• RPN (Reverse Polish Notation)
• 10-digit LED calculator display, 10^-99 to ¹⁰⁺⁹⁹
• Four stack registers with roll down, labelled X, Y, Z, T
• One storage register with arithmetic memory operators
• Math, trigonometric, polar⇔rectangular, logarithmic, power and other miscellaneous functions
• One additional window with views of:
  • stack/storage registers
  • paper tape keystroke log
• Copy-from and Paste-to the calculator display (except Apple TV)
• Simple Paper Tape annotations

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This document — also available as a PDF download GO-21 Help — is not an exhaustive reference manual; rather, it's a terse outline of the calculator's operation and function keys. The information is structured so that prerequisite material generally comes first, thus, you are encouraged to read the topics sequentially.

In this document normal calculator keys are shown in bold, such as +, or x, or 4, or SIN. Most keys can perform one other function, however, labeled in blue. To execute one of these functions you first touch the colored prefix key followed by the desired function key.

So to compute the inverse sine of a number you'd touch two keys, the blue prefix key followed by the SIN key. However, this document will simply show the key as sin^-1: the font color implies the prefix character is used.

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The GO-21 LED window acts as a display area, as well as a touch sensitive input area that initiates further activities not available on an actual HP-21.

A similar concept exists for Apple TV, based on focus navigation rather than touch, see section Apple TV Particulars for details.

The display shows the X stack register, usually the result of the latest calculation. Single tapping the display brings up the Copy / Paste / Paper Tape menu, allowing you to export the value of X, import a new value of X, or annotate the paper pape (Copy / Paste unavailable on Apple TV).

In GO-21, numbers in the display normally appear rounded to only two decimal places. For example, the fixed constant π, which is actually in the calculator as 3.14159265358979, normally appears in the display as 3.14 (unless you tell the calculator to show you the number rounded to a greater or lesser number of decimal places).

Although a number is normally shown to only two decimal places, GO-21 always computes internally using each number as a 14-digit mantissa and a two-digit exponent of 10.

• Display Control Key: DSP

  A Display Key allows you to control the manner in which a number is displayed — the number itself is not altered by the key. You can choose one of three ways to display a number: Fixed Decimal Point, Scientific or Engineering notation. No matter what notation you choose, these rounding options affect the display only, GO-21 always calculates internally with the entire number.

  These key sequences control how numbers are displayed:

  • DSP . n

    Selects Fixed Decimal Point notation (FIX) where  . n specifies the number of decimal places (0 - 9) to which the display is rounded. The number begins at the left side of the display and includes trailing zeros to fill the width, if needed.

  • DSP n

    Selects Scientific notation (SCI) where n specifies the number of decimal places (0 - 7) to which the display is rounded. Again, the number is left-justified and includes trailing zeros to fill the width, if needed. The exponent occupies the rightmost two digits

  • DSP n

    Selects Engineering notation (ENG) where the first three digits of a number are always present, n specifies the number of additional digits (0 - 5) displayed after the first three, and exponents of ten that are multiples of three (e.g., 10³, 10^-6, 10⁹). This is particularly useful in scientific and engineering calculations, where units of measure are often specified in multiples of three. Otherwise ENG behaves similarly to SCI.

    Multiplier	Prefix	Symbol
    1012	tera	T
    109	giga	G
    106	mega	M
    103	kilo	k
    10-3	milli	m
    10-6	micro	µ
    10-9	nano	n
    10-12	pico	p
    10-15	femto	f
    10-18	atto	a

• Automatic Display Switching

  GO-21 switches the display from fixed point notation to full scientific notation (DSP 7) whenever the number is too large or too small to be seen with a fixed decimal point. This feature keeps you from missing unexpectedly large or small answers.

  After automatically switching from fixed to scientific, when a new number is keyed in or v is pressed the display automatically reverts back to the fixed point display originally selected.

• Keying In Exponents of Ten

  You can key in numbers multiplied by powers of 10 by pressing EEX (enter exponent of ten) followed by number keys to specify the exponent of 10.

