Rectangular to Polar on TI-84 Plus CE and TI-36X Pro: Exact Keystrokes

Quick answer: On a TI-84 Plus or TI-84 Plus CE, press [2nd] [APPS] to open the ANGLE menu. Choose 5:R►Pr(, type x , y ) and press [ENTER] to get r. Open the menu again, choose 6:R►Pθ(, type the same x , y ) and press [ENTER] to get θ. The angle comes out in whatever unit your calculator’s MODE is set to (DEGREE or RADIAN).

The TI-84 has no single “convert” button that returns both values at once like the Casio Pol( function does. Instead it gives you one function for the radius and one for the angle. This guide covers both TI-84 methods, the reverse conversion, the TI-36X Pro, and the one mistake that causes most wrong answers: the angle range.

If you just need the answer, the rectangular to polar calculator on our homepage does the conversion and shows each step.

TI-84 Plus CE ANGLE menu with R►Pr and R►Pθ highlighted Figure 1: The TI-84 ANGLE menu. Items 5–8 are the four coordinate conversion functions.

Step 0: Set Degree or Radian Mode First

Press [MODE], move down to the row that shows RADIAN DEGREE, highlight the unit you want, and press [ENTER]. Then press [2nd] [MODE] (QUIT) to return to the home screen.

This matters because R►Pθ( returns the angle in the current mode. The same point gives 53.13010235 in DEGREE mode and 0.927295218 in RADIAN mode, and both are correct.

Method 1: R►Pr( and R►Pθ( (TI-84 Plus, Plus CE, TI-83 Plus)

The ANGLE menu is the second function of the [APPS] key. It contains:

Item	Function	What it returns
`5:R►Pr(`	Rectangular → polar radius	$r = \sqrt{x^2 + y^2}$
`6:R►Pθ(`	Rectangular → polar angle	$\theta$ , in the current angle mode
`7:P►Rx(`	Polar → rectangular x	$x = r\cos\theta$
`8:P►Ry(`	Polar → rectangular y	$y = r\sin\theta$

Worked example: convert (3, 4) to polar

Press [2nd] [APPS] 5 → the screen shows R►Pr(
Type 3 [,] 4 [)] and press [ENTER] → 5
Press [2nd] [APPS] 6 → the screen shows R►Pθ(
Type 3 [,] 4 [)] and press [ENTER] → 53.13010235 (DEGREE mode)

So $(3, 4)$ in rectangular form is $(5,\ 53.13^\circ)$ in polar form.

The [,] key is the comma key in the row above [7] [8] [9]. Do not use the decimal point.

Tip: you can skip retyping the coordinates. After step 2, press [2nd] [ENTER] (ENTRY) to recall R►Pr(3,4), move the cursor onto r, and replace the function with R►Pθ( from the menu.

Entering negative coordinates

Use the negation key [(−)] (next to [ENTER] on the bottom row) for negative numbers, not the subtraction key [−]. Typing R►Pr(−3,−4) with the subtraction key gives ERR:SYNTAX.

Texas Instruments’ own knowledge base example converts $(-1, 0)$ : R►Pr(−1,0) returns 1 and R►Pθ(−1,0) returns 3.141592654 in RADIAN mode, which is $\pi$ .

The Negative-Angle Trap (Quadrants III and IV)

R►Pθ( returns an angle in the range $-180^\circ < \theta \le 180^\circ$ (or $-\pi < \theta \le \pi$ in radians). That is the same convention as the atan2(y, x) function in most programming languages, and it always picks the correct quadrant. However, points below the x-axis come back as negative angles:

Point	Quadrant	`R►Pθ(` result (DEGREE)	Same angle in 0°–360°
$(3, 4)$	I	$53.13^\circ$	$53.13^\circ$
$(-3, 4)$	II	$126.87^\circ$	$126.87^\circ$
$(-3, -4)$	III	$-126.87^\circ$	$233.13^\circ$
$(3, -4)$	IV	$-53.13^\circ$	$306.87^\circ$

Both columns describe the same direction. If your textbook or homework system expects $0^\circ \le \theta < 360^\circ$ , add $360^\circ$ to any negative result (or $2\pi$ in radian mode). Our guide to quadrants and atan2 explains why this happens.

