Arctan Calculator (Inverse Tangent)

Arctan Calculator (Inverse Tangent). Enter any real number into the Arctan Calculator and find the inverse tangent — the angle whose tangent equals your input. Type your value into the x input and get the resulting angle in both degrees and radians instantly. You can also choose to enter the ratio as opposite over adjacent sides for triangle-based problems. Results include the principal value within the standard range of −90° to 90°. Also try the find f(α + β) with Sum and Difference Identities Calculator.

Results

Angle in Degrees

Angle in Radians

Angle in Terms of π

Tangent Value Used

Results Table

What is arctan?

Arctan (arctangent) is the inverse of the tangent function. Given a tangent value x, arctan(x) returns the angle whose tangent equals x. The result is always within the principal range of −90° to 90° (or −π/2 to π/2 in radians). See also our use the Cofunction Calculator.

Is arctan the same as tan⁻¹?

Yes, arctan(x) and tan⁻¹(x) are two different notations for the same inverse tangent function. Both give you the angle whose tangent is x. The tan⁻¹ notation is commonly used on calculators and in textbooks.

What is arctan(1)?

arctan(1) = 45° or π/4 radians. This is because tan(45°) = 1, so the inverse tangent of 1 is 45°.

What is the arctan of √3?

arctan(√3) = 60° or π/3 radians. Since tan(60°) = √3 ≈ 1.7321, the inverse tangent of √3 is 60°.

What is the range of arctan?

The principal value range of arctan is from −90° to 90° (exclusive), or equivalently −π/2 to π/2 in radians. This restricted range makes arctan a proper function with a unique output for every input.

What is the derivative of arctan?

The derivative of arctan(x) with respect to x is 1 / (1 + x²). This is a commonly used result in calculus, especially for integration by substitution.

What is the integral of arctan?

The integral of arctan(x) is x·arctan(x) − (1/2)·ln(1 + x²) + C, where C is the constant of integration. This is derived using integration by parts.

How do I calculate arctan on a calculator?

On most scientific calculators, press the Shift (or 2nd) key followed by the tan button to activate the tan⁻¹ function. Then enter your value and press equals. Make sure your calculator is set to the correct mode (degrees or radians) before computing. You might also find our Law of Cosines Calculator useful.