Arccosine Calculator

Enter a decimal or a simple fraction (e.g., 0.5 or 2/3) to get arccos in degrees and radians.

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Arccosine Calculator

Do you need a simple and accurate way to calculate the arccosine (cos⁻¹) of a value? Our Arccosine Calculator makes it quick and effortless to find angles in both degrees and radians. Whether you’re a student learning inverse trigonometric functions, a teacher preparing examples, or an engineer working with technical designs, this tool ensures fast, precise, and error-free results every single time.

Understanding Arccosine (cos⁻¹)

Arccosine Definition:
The arccosine function, also written as cos⁻¹(x), is the inverse of the cosine function. It allows you to determine the angle when the cosine value is already known.
θ = arccos(x)

Domain: −1 ≤ x ≤ 1
Range in radians: [0, π]
Range in degrees: [0°, 180°]

👉 In other words, arccosine gives you the angle (in degrees or radians) that corresponds to a given cosine value.

Formula for Arccosine

If cos(θ) = x, then:θ = arccos(x)
This calculator instantly applies the formula, giving you accurate results for valid inputs between −1 and 1.

Examples of Arccosine Calculations

Using Decimal Values:

arccos(0.5) = 60° = 1.047 rad → ✅ Result: 60° (1.047 rad)

arccos(0.7071) ≈ 45° = 0.785 rad → ✅ Result: 45° (0.785 rad)

arccos(0.866) ≈ 30° = 0.523 rad → ✅ Result: 30° (0.523 rad)

Using Fraction Values:

arccos(1/2) = 60° = 1.047 rad → ✅ Result: 60° (1.047 rad)

arccos(4/7) ≈ 55° = 0.962 rad → ✅ Result: 55° (0.962 rad)

arccos(2/3) ≈ 48° = 0.841 rad → ✅ Result: 48° (0.841 rad)

Features of Our Arccosine Calculator

✅ Provides instant results in degrees and radians

✅ Handles decimal and fraction inputs with accuracy

✅ Simple, user-friendly, and clean design

✅ Works seamlessly on mobile, tablet, and desktop

✅ Free to use — no registration required

✅ Eliminates errors from manual calculations

Who Should Use This Calculator?

Students & Teachers – For assignments, problem-solving, and classroom demonstrations

Engineers & Architects – To apply arccos in technical and design work

Scientists & Researchers – For wave motion, oscillation, and physics problems

Programmers & Developers – For implementing trigonometric functions in applications

Everyday Learners – To understand the connection between cosine and arccosine

Why Use an Online Calculator Instead of Manual Calculation?

Although it’s possible to calculate arccos manually using trigonometric tables or a scientific calculator, this can be time-consuming and prone to errors — especially with decimal approximations or square-root fractions. Even a minor mistake can give an incorrect angle.
Our Arccosine Calculator removes the hassle by delivering instant, accurate, and error-free results, saving you valuable time and effort.

Practical Applications of Arccosine

Trigonometry & Geometry – Finding angles when the cosine value is known

Physics & Engineering – Modeling waveforms, oscillations, and mechanical systems

Architecture & Construction – Calculating inclines and structural angles

Navigation – Using cosine ratios to determine bearings and distances

Education – Helping students clearly grasp inverse trigonometric functions

✅ The Arccosine Calculator is a must-have tool for anyone working with trigonometry, geometry, physics, or engineering. Whether you’re a student, teacher, professional, or researcher, this calculator ensures fast, accurate, and reliable arccosine calculations in both degrees and radians for decimal and fraction values.

👉 Try our Arccosine Calculator today on Hive Calculator and make your trigonometric calculations smarter, faster, and error-free!