Arctangent Calculator

About Arctangent Calculator

Arctangent returns the angle whose tangent is x, in the range (-90°, 90°). arctan(1) = 45°.

How to use this calculator

1. Enter the tangent value, such as 1 or 0.5.
2. Choose the angle unit if the calculator lets you switch between degrees and radians.
3. Click calculate to get the inverse tangent.
4. Check that the answer is reasonable, especially for negative values or values close to 0.

The formula explained

The formula \(\arctan(x)=\tan^{-1}(x)\) computes the angle whose tangent is \(x\). Because tangent repeats, arctan returns the principal angle, usually between \(-90^\circ\) and \(90^\circ\) or between \(-\pi/2\) and \(\pi/2\).

• x = the tangent value you enter
• \(\arctan(x)\) = the angle whose tangent equals x
• \(\tan^{-1}(x)\) = another notation for arctangent

Step by step method

1. Identify the tangent ratio or decimal you want to convert into an angle.
2. Use the inverse tangent function to find the angle.
3. If needed, convert the result between radians and degrees.

Worked example

Problem. Find the angle whose tangent is 1.

1. Set up the calculation: \(\theta = \arctan(1)\).
2. Since \(\tan(45^\circ)=1\), the inverse tangent gives \(\theta=45^\circ\).
3. In radians, this is \(\theta=\pi/4\).

Tips and common mistakes

• Make sure you know whether your calculator is in degrees or radians before interpreting the answer.
• If the input is negative, the arctangent result will also be negative, for example \(\arctan(-1)=-45^\circ\).

Frequently asked questions