  You can save time when keying in exact powers of 10 by merely pressing EEX and then pressing the desired power of 10.

  To key in negative exponents of 10, key in the number, press EEX, press x to make the exponent negative, then key in the power of 10.

• Calculator Overflow and Underflow

  When a number is greater than 9.9999999 x 10⁹⁹ an overflow has occurred and 9.9999999+99 is displayed instead.

  For numbers 10^-100 and smaller an underflow has occurred and 0.000000000 is displayed instead.

• Error Display

  Illegal operations such as a divide by zero and taking the square root of a negative number display the word Error. Use v to clear the display.

• Low Power Display

  A GO-2+ SciRPN calculator App blinks its decimal point when the host device is running on battery and the power level is ≤ 1.1%.

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Automatic storage of intermediate results is the reason that GO-21 slides so easily through the most complex equations. The displayed X register, which is the only visible register in the calculator display, is one of four registers inside the calculator that are positioned to form the automatic memory stack. We label these registers X, Y, Z, and T. They are "stacked" one on top of the other with the displayed X register on the bottom.

• Manipulating Stack Contents

  The s (roll down) and a (X exchange Y) keys allow you to review the stack contents or to shift data within the stack for computation at any time. Each time you press the s key the stack contents shift downward one register, with the contents of X rotating up to the T register. Notice that the contents of the registers are shifted - the registers themselves maintain their positions. Always remember, though, that it takes four presses of the s key to return the contents to their original registers.

  The a (X exchange Y) key exchanges the contents of the X and Y registers without affecting the Z and T registers.

  To clear the displayed X register only, press v. To clear the entire automatic memory stack, including the displayed X register, press CLR (clear stack). This replaces all numbers in the stack with zeros.

  The z key lifts the stack, by copying the contents of Z into T, Y into Z, X into Y, hence losing the contents of T and duplicating the contents of X.

  The opposite of lifting the stack is called dropping the stack. When the stack drops, Y is copied to X, Z is copied to Y, and T is copied to Z, hence losing the contents of X and duplicating the contents of T.

• Functions and the Stack

  One-number functions such as m execute upon the number in the X-register only, and the answer writes over that number. No other stack registers are affected by executing a one-number function.

  Two-number functions such as p, or arithmetic operations such as /, execute upon two stack registers, X and Y. Obviously, for the power function first enter the base followed by z to lift it into Y, then enter the power into X and press p to perform the function.

  For arithmetic operations imagine the stack as an old-fashioned sheet of paper, where in the case of division, the divedend (Y) is written on top of the divisor (X), then the / operation is executed. Addition, subtraction and muliplication work the same way, both numbers are positioned in the stack in the natural order, there are no exceptions to this rule.

  You can use s and a as required to re-order the operands. In all cases after the function or operation is executed the stack drops and the answer is written over X (the old Y before the stack drop).

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In addition to the automatic storage of intermediate results that is provided by the four-register automatic memory stack, GO-21 also has one addressable storage register that is unaffected by operations within the stack. This storage register allows you to set aside a number as a constant or for use in later calculations. The storage register resides in Continuous Memory and maintains its contents even when the calculator is turned OFF.

• Manipulating the Storage Register

  • Store
    

    To store the X value appearing in the display press STO. When a number is stored, it is merely copied into the storage register, and remains in the displayed X register.

  • Recall
    

    To copy a number from the storage register into the displayed X register, press the RCL key.

    Recalling a number causes the stack to lift unless the preceding keystroke was z or v.

    When you recall a number, it is copied from the storage register into X, and it also remains in the storage register. You can recall a number from the storage register any number of times without altering it; the number will remain in the storage register as a 10-digit number with a two-digit exponent of 10 until you overwrite it by storing another number there, or until you clear the storage register.

  • Clear
    

    To clear the number from the storage register, simply store the quantity zero in the register by pressing 0 STO.

