Polar Coordinates Calculator

Polar Coordinates are often used in mathematical applications where circular or rotational symmetry is involved. This calculator lets you convert a point (x, y) in the Cartesian plane to polar coordinates (r, θ).

Formulas for Conversion

The formulas used for conversion are:
\[ r = \sqrt{x^2 + y^2} \]
\[ \theta = \arctan \left(\frac{y}{x}\right) \]

Understanding Polar Coordinates

Polar coordinates express a point’s location using a radius \( r \) and an angle \( \theta \) measured from the positive x-axis. This system is particularly useful in fields such as physics, engineering, and mathematics.

Example Calculation

If \( x = 3 \) and \( y = 4 \):
\[ r = \sqrt{3^2 + 4^2} = 5 \]
\[ \theta = \arctan\left(\frac{4}{3}\right) = 0.93 \text{ radians} \]

For additional mathematical tools, you can explore:

• [Reference Angle Calculator]
• [Coterminal Angle Calculator]
• [Linear Equation Calculator]
• [Rotation Calculator]