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Polar To Rectangular Calculator

Best handy calculator tool to convert the polar coordinates to rectangular coordinates is available here. All you have to do is enter polar coordinates i.e radius and angle in the input fields and tap on the calculate button of the Polar to Rectangular Calculator to obtain the rectangular coordinates i.e x and y in no time.

Polar To Rectangular Calculator: At times, we feel boring to do our calculations. In such cases, if you ever need help wih converting Polar Coordinates to Cartesian Coordinates take the help of this free tool. Learn the process of converting polar to rectangular from the below sections. Also, have a look at the solved sample examples to understand the concept much better.

How to Convert Polar Coordinates to Rectangular Coordinates?

Follow the detailed procedure to convert polar coordinates to rectangular coordinates mentioned below. These guidelines makes it easy for you during the calculations.

  • We need to convert polar coordinates (R, θ) to rectangular coordinates (x, y).
  • The rectangular coordinates for the given polar coordinates will be y = R sin θ and x = R cos θ.
  • Take angle in radians or degrees and R (radius) as any decimal number.
  • Substitute your values in the above formulas.
  • Proceed with the calculation to the x and y values.

Example

Question: Convert the polar coordinates (5 , 2.01) and (0.2 , 53°) to rectangular coordinates to three decimal places?

Solution:

Given polar coordinates are (5 , 2.01) and (0.2 , 53°)

The first coordinates are (5, 2.01)

R = 5, θ = 2.01 radians

x = R cos θ, y = R sin θ

x = 5 cos 2.01 = 5 * (-0.425) = -2.125

y = 5 sin 2.01 = 5* 0.905 = 4.525

Second coordinates are (0.2, 53°)

In this case, R = 0.2, θ = 53°

x = R cos θ = 0.2 cos 53°

= 0.2 * 0.6 = 0.120

y = R sin θ = 0.2 sin 53°

= 0.2 * 0.8 = 0.160

The rectangular coordinates for (5 , 2.01) is (-2.125, 4.525) and for (0.2 , 53°) is (0.120, 0.160).

Polar to Rectangle Calculator

FAQs on Polar To Rectangular Calculator

1. How do you convert Polar to Rectangular using online calculator?

At first choose whether your angle is in degrees or radians. Enter your radius and angle values in the specified input boxes and hit on the calculate button to get the rectangular coordinates for those polar coordinates in a short span of time easily.


2. What is meant by Polar to Rectangular Coordinate Conversion?

The polar coordinates are in the form of (r, θ), where r is the radius and θ is the angle between them. Whereas rectangular coordinates are in the form of (x, y). These are points in the graph. Rectangular coordinates are also called as Cartesian Coordinates. The formula used for the conversion of polar coordinates to rectangular coordinates is x = r cos θ, y = r sin θ.


3. Where can I find the best calculator to convert Polar Coordinates to Cartesian Coordinates?

Onlinecalculator.guru is a trusted website that offers several mathematical calculators like Rectangular to Polar Calculator, Polar to Rectangular, Integration, many more that makes your calculations easy and fast.


4. Convert (3, 30°) to rectangular coordinates?

Given polar coordinates are (3, 30°).

Rectangular coordinates (x, y) = (r cos θ, r sin θ)

= (3 cos 30°, 3 sin 30°)

= (3* 0.8660, 3*0.5)

(x, y) =(2.598, 1.5)