Find Rectangular Coordinates From Polar Coordinates Calculator

Change radius and angle into x and y. Adjust units, origin offsets, and precision settings. Download clean outputs for reports, checks, and coursework fast.

Calculator

Use one point per line. Enter r, angle or label, r, angle.

Formula Used

The calculator converts polar coordinates (r, θ) into rectangular coordinates (x, y).

x = h + s × r × cos(θ)

y = k + s × r × sin(θ)

Here, r is radius. θ is the angle. h and k are origin shifts. s is the scale factor.

For degrees, the angle is first changed into radians by using θ radians = θ degrees × π / 180.

How to Use This Calculator

  1. Enter the radius value.
  2. Enter the angle value.
  3. Select degrees, radians, gradians, or turns.
  4. Add origin shifts when the polar center is moved.
  5. Set a scale factor when needed.
  6. Choose the decimal precision.
  7. Use batch input for many points.
  8. Click Calculate, CSV, or PDF.

Example Data Table

Label r θ Unit x y Note
A 5 53.130102 Degrees 3 4 Quadrant I
B 8 210 Degrees -6.9282 -4 Quadrant III
C 3 1.5708 Radians 0 3 On y-axis

Polar Coordinates in Rectangular Form

Polar coordinates describe a point by distance and direction. The distance is called radius. The direction is the angle from the positive x axis. Rectangular coordinates describe the same point with horizontal and vertical distances. These values are usually written as x and y.

Why Conversion Matters

Many Maths problems move between both systems. Polar form is helpful for rotation, circular motion, spirals, and trigonometric curves. Rectangular form is easier for graphing on a standard grid. It is also useful for slope, distance, intercepts, and algebraic equations. This calculator connects both views in one step.

Advanced Inputs

The calculator accepts degrees, radians, gradians, and turns. It can normalize angles before conversion. This keeps large angles easier to read. You can add an origin shift when the polar axis starts at another point. You can also use a scale factor for drawings, maps, or model layouts. Precision control helps you round answers for homework, reports, or checking work.

Reading the Result

The x value tells how far the point moves left or right. A positive x moves right. A negative x moves left. The y value tells how far the point moves up or down. A positive y moves up. A negative y moves down. The quadrant note helps confirm the sign pattern. Axis points are also identified.

Batch Work

Use the batch box when several points are needed. Enter one point per line. You may use radius and angle only. You may also add a label before them. The same angle unit, scale, origin, and rounding settings apply to all rows. This makes tables fast and consistent.

Good Practice

Always check the angle unit first. A degree angle entered as radians gives a very different answer. Keep the radius sign in mind. A negative radius points in the opposite direction. Use enough decimals when the result will be reused in another calculation. Round only at the final step when possible. Use the export buttons after checking the table. The CSV file works well in spreadsheets. The PDF file is useful for printed notes. Save the sample table as a guide when testing your own polar coordinate entries. It also supports class demonstration checks during lessons.

FAQs

What are polar coordinates?

Polar coordinates describe a point using radius and angle. Radius gives distance from the origin. Angle gives direction from the positive x axis.

What are rectangular coordinates?

Rectangular coordinates describe a point with x and y values. The x value is horizontal. The y value is vertical.

What formula converts polar to rectangular?

Use x = r cos(θ) and y = r sin(θ). This calculator also supports origin shifts and scale factors.

Can I use radians instead of degrees?

Yes. Select radians in the angle unit field. The calculator also supports degrees, gradians, and turns.

What does normalize angle mean?

It rewrites the angle into one standard cycle. For degrees, 450 becomes 90. The point stays equivalent.

Can radius be negative?

Yes. A negative radius points in the opposite direction. The calculator keeps that sign during conversion.

How do origin shifts work?

Origin shifts move the polar center. The h value moves x. The k value moves y.

Can I calculate many points together?

Yes. Use the batch box. Enter one point per line as r, angle or label, r, angle.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.