Rectangular and polar coordinates: Pol, Rec and ►r∠φ in Scientific calculator plus 991 for Android

Pol, on SHIFT +, turns rectangular (Cartesian) coordinates into polar ones: in degrees, Pol(√2, √2) gives 2∠45, a distance of 2 at an angle of 45°. Rec, on SHIFT −, goes the other way: Rec(√2, 45) gives x = 1 and y = 1, one above the other. The two numbers go in the brackets, parted by a comma, which is SHIFT ). The angle is in the angle unit that is set, DEG in these examples. For a complex number, ►r∠φ in CMPLX mode gives its polar form.

To polar: SHIFT + (Pol): Pol(x, y)
To rectangular: SHIFT − (Rec): Rec(r, θ)
Comma: SHIFT )
Angle unit: DEG, RAD or GRA, whichever is set

A point can be given by its rectangular (Cartesian) coordinates, x and y, or by its polar coordinates: its distance r from the origin and the angle θ from the positive x-axis. Pol and Rec convert between the two. Both are SHIFT functions, printed in yellow above the + and − keys.

Rectangular to polar: Pol

How to convert to polar coordinates

Check the DEG, RAD or GRA key just under the display: Pol gives θ in that unit.
Press SHIFT + Pol to start the function.
Type x, then press SHIFT ) , for the comma and type y. If x ends in a square root, such as √2, first press ▶ right to move the cursor out of the root.
Press =. The answer is r, the angle sign, then θ.

SHIFT +, √x, 2, right, SHIFT ), √x, 2, =, in degrees

in Pol(√2, √2)

out 2∠45

Pol(√2, √2) on the phone, with DEG set: 2∠45.

Polar to rectangular: Rec

Rec works the same way, with r and θ in the brackets: press SHIFT - Rec and type r, the comma and θ, pressing ▶ right after √2 as before. The answer comes on two lines, x above y.

SHIFT −, √x, 2, right, SHIFT ), 45, =, in degrees

in Rec(√2, 45)

out [x = 1; y = 1]

Rec(√2, 45) on the phone, with DEG set: x = 1 above y = 1, in one pair of square brackets.

Pol gives θ, and Rec reads it, in the angle unit that is set, DEG, RAD or GRA; Angle units and trigonometry shows how to change it.

For complex numbers: ►r∠φ

A complex number a + bi is a point too, and in CMPLX mode ►r∠φ converts it: put at the end of a calculation, it gives the answer in polar form, and ►a+bi turns it back. Both are on the complex menu, which SHIFT 2 CMPLX opens in that mode, and Complex numbers covers them.

At a glance

Keys	Function	Example, in degrees
`SHIFT + Pol`	Rectangular to polar	Pol(√2, √2) = 2∠45
`SHIFT - Rec`	Polar to rectangular	Rec(√2, 45): x = 1, y = 1
`SHIFT ) ,`	The comma between the two numbers
`▶ right`	Leaves a root before the comma

Questions

How do I convert rectangular coordinates to polar?

Press SHIFT + (Pol), type x, press SHIFT ) for the comma, type y and press =. In degrees, Pol(√2, √2) gives 2∠45: r = 2 and θ = 45°. If x ends in a square root, such as √2, press the right arrow after it to leave the root before the comma.

How do I convert polar coordinates to rectangular?

Press SHIFT − (Rec), type r, press SHIFT ) for the comma, type θ and press =. For Rec(√2, 45), press the right arrow after √2 to leave the root. In degrees it gives x = 1 on the first line and y = 1 on the second.

Does the angle have to be in degrees?

No. Pol gives θ, and Rec reads it, in the angle unit that is set: DEG, RAD or GRA, on the key just under the display. The examples here are in degrees.

Angle units and trigonometry degrees, radians, gradians, the six trig functions and inverses, hyperbolics, DMS
Complex numbers CMPLX mode, a + bi and r∠θ, Re, Im, Abs, Arg, the conjugate and the polar form
Numbers, arithmetic and complex numbers which mode and which page, the keys, and how numbers are held

Written from the calculator's own manual and from the app itself, version 7.6.0; every figure is one the manual shows or a capture of the app proves. Last revised on 29 September 2026.

Bug reports and feature requests go to kimcuc@samatica.com — a person reads it.