Enter Polar Values
Example Data Table
| Radius r | Angle θ | Unit | x = r cos θ | y = r sin θ | Rectangular Pair |
|---|---|---|---|---|---|
| 10 | 0 | Degrees | 10.0000 | 0.0000 | (10.0000, 0.0000) |
| 10 | 45 | Degrees | 7.0711 | 7.0711 | (7.0711, 7.0711) |
| 8 | 120 | Degrees | -4.0000 | 6.9282 | (-4.0000, 6.9282) |
| 5 | 3.1416 | Radians | -5.0000 | 0.0000 | (-5.0000, 0.0000) |
Formula Used
Polar coordinates describe a point with distance and direction. The distance is called r. The direction is called θ. Rectangular coordinates describe the same point with horizontal and vertical positions.
The calculator uses these formulas:
x = r × cos(θ)
y = r × sin(θ)
If the angle is entered in degrees, it is first changed into radians:
radians = degrees × π / 180.
If the angle is entered in gradians, it is changed into radians:
radians = gradians × π / 200.
How to Use This Calculator
- Enter the polar radius in the radius field.
- Enter the angle value in the angle field.
- Select degrees, radians, or gradians.
- Choose the decimal precision for the answer.
- Use the scale factor when the radius needs adjustment.
- Select the output format.
- Press the calculate button.
- Download the result as CSV or PDF when needed.
Polar to Rectangular Coordinate Conversion Guide
What This Calculator Does
A polar coordinate gives a point by distance and direction. The distance is the radius. The direction is the angle. Rectangular coordinates give the same point with x and y values. This calculator changes polar form into rectangular form with clear steps.
Why The Conversion Matters
Many math and engineering problems use both coordinate systems. Polar form is useful for rotation, curves, waves, and circular motion. Rectangular form is useful for graphs, measurements, tables, and algebra. Converting between them helps compare results in a common format.
Understanding Radius And Angle
The radius tells how far the point is from the origin. A positive radius moves in the angle direction. A negative radius points the opposite way. The angle starts from the positive x-axis. It then rotates counterclockwise for positive values.
Reading The Result
The x value shows horizontal position. A positive x value lies to the right of the origin. A negative x value lies to the left. The y value shows vertical position. A positive y value is above the origin. A negative y value is below it.
Angle Units
You can enter angles in degrees, radians, or gradians. Degrees are common in school work. Radians are common in advanced math and calculus. Gradians are sometimes used in surveying. The calculator converts each unit before applying trigonometric formulas.
Precision And Exports
Decimal precision controls rounding. Use fewer decimals for quick answers. Use more decimals for reports or technical checks. The CSV option is useful for spreadsheets. The PDF option is useful for printing, sharing, or saving a clean calculation record.
FAQs
1. What are polar coordinates?
Polar coordinates describe a point using radius and angle. The radius is the distance from the origin. The angle shows the direction from the positive x-axis.
2. What are rectangular coordinates?
Rectangular coordinates describe a point using x and y values. The x value shows horizontal position. The y value shows vertical position.
3. Which formula converts polar to rectangular form?
The formulas are x = r cos θ and y = r sin θ. The angle must be in radians before the trigonometric functions are applied.
4. Can I enter angles in degrees?
Yes. Select degrees from the angle unit menu. The calculator automatically converts the degree value into radians before calculating x and y.
5. What does the radius scale factor do?
The scale factor multiplies the radius before conversion. Use 1 for normal conversion. Use another value when the radius needs resizing.
6. Why is my x or y value negative?
A negative value shows direction from the origin. Negative x points left. Negative y points downward. The signs depend on the angle quadrant.
7. Can this calculator show detailed steps?
Yes. Select the step option before calculating. The result will show angle conversion, scaled radius, and the formulas used for x and y.
8. Can I export the answer?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a clean printable record of the conversion result.