Worksheets · Precalculus

Rectangular to polar worksheet

Going the other way, r is the distance from the origin, so Pythagoras gives it. The angle comes from the inverse tangent of y over x, and then you check which quadrant the point is actually in.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Rectangular to Polar

Date Period

Convert each point to polar form.

  1. Convert rectangular to polar

    Convert to polar with r>0 and 0∘≤θ<360∘: (−2,−2)
  2. Convert to polar with r>0 and 0∘≤θ<360∘: (−52,52)
  3. Convert to polar with r>0 and 0∘≤θ<360∘: (42,42)
  4. Convert to polar with r>0 and 0∘≤θ<360∘: (22,−22)
  5. Convert to polar with r>0 and 0∘≤θ<360∘: (−32,−32)
  6. Convert to polar with r>0 and 0∘≤θ<360∘: (−2,2)
  7. Convert to polar with r>0 and 0∘≤θ<360∘: (52,−52)
  8. Convert to polar with r>0 and 0∘≤θ<360∘: (22,22)
  9. Convert to polar with r>0 and 0∘≤θ<360∘: (−32,32)
  10. Convert to polar with r>0 and 0∘≤θ<360∘: (42,−42)

  1. Convert to polar in degrees, rounded

    Convert (35,−12) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.
  2. Convert (−24,−10) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.
  3. Convert (−28,45) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.
  4. Convert (24,7) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.
  5. Convert (21,−20) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.
  6. Convert (3,4) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.
  7. Convert (−9,40) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.
  8. Convert (33,56) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.
  9. Convert (−11,−60) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.
  10. Convert (−30,−16) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Rectangular to PolarAnswer keyVersion 1

Date Period

Convert each point to polar form.

  1. Convert rectangular to polar

    Convert to polar with r>0 and 0∘≤θ<360∘: (−2,−2)(2,225∘)
  2. Convert to polar with r>0 and 0∘≤θ<360∘: (−52,52)(10,135∘)
  3. Convert to polar with r>0 and 0∘≤θ<360∘: (42,42)(8,45∘)
  4. Convert to polar with r>0 and 0∘≤θ<360∘: (22,−22)(4,315∘)
  5. Convert to polar with r>0 and 0∘≤θ<360∘: (−32,−32)(6,225∘)
  6. Convert to polar with r>0 and 0∘≤θ<360∘: (−2,2)(2,135∘)
  7. Convert to polar with r>0 and 0∘≤θ<360∘: (52,−52)(10,315∘)
  8. Convert to polar with r>0 and 0∘≤θ<360∘: (22,22)(4,45∘)
  9. Convert to polar with r>0 and 0∘≤θ<360∘: (−32,32)(6,135∘)
  10. Convert to polar with r>0 and 0∘≤θ<360∘: (42,−42)(8,315∘)

  1. Convert to polar in degrees, rounded

    Convert (35,−12) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.(37,341.1∘)
  2. Convert (−24,−10) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.(26,202.6∘)
  3. Convert (−28,45) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.(53,121.9∘)
  4. Convert (24,7) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.(25,16.3∘)
  5. Convert (21,−20) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.(29,316.4∘)
  6. Convert (3,4) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.(5,53.1∘)
  7. Convert (−9,40) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.(41,102.7∘)
  8. Convert (33,56) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.(65,59.5∘)
  9. Convert (−11,−60) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.(61,259.6∘)
  10. Convert (−30,−16) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth.(34,208.1∘)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Convert (−1,1) to polar form

  1. r is the root of 1 plus 1, which is root 2.
  2. The inverse tangent of -1 suggests -pi over 4.
  3. The point is in the second quadrant, so add pi.

The answer is (2,3π4).

Where students go wrong

Trusting the calculator angle. Inverse tangent only ever returns an angle in the first or fourth quadrant, so for a point on the left of the y-axis you have to add pi yourself.

Also called converting rectangular to polar or cartesian to polar.

What you can put on this worksheet

Rectangular to polar
Convert to polar with r>0 and 0∘≤θ<360∘: (−32,−32) → (6,225∘)
In degrees, with a calculator
Convert (35,−12) to polar form, with r>0 and θ in degrees on [0∘,360∘), to the nearest tenth. → (37,341.1∘)

Questions about these worksheets

Yes. Every rectangular to polar sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the rectangular to polar questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: rectangular to polar and in degrees, with a calculator. Tick as many as you want and set how many of each, or let it spread them evenly.

Trusting the calculator angle. Inverse tangent only ever returns an angle in the first or fourth quadrant, so for a point on the left of the y-axis you have to add pi yourself.