Free · Trigonometry calculators 📐

Arctangent Value and Principal Angle Conversion

No. It selects one principal angle in the open interval from −π/2 to π/2. Tangent repeats periodically, but angles outside this branch are rejected in the backward control.

Formula & worked example
Private in your browser
No signup

Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: x -1 gives y -45.

y = arctan x; x = tan y on the principal interval

Worked example

Enter these known values and leave the other values blank.

x: -1

y: -45 deg

Assumptions and limitations

Arctangent selects the principal real angle rather than every periodic solution of tangent. The interval is open at −π/2 and π/2. Units change the representation of the same angle; the principal branch remains unchanged.
Use compatible units and enough independent values. Clear unknowns before solving backward. Original reference drawings are schematic and do not scale to entered values.

Common questions

Does arctangent return every tangent solution?