Convert between polar and rectangular

Turn a point (x, y) into a distance r and an angle θ.

A point can be given as (x, y) or as a distance r from the origin and an angle θ. The distance is r = √(x² + y²) and the angle is θ = tan⁻¹(y ÷ x).

Example: (3, 4) has r = 5 and θ = 53.13010235 degrees.

Classic Graphing 84

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

Switch to degrees. Open the ANGLE menu (2nd apps) and pick 5, R►Pr(. Type 3, 4 and close the bracket.
mode▼▼▶enter2ndQUITmode2ndANGLEapps53,4)enter
Do the same with 6, R►Pθ(, to get the angle.
2ndANGLEapps63,4)enter

You should seeR►Pr(3,4) 5 R►Pθ(3,4) 53.13010235

Classic Graphing 84 key reference

Natural Scientific 991

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

The calculator starts in degrees. Press SHIFT then + for Pol(. Type 3, 4 (the comma is SHIFT then the ) key) and close the bracket.
SHIFTPol+3SHIFT,)4)=

You should see{5,53.13010235}

Natural Scientific 991 key reference

Natural Color Graphing

Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.

Set degrees. Open OPTN, press F6 for more menus, F3 for ANGLE, then F3 for Pol(. Type 3, 4 and close the bracket.
SHIFTSET UPMENU▼▼F2EXITOPTNF6F3F33,4)EXE

You should see{5,53.13010235}

Natural Color Graphing key reference

Classic CAS

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

Set degrees. Work out r with the square-root formula and ctrl enter.
menu9▼▶enterenterenterctrl√x²3x²+4x²ctrl≈enter
Work out θ with tan⁻¹(4 ÷ 3).
ctrltan⁻¹tan4÷3)ctrl≈enter

You should see√(3²+4²) 5. 53.1301

Classic CAS key reference

RPN Scientific 15

Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.

The stack takes y first, then x. Key in 4 ENTER 3.
4ENTER3
Press g then 1 for →P. The distance r appears in X (5) and the angle sits in Y.
g→P1

You should see53.1301 5.0000

RPN Scientific 15 key reference

RPN Advanced 42

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

Key in 4 ENTER 3 (y first, then x).
4ENTER3
Open the CONVERT menu (shift then 5) and press the last menu key, →P. The distance r shows in X.
⇧CONVERT5XEQ

You should seex: 5.0000

RPN Advanced 42 key reference

RPN Power 48

Start on the main screen: Press ON to cancel what you are typing, then use the stack view. Open the MODE or VAR menu any time; the stack is always shown above the menu row.

Choose DEG. Key in 3 ENTER 4, then the left shift and 1 to make the complex number (3,4). The left shift and × (ABS) gives its length r.
MODEF53ENTER4◀R→C1◀ABS×
The angle is tan⁻¹(4 ÷ 3): 4 ENTER 3 ÷, then left shift TAN.
4ENTER3÷◀ATANTAN

You should see2: 5 53.1301023541

RPN Power 48 key reference

Tips

The angle depends on the angle mode. In radian mode (3, 4) gives 0.927295218 instead of 53.13.
tan⁻¹(y ÷ x) only gives angles in the right half of the plane. When x is negative, add 180 degrees or use the Pol( command.