Free · Mathematical relations and geometry

Principal Tangent Angle and Ratio

Convert a principal angle between −90 and 90 degrees to its tangent, or recover its principal angle from the tangent.

Calculator inputs

Loading 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.

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

A 45 degree angle has tangent 1. A tangent of −1 gives the principal angle −45 degrees.

t=tan θ; θ=arctan t for −π/2<θ<π/2

Enter these known values and leave the other values blank.

This two-way model uses the principal interval strictly between −90 and 90 degrees so the inverse is unique.
Tangent is dimensionless. The selected angle unit converts degrees, radians or multiples of π radians.
Angles at the endpoints are excluded because tangent has poles there. Other periodic tangent solutions differ by 180 degrees.

A full tangent curve is periodic and cannot have a unique inverse. The principal interval selects exactly one real angle for every real tangent.

The reversible tangent relation selects its unique principal interval. The source omitted its inverse branch domain.