Method 2: Complex Numbers with ►Polar (TI-84 Plus CE)

If you work with phasors or impedance, it is often faster to treat the point as the complex number $x + yi$ .

Type 3 [+] 4 [2nd] [.]. The i symbol is the second function of the decimal key, so the screen shows 3+4i.
Press [MATH], then press the right arrow to the CPX tab.
Choose 7:►Polar and press [ENTER].

In DEGREE mode the result is displayed in exponential form, $5e^{(53.13010235i)}$ . That means $r = 5$ and $\theta = 53.13^\circ$ , the same as $5\angle 53.13^\circ$ .

You can also pull out each part separately from the same CPX menu:

5:abs( 3+4i ) returns the magnitude 5
4:angle( 3+4i ) returns the angle 53.13010235

To go the other way, type the polar form and use 6:►Rect. If you want every answer shown in polar form automatically, change the complex format row in [MODE] from a+bi to re^θi.

For more on why engineers use this form, see converting complex numbers from rectangular to polar form and our AC circuit phasor guide.

Polar to Rectangular on the TI-84

Use items 7 and 8 of the ANGLE menu. For $(r, \theta) = (5, 53.13^\circ)$ in DEGREE mode:

[2nd] [APPS] 7 → P►Rx(5,53.13) [ENTER] → about 3.0000
[2nd] [APPS] 8 → P►Ry(5,53.13) [ENTER] → about 4.0000

The tiny difference from exactly 3 and 4 comes from rounding the angle to 53.13. Use the full value 53.13010235 to get 3 and 4 exactly. The math behind these functions is explained in polar to rectangular formulas and examples.

TI-36X Pro (Scientific Calculator)

The TI-36X Pro handles the conversion through its complex-number menu. This is the method Texas Instruments documents in its TI-36X Pro knowledge base article:

Rectangular to polar

Enter the number in rectangular form, for example 4.33 + 2.50i
Press [2nd] [complex]
Select 4: ►r∠θ and press [enter]
With two-decimal display, the result is 5.00∠30.00, meaning $r = 5$ and $\theta = 30^\circ$

Polar to rectangular

Type 5, then press [2nd] [complex] and select 1: ∠
Type 30 and press [enter]
The result is 4.33+2.50i

The TI-36X Pro also has rectangular/polar conversion functions in its angle menu, labeled angle on the keypad. The menu numbering varies between keypad versions, so check the R►P section of the official TI-36X Pro guidebook for your model.

Troubleshooting

Problem	Likely cause	Fix
Angle is 0.927 instead of 53.13	Calculator in RADIAN mode	`[MODE]` → select DEGREE
Angle is negative	Point is in Quadrant III or IV	Add 360° (or $2\pi$ )
`ERR:SYNTAX`	Subtraction key used for a negative number	Use the `[(−)]` key
Answer differs slightly from the textbook	Rounded angle used as input	Use more decimal places, or the stored `Ans` value

Frequently Asked Questions

Can the TI-84 convert rectangular to polar in one step?

Not with the ANGLE menu, because R►Pr( and R►Pθ( each return one value. The complex-number method (MATH → CPX → ►Polar) returns both $r$ and $\theta$ in one expression.

Why does my TI-84 give a negative angle?

R►Pθ( uses the range $-180^\circ < \theta \le 180^\circ$ . Negative results are correct directions measured clockwise. Add 360° if you need a positive angle.

Does this work on the TI-83 Plus and TI-84 Plus Silver Edition?

Yes. The ANGLE menu items R►Pr(, R►Pθ(, P►Rx( and P►Ry( are in the same place ([2nd] [APPS]) across the TI-83 Plus and TI-84 Plus family.

How do I check my answer?

Enter the same point in our online rectangular to polar converter. It shows $r$ , $\theta$ in degrees or radians, the quadrant, and every intermediate step. If you also use a Casio, see how to convert rectangular to polar on a Casio calculator.