Free · Mathematical relations and geometry

Inverse Tangent and Principal Degree Angle

Find the unique inverse-tangent angle between −90 and 90 degrees or recover the corresponding ratio.

Calculator inputs

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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.

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A tangent ratio of −1 corresponds to −45° on the principal branch. A ratio of 1 corresponds to 45°.

y=arctan x, with −π/2<y<π/2

Enter these known values and leave the other values blank.

The real principal angle lies strictly between −90 and 90 degrees.
The angle is constrained to the exact principal interval. Endpoints have no finite tangent.
Inverse tangent differs from reciprocal tangent. The derived degree helper supports the contextual special-angle notes.

Leave the unknown control empty and enter the quantities needed by the selected relation. Read the assumptions for any branch or domain restrictions.

It is an exact mathematical model with independently checked numbers. Display rounding does not change the values used for subsequent calculations.

The exact principal inverse-tangent interval replaces the permissive effect of the source rounded 1.5708-radian limits.