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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.

Angle (rad): 0.785398 rad

Angle (rad)

0.000000rad
Angle: 45 °

Angle

0.000000°

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