Free · Coordinate geometry calculators 📈

Polar & Cartesian Coordinates: Choose a Direction

Switch between radius-and-angle inputs and signed x/y inputs while keeping angle units and quadrant conventions explicit.

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.

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

A radius of 2 at 60° gives x = 1 and y = √3. In the reverse mode, (−1, 1) gives radius √2 and principal direction 135°.

x = r cos θ; y = r sin θ; r = √(x² + y²); θ = atan2(y, x)

Enter these known values and leave the other values blank.

A radius is nonnegative. The angle is counterclockwise from the positive x-axis; select degrees, radians, gradians, turns or multiples of π as needed.
The two modes are separate forward calculations. Switching modes does not automatically transfer results into the other set of inputs.
Cartesian components share the radius’s length scale. Angles differing by a full turn describe the same nonzero point.
A zero radius maps to the origin for every entered angle. In the reverse mode, the origin has zero radius and no unique direction, so its angle stays blank.

It returns the principal direction between −180° and 180°. For example, −90° and 270° indicate the same downward direction.

This convention uses nonnegative radius. Reverse the direction by half a turn instead of using a negative radius.

Bookify leaves the inverse direction undefined at the zero vector while retaining its zero radius.