# Polar vs. Cartesian Coordinates

In the Cartesian system the coordinates are perpendicular to one another with the same unit length on both axes.

Cartesian coordinates in the figure below: (2,3)

A Polar coordinate system is determined by a fixed point, a origin or pole, and a zero direction or axis. Each point is determined by an angle and a distance relative to the zero axis and the origin.

Polar coordinates in the figure above: (3.6, 56.31)

Polar coordinates can be calculated from Cartesian coordinates like

r = (x^{2}+ y^{2})^{1/2}(1)

where

r = distance from origin to the point

x = Cartesian x-coordinate

y = Cartesian y-coordinate

θ = atan(y / x)

= tan^{-1}(y / x) (2)

where

θ = angle relative to the zero axis (degrees)

Cartesian coordinates can be calculated from Polar coordinates like

x = r cos(θ) (3)

y = r sin(θ) (4)

### Online Cartesian to Polar Coordinates Converter

### Online Polar to Cartesian Coordinates Converter

## Related Topics

### • Mathematics

Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

## Related Documents

### Area Survey App

Online app that can be used to make an exact plot of a surveyed area - like a room, a property or any 2D shape.

### Cartesian Coordinate System - Distance and Intermediate Position Between Two Points

Distance and intermediate position between two point in a cartesian x and y coordinate system.

### Circle - Equation

The equation for a circle

### Complex Numbers

Complex numbers are used in alternating current theory and mechanical vector analysis.

### Differential Calculus

Derivatives and differentiation expressions.

### Distance between 3D Points

Distance between two points in a three dimension x, y and z coordinate system - online calculator.

### Latitude and Longitude Converter

Convert between Degrees, Minutes and Seconds and Decimal Units (or vice versa).

### Minutes to Decimal Hours

Convert minutes to descimal hours.

### Pythagorean Theorem

Verifying square corners.

### Radians vs. Degrees

Radian is the SI unit of angle. Convert between degrees and radians. Calculate angular velocity.

### Standard Differentials and Integrals

Equations for differentials and integrals.

### Steradian

A unit of solid-angle measure in the International System of Units (SI)

### Taylor Series

Function as an infinite sum of terms.

### Trench Excavation

Estimate trench excavation - online calculator.

### Triangle

Triangle analytical geometry.

### UTM to Latitude and Longitude Converter

Free online UTM to Latitude and Longitude coordinates converter.