• Storage Register Arithmetic

  Arithmetic is performed upon the contents of the storage register by pressing:

  • M+ (X added to storage register, sum placed in storage register.)
  • M− (X subtracted from storage register, difference placed in storage register.)
  • M× (X multiplied by storage register, product placed in storage register.)
  • M÷ (Storage register divided by X, quotient placed in storage register.)

  When storage register arithmetic operations are performed, the answer is written into the storage register, while the contents of the displayed X register and the rest of the stack remain unchanged.

  If the magnitude of a number in the storage register exceeds 9.999999999 x 10⁹⁹, the display immediately shows OF (overflow) to indicate that the storage register has overflowed.

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GO-21 provides views of the calculator's internal state unavailable on the real hardware. This makes using the calculator much easier. Access to this additional information is controlled by a double tap on the calculator display. If the information view is visible, a double tap hides the view. If the view is not visible, the information view appears. So a double tap toggles the visibility of the auxiliary information. If you eschew gestures and prefer buttons, enable the Accessibility setting Auxiliary View Assist.

(Note: unlike for iPhone and iPod touch, which have tiny screens, on Mac and iPad the information view is by default always visible, but you can hide it with a double tap. For Apple TV the information view is always visible and cannot be hidden.)

The auxiliary information view includes this touch point that toggles what the view shows.

The auxiliary view shows the 4 stack registers and the memory register. Touching the switch-views control transitions to the paper tape window and shows up to 200 lines of key-press history to help you make sense of the values you see in the stack-register window.

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• Change Sign

  Press x to change the sign of the mantissa or exponent of the X register.

• Prefix Clear

  To clear the blue prefix you have mistakenly pressed, merely press z, then press the correct key.

• Reciprocals

  To calculate the reciprocal of a number in the displayed X register, press O.

• Square Roots

  To calculate the square root of a number in the displayed X register, press m.

• Using Pi

  The value π accurate to 14 places (3.14159265358979) is provided as a fixed constant in GO-21. Merely press % whenever you need it in a calculation.

• Trigonometric Functions

  GO-21 provides you with six trigonometric functions. It also calculates angles in decimal degrees or radians. Use the slide switch to select P or {.

  Note: 360 degrees = 2π radians = 400 grads.

  The six trigonometric functions provided by the calculator are:

  • sin (sine)
  • sin⁻¹ (inverse sine)
  • cos (cosine)
  • cos⁻¹ (inverse cosine)
  • tan (tangent)
  • tan⁻¹ (inverse tangent)

  Each trigonometric function assumes angles in decimal degrees or radians. Trigonometric functions are one-number functions, so to use them you key in the number, then press the function keys.

• Polar/Rectangular Coordinate Conversion

  Two functions H and o are provided for polar/rectangular coordinate conversions. Polar angle θ is assumed in decimal degrees or radians, depending upon the trigonometric mode selected.

  To convert values in the X and Y registers representing rectangular (x, y) coordinates, respectively, to polar (r, θ) coordinates, magnitude and angle, respectively, press H. Magnitude r then appears in the X register and angle θ is placed in the Y register.

  Conversely, to convert values in the X and Y registers representing polar (r, θ) coordinates, respectively, to rectangular coordinates (x, y), press o. Coordinate x then appears in the X register and coordinate y is placed in the Y register.

• Logarithm and Exponential Functions

  GO-21 computes both natural and common logarithms as well as their inverse functions (antilogarithms):

  • LN is log_e (natural log). It takes the log of the value in X to base e (2.718...).
  • F is antilog_e (natural antilog). It raises e (2.718...) to the power of the value in X. (To display the value of e, press 1 F.)
  • LOG is log₁₀ (common log). It computes the log of the value in the X register to base 10.
  • 10^x is antilog₁₀ (common antilog). It raises 10 to the power of the value in the X register.

