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°.

Enter the tangent value to find the corresponding angle.

Length of the side opposite to the angle.

Length of the side adjacent to the angle.

Results

Angle in Degrees

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Angle in Radians

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Angle in Terms of π

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Tangent Value Used

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Angle: Degrees vs Radians (scaled)

Results Table

Frequently Asked Questions

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).

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.

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