MATH CALCULATOR
Polar to Cartesian Calculator
Convert polar coordinates to Cartesian coordinates with ease using our online calculator.
What is the Polar to Cartesian Calculator & How does it work?
The conversion from polar coordinates (r, ΞΈ) to Cartesian coordinates (x, y) is a fundamental concept in mathematics and engineering. Polar coordinates represent points on a plane using a distance from a reference point (the origin) and an angle from a reference direction.
The formulas for converting polar coordinates to Cartesian coordinates are:
x = r cdot cos(theta)
x = Cartesian coordinate (horizontal distance from origin)
r = radial distance from the origin
ΞΈ = angle in radians from the positive x-axis
r = radial distance from the origin
ΞΈ = angle in radians from the positive x-axis
Similarly,
y = r cdot sin(theta)
y = Cartesian coordinate (vertical distance from origin)
r = radial distance from the origin
ΞΈ = angle in radians from the positive x-axis
r = radial distance from the origin
ΞΈ = angle in radians from the positive x-axis
Parameters
Resultβ
Frequently Asked Questions
How do I convert polar coordinates to Cartesian coordinates?
Use the formulas x = r * cos(ΞΈ) and y = r * sin(ΞΈ), where r is the radial distance, ΞΈ is the angle in radians, and (x, y) are the Cartesian coordinates.
What do r and ΞΈ represent in polar coordinates?
r represents the radial distance from the origin, and ΞΈ represents the angle in radians from the positive x-axis.
Can I use this calculator for any angle unit?
This calculator uses radians by default. You may need to convert degrees to radians manually before using the calculator.
What is the Cartesian coordinate system?
The Cartesian coordinate system represents points on a plane using x and y coordinates, where x is the horizontal distance from the origin and y is the vertical distance.
Why would I need to convert polar to Cartesian coordinates?
Conversion is often needed in fields like physics, engineering, and computer graphics for calculations that are easier in Cartesian form.
Is there a limit to the values of r and ΞΈ I can use?
There is no inherent limit, but very large or small values may result in numerical precision issues depending on your calculator’s capabilities.
Can this calculator handle complex numbers?
This calculator is designed for real numbers. For complex number conversions, you would need a different tool.
Results are for informational purposes only and do not constitute professional advice.