Arctangent Calculator

Enter a decimal or a simple fraction (e.g., 0.5 or 4/3) to get arctan in degrees and radians.

Number

Arctangent Calculator

Need a quick and accurate way to calculate the arctangent (tan⁻¹) of a value? Our Arctangent Calculator provides instant results in both degrees and radians, helping you solve trigonometric problems with ease. Whether you’re a student learning inverse trigonometric functions, a teacher preparing practice examples, or an engineer applying angles in design and analysis, this tool ensures fast, reliable, and error-free results every time.

Understanding Arctan (tan⁻¹)

Arctangent Definition:
The arctangent function, also written as tan⁻¹(x), is the inverse of the tangent function. It is used to determine the angle when the tangent value is known.
θ = arctan(x)

Domain: −∞ < x < ∞
Range in radians: [−π/2, π/2]
Range in degrees: [−90°, 90°]

👉 In simple terms, arctan tells you the angle whose tangent is equal to a given number, including both positive and negative inputs.

Formula for Arctangent

If tan(θ) = x, then:
θ = arctan(x)
Our Arctangent Calculator applies this instantly, providing accurate results for any real number in both degrees and radians.

Examples of Arctangent Calculations

Using Decimal Values:

arctan(1) = 45° = 0.785 rad → ✅ Result: 45° (0.785 rad)

arctan(0.5) ≈ 26.56° = 0.463 rad → ✅ Result: 26.56° (0.463 rad)

arctan(−12) = −85° = −1.487 rad → ✅ Result: −85° (−1.487 rad)

Using Fraction Values:

arctan(1/3) = 18.43° = 0.321 rad → ✅ Result: 18.43° (0.321 rad)

arctan(10/8) = 51° = 0.896 rad → ✅ Result: 51° (0.896 rad)

arctan(−4/6) = −34° = −0.588 rad → ✅ Result: −34° (−0.588 rad)

Features of Our Arctan Calculator

✅ Provides instant results in degrees and radians

✅ Handles decimals, fractions, and negative numbers accurately

✅ User-friendly interface designed for students and professionals

✅ Works smoothly on mobile, desktop, and tablets

✅ Free to use — no registration required

✅ Eliminates errors from manual calculations

Who Should Use This Calculator?

Students & Teachers – For practicing inverse trigonometry problems in degrees and radians

Engineers & Architects – To solve design and analysis problems involving slopes and angles

Scientists & Researchers – For modeling physical systems that use tangent relationships

Programmers & Developers – To implement trigonometric functions in algorithms and simulations

Everyday Learners – To understand how tangent and arctangent functions work

Why Use an Online Calculator Instead of Manual Calculation?

While arctan can be calculated manually with a scientific calculator, it can be tedious and error-prone, especially when working with fractions, decimals, or negative numbers. Even a small mistake can lead to incorrect results in geometry, physics, or coding applications.
Our Arctangent Calculator removes this problem by delivering instant, accurate, and easy-to-read results, saving you time and effort.

Practical Applications of Arctan

Trigonometry & Geometry – Finding missing angles when tangent ratios are known

Physics & Engineering – Calculating slopes, inclines, and projectile angles

Computer Graphics – Determining rotation and orientation using inverse tangent functions

Navigation – Solving bearing and directional problems

Education – Helping students master inverse trigonometric functions with clarity

✅ The Arctangent Calculator is an essential 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 arctangent calculations in both degrees and radians, for decimal, fraction, and negative values.

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