• Raising Numbers to Powers

  The p key is used to raise numbers to powers. This function raises a positive real number to any real power; that is, the power may be positive or negative, and it may be an integer, a fraction, or a mixed number. p also permits you to raise any negative real number to the power of any integer within the calculating range of the calculator.

  In conjunction with O, p provides a simple way to extract roots. For example, the cube root of 5 is equivalent to 5^1/3 e.g.:

  5 z

  3 O

  p

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If you attempt a calculation containing an improper operation - say, division by zero - the display will show Error. To clear, press v.

The following are improper operations:

• ÷ where X = 0
• Y^x where Y < 0 with X not an integer, or where Y = 0 with X < 0, or where X = Y = 0
• √X where X < 0
• 1/x where X = 0
• log where X <= 0
• ln where X <= 0
• sin^-1 where absolute value of X > 1
• cos^-1 where absolute value of X > 1
• M÷ where X = 0

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Settings are built into the calculator, except Apple TV where they are part of the tvOS Settings App. Available Settings options are device dependant - here are their default values:

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Reminder: There are no gestures on Apple TV thus this section is not applicable, see the section Apple TV Particulars for details. On macOS taps/touches are pointer clicks, pans/swipes/scrolls are pointer drags.

• Shake to clear X. Not available on macOS.
• Single tap the calculator display for Copy / Paste / Paper Tape.
• Double tap the calculator display to show/hide the stack/memory view.
• Two-finger pan for iPad to reposition the stack/memory and calculator views on iOS.
• Touch switch-views control to alternate between two views.
• Swipe left and right to manipulate slide switches, if activated in Settings. Not available on macOS.
• Flick left on the calculator display to erase last mantissa character entered.
• Triple tap the calculator display to show/hide the Info button  .

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All calculator capabilities are supported on macOS.

• Mac Window Mechanics

  The App has a single window with the three standard window control buttons in the top-left corner:

  

  • The red button closes the window and quits the App.
  • The yellow button minimizes the window to the Dock.
  • The green button toggles the window between two size states: a minimalist size and the window's previous size. When zooming to its minimalist size the Auxiliary Information View is hidden, which is then restored when zooming back to the window size.

• Mac Menu Actions

  Some App actions have been duplicated in the macOS menus:

  • Application : Settings opens the Settings view.
  • Edit : Copy exports the value of X to the pasteboard.
  • Edit : Paste imports a new value of X from the pasteboard.
  • Edit : Paper Tape manipulates the paper tape.
  • Help : Help shows the documentation in a Help Book.

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All calculator capabilities are supported on tvOS except for Copy / Paste.

• ATV Focus Navigation

  Use the Apple TV remote to move the screen focus left, right, up and down until the desired object is highlighted, then click. The calculator keys are arranged in a regular grid so focus navigation is easy. But to reach the Info button and switch-view control there is a special path passing through a focus portal key that you must follow in order to move the screen focus in and out of the calculator:

  • Left focus portal key O
    From the left portal key, focus left once to reach the stack and paper tape, focus left a second time to reach the Info button. Simply reverse your path to return to the calculator.

  • Right focus portal key t
    From the right portal key, focus right once to reach the Info button, and reverse your path to return to the calculator.

  You may rightly view this focus ordering as if the following objects exist in their own logically horizontal row that you can freely traverse left and right:

  Stack

  O

  SIN

  COS

  TAN

  t

  A focused, clickable object is highlighted: calculator keys with a translucent white overlay, and other objects with a light gold background. When the calculator first starts the initial screen focus is on the Info button for quick access to Help and Settings, as seen in this picture. Note that the OFF - ON switch can never receive the focus because the calculator is always on.

  

  The Info button actually identifies with both the switch-view control and the t key, this means that the focus order is really a ring that you may circle in either direction:

  

  As with iOS and macOS, you can view and scroll the paper tape on tvOS. Move the focus to the switch-views control , tap the control until the scrollable view of interest is visible, then pan up and down to scroll the contents. When you are finished, pan left or right to move the screen focus to the next object in the focus ring. Remember that a view is only scrollable when it has the light gold focus.

