a few values, and it returns an accurate result together with a step-by-step explanation, so it works as both a calculator and a quick reference for the underlying concept.
What range does arccos return?
Arccos returns angles between 0° and 180° (0 to π radians), the principal range chosen so the function is single-valued. A cosine of 1 gives 0°, 0 gives 90°, and −1 gives 180°. This differs from arcsin, which returns −90° to 90°. The calculator shows the principal angle and, where relevant, the supplementary solution.
Is cos⁻¹ the same as 1/cos?
No — cos⁻¹(x) is the inverse cosine function, which answers 'what angle has this cosine?', while 1/cos(x) is the secant, the reciprocal of the cosine VALUE. The notation is confusingly similar but the meanings are completely different: cos⁻¹(0.5) = 60°, while 1/cos(60°) = 2. The calculator applies the inverse function, not the reciprocal.
Is it free and private to use?
Yes — the Inverse Cos Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
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.
What does the Inverse Cos Calculator do?
Calculates inverse cosine using θ = cos⁻¹(x), defined for −1 ≤ x ≤ 1, live in your browser. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Inverse Cos Calculator use?
It uses θ = cos⁻¹(x), which is only defined for input values between −1 and 1, and returns an angle between 0° and 180°. Enter the cosine ratio and the tool gives the angle in degrees or radians. For example, cos⁻¹(0.5) = 60°, which is useful for finding angles in right-triangle problems when you know the adjacent side and hypotenuse.
Is the Inverse Cos Calculator free and private?
Yes — it is free with no sign-up or limits, and calculations run entirely in your browser so nothing is uploaded. CalcaTools covers its costs with display advertising. The tool returns the angle in degrees and radians for any valid cosine input between −1 and 1, with the principal range explained.
How accurate is the Inverse Cos Calculator?
The Inverse Cos Calculator applies the standard formula: θ = cos⁻¹(x), defined for −1 ≤ x ≤ 1; result ranges from 0° to 180°. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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