What is the arctangent (inverse tangent) of a value?

The arctangent of a value x is the angle whose tangent is x. It is the inverse operation of the tangent function. For example, arctan(1) = π/4 radians (45°), because tan(45°) = 1.

What is the principal value of arctan?

The principal value of arctan is the angle in the range -π/2 to π/2 radians (-90° to 90°). This calculator returns the principal value, ensuring a unique result for any input.

Can I input negative values?

Yes, you can input any real number, including negative values. The arctan of a negative number is negative, within the principal range. For example, arctan(-1) = -π/4 radians (-45°).

Math

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Arctan Calculator.

Calculate the principal inverse tangent in radians and degrees.

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Set your values

Results update as you type.

02 / ANSWER

Tangent value

Angle (rad)

0.785398rad

Angle

45°

Results update automatically as you type.

Use Cases

Solve trigonometric equations

Find the angle when you know the tangent ratio, useful in geometry, physics, and engineering problems.

Example: If tan(θ) = 0.5, then θ = arctan(0.5) ≈ 26.57°.

Convert slope to angle

Determine the angle of a slope or incline from its rise-over-run ratio.

Example: A slope of 0.2 (20% grade) corresponds to arctan(0.2) ≈ 11.31°.

Frequently Asked Questions

What is the arctangent (inverse tangent) of a value?: The arctangent of a value x is the angle whose tangent is x. It is the inverse operation of the tangent function. For example, arctan(1) = π/4 radians (45°), because tan(45°) = 1.
What is the principal value of arctan?: The principal value of arctan is the angle in the range -π/2 to π/2 radians (-90° to 90°). This calculator returns the principal value, ensuring a unique result for any input.
Can I input negative values?: Yes, you can input any real number, including negative values. The arctan of a negative number is negative, within the principal range. For example, arctan(-1) = -π/4 radians (-45°).

Tips & Common Mistakes

Tips

Remember that arctan returns angles in radians by default; use the degree conversion if needed.
For positive inputs, the result is between 0 and 90°; for negative inputs, between -90° and 0°.
Use the arctan function to find angles in right triangles when you know the opposite and adjacent sides.
Check your calculator mode (radians vs degrees) to ensure your result matches your expected unit.

Common Mistakes to Avoid

Confusing arctan with cotangent: arctan(x) is the inverse tangent, not 1/tan(x).
Forgetting that the result is limited to the principal range, so arctan(tan(θ)) may not equal θ if θ is outside -90° to 90°.
Using degrees when you need radians, or vice versa, without converting.

Last updated: August 13, 2026