  Note: when a scrollable view is visible it inserts itself into the focus ring.

  

• ATV LED Display Focus Actions

  Similarly to iOS and macOS, after moving the screen focus up from the focus ring to the calculator's display area you can initiate context sensitive actions unavailable on a real device:

  • Paper Tape Actions... allows you to erase or annotate the paper tape.

  

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GO-21, GO-25 and GO-29 all provide support for hardware keyboards. You can enter digits and a decimal point into the X register by simply typing those characters, even from a numeric keypad. Use delete instead of a flick left in the display to delete the last character typed, and return instead of z to push the completed number onto the stack.

To enter an exponent of 10 for a floating point number type e instead of c. To change the sign of a mantissa or exponent type c instead of x. To perform any of the four basic arithmetic operations - + ? / on these numbers type - + * /, respectively.

So the keyboard works rather well for simple calculator operations, but it's non-trivial to do more because there are no familiar mappings between keyboard and calculator keys. However, all 30 keys and the 2 slide switches of these calculators have a keyboard equivalent, with 27 keys common to all devices and 6 keys specific to an individual model:

• ⌘? shows the Info view for Help and Settings
• keys colored red map to virtual calculator keys
• on tvOS there are even keys to mimic an Apple TV remote:

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• X, Y, Z and T registers, and the memory register are continuous and survive a power Off.
• The DSP setting is persistent and does not reset to FIX 2 after a power cycle.
• DSP n switches to Engineering display notation.
• A blinking decimal point indicates very low battery power (except Apple TV).

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• Calculator artwork by David Marriott, Melbourne, Australia.
• International keyboard handling by Willy Kunz, Zurich, Switzerland.
• HP-21 Owner’s Handbook

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OS Version Compatibilty

iOS	16.0	-	26.5.1
iPadOS	16.0	-	26.5.1
tvOS	16.0	-	26.5.1
macOS	13.0	-	26.5.1
visionOS	1.0	-	26.5.1

26.5.1 - 2026.06.11

• Repair broken icon and update documentation.
• Update to Apple OS versions 26.5.1.

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O, 7
%, 7
m, 7
H, 7
o, 7
G, 7
Acknowledgements, 15
Apple TV Particulars, 12
ATV Focus Navigation, 12
ATV LED Display Focus Actions, 12
Automatic Display Switching, 3
Auxiliary Information Views, 6
Calculator Overflow and Underflow, 3
Capabilities At A Glance, 1
x, 7
CLR, 4
v, 4
Controlling the LED Display, 3
Copy, 3
k, 7
L, 7
DEG, 3
Display Control Key: DSP, 3
DSP, 3
F, 7
c, 4
Engineering notation, 3
z, 4
Error Display, 3
Fixed Point notation, 3
Function Keys, 7
Functions and the Stack, 7
Gesture Summary, 10
GO-21 versus HP-21 Differences, 14
Improper Mathematical Operations, 8
Introduction, 2
Keyboard Usage, 13
Keying In Exponents of Ten, 3
LED Display, 3
LN, 7
LOG, 7
Logarithm and Exponential Functions, 7
Low Power Display, 3
M+, 7
M-, 7
M×, 7
M÷, 7
Mac Menu Actions, 11
Mac Window Mechanics, 11
Macintosh Particulars, 11
Manipulating Stack Contents, 7
Manipulating the Storage Register, 5
OFF, 2
ON, 2
Paper Tape, 3
Paste, 3
Pi, Using, 7
Polar/Rectangular Coordinate Conversion, 7
Prefix Clear, 7
prefix key, blue, 2
RAD, 3
f, 5
Reciprocals, 7
s, 4
Scientific notation, 3
Settings, 9
j, 7
K, 7
Square Roots, 7
Stack Operations, 4
d, 5
Storage Register, 5
Storage Register Arithmetic, 5
l, 7
B, 7
What's New?, 16
a, 4
p, 7
            
        

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