Version 1.0, (c) 2019 by deetee/zooxo
This software is covered by the 3-clause BSD license.
*** SCOTT has got a powerful successor: IVT - see more at https://github.com/zooxo/ivt ***
See a video at: https://youtu.be/h7Wjb0mhJ38
To examine how much "calculator power" a simple microcontroller like the ATTINY85 is able to perform was already the intention of ScArY (www.github.com/zooxo/scary). Unfortunately ScArY was based on a premanufactured development board (QYF-TM1638) and was restricted to a 7 segment display.
Beside an ATTINY85 microcontroller SCOTT is based on an OLED display and a 16 key one wire keypad. As SCOTT is powered by one 3V battery only a good power management is essential.
Two of the five regular I/O-pins of the ATTINY are used to control the display (I2C communication) and one (analog) pin is used to handle the one wire keypad. So far two pins are available for further developments (i.e. sensors).
SCOTT uses the internal RAM of the SSD1306 display controller as screenbuffer, what saves valuable RAM of the ATTINY. And to speed up the relatively slow I2C-communication with the display SCOTT splits the controller RAM. So while one half of the RAM is used to display its content the other half is filled with content via the I2C line. With a RAM swap the new content is displayed rapidly (without the effect of "dropping in characters").
Like in ScArY the functionality of SCOTT outweights comfort and error handling which can be seen for instance at the permanent scientific display format or a "non interpretable" display after dividing by zero.
Features of SCOTT:
- Scientific RPN calculator (similar to those famous HP calculators)
- Power settings: Set the contrast of the display and save the value permanently to EEPROM, display the recent battery voltage and shift SCOTT into a deep sleep mode.
- Function menu to browse and call every operation of SCOTT comfortable with cursor and function keys ("catalog").
- Basic functions for number input, basic arithmetical operation and memory.
- Low level functions like squareroot, power and inverse.
- High level functions like exponential, logarithmic, trigonometric and hyperbolic.
- User definable keys to store and load 10 physical constants to/from EEPROM permanently.
- User definable keys for fast access of 10 functions/commands.
- Basic financial function (present value).
- Conversion of polar and rectangular coordinates.
- Gaussian normal distribution (CDF, PDF).
- Statistics (Mean value, standard deviation).
- Linear Regression (a, b - where y = a x + b).
- Type recorder (record and play 3 user defined sequences of keypresses).
Enjoy!
deetee
mantissa exponent mantissa exponent
____|________________|____ ____|________________|____
| | | | | | |
| | - e e | | - m . m m m m m - e e |
| - m . m m m m m o ^ | | M1(7) M2(8) M3(9) |
|__|__________________|_|__| |__|________|________|_____|
| | | | | |
sign | shift indicator MENU (function keys 7, 8 and 9)
record indicator
[SHIFT] 7 [(MENU)] (F1) 8 [SUM+] (F2) 9 [/](F3)
EE [ROT](UP) 4 [CONST] 5 [CMD] 6 [*]
+- [ROT](DOWN) 1 [RCL] 2 [STO] 3 [-]
C [OFF] 0 [BATT] . [SWAP] ENTER [+]
0 1 2 3 4 5 6 7 8 9 . ... Digits and decimal point
CHS EE ... Change sign and enter exponent (actually Y*10^X)
ENTER ... Enter number (push stack)
C ... Clear X, clear entry or escape/stop
f ... Function or shift to choose shifted keys
+ - * / ... Basic operations
STO RCL ... Store number to respectively recall number from memory
ROT ... Rotate stack up or down
SUM+ ... Enter X-data for statistics or X,Y-data for linear regression
SWAP ... Swap X and Y register of stack (X<->Y)
MENU ... Browse menu
CONST ... Recall one of 10 user defined constants
CMD ... Execute one (of 10) user defined command keys
BATT ... Shows the battery voltage in V
OFF ... Deep sleep mode
SQRT POW INV ... Basic Functions
EXP LN !
->P ->R PV ... Polar/Rectangular Conversion, Present Value (Annuity)
ND STA LR ... Normal Distribution, Statistics, Linear Regression
SIN COS TAN ... Trigonometric Functions
ASIN ACOS ATAN
SINH COSH TANH ... Hyperbolic Functions
ASINH ACOSH ATANH
CONST CMD LIT ... Set Constant, User Defined Command Key and Brightness
REC1 REC2 REC3 ... Record user keypress sequence ("Type Recorder")
PLAY1 PLAY2 PLAY3 ... Play user keypress sequence ("Type Recorder")
1 Enter mantissa (with '.' if applicable)
Press ENTER to push mantissa to stack
2 To enter power of ten:
Enter exponent and (if applicable) change sign of exponent with +/-
3 Press EE to link the mantissa with the exponent
4 If applicable: Toggle sign of number with +/-
As SCOTT saves the state (stack and brightness values) when the deep sleep mode (OFF) is entered manually it also loads the state after switching on. But flashing the ATTINY may clear the EEPROM. So the loaded state when switching on the first time after flashing gets undefined values ( ... and a "non interpretable" display).
The following procedure may help to bring SCOTT in a defined state: 1 Press C (X=0) ... a regular 0-value is shown (register X) 2 Press ENTER 3 times ... clear the stack (X=Y=Z=T=0) 3 Press STO (f-2) ... clear mem 4 Press OFF (f-C) ... save state to EEPROM (activate deep sleep) 5 Press f ... wake up from deep sleep mode
To enter the menu catalog press MENU (f-7) and browse the menu items with the UP and DOWN keys (EE and +-). To execute one of the three displayed functions press F1, F2 or F3 (7, 8 or 9).
SCOTT is capable to save up to 10 constants permanently to the EEPROM memory. See "Appendix - Physical Constants" for some physical constants.
Example to write PI to slot 4:
1 3.141593 ENTER ... enter value for PI
2 Press 4 ... enter desired slot (number 4)
3 MENU (f-7) ... enter MENU
4 Press 8xDOWN ... goto menu line 9 (alternatively press 3xUP)
5 Press 7 (F1) ... set CONST
Example to load stored constant (from slot 4):
1 Press 4 ... enter desired slot (number 4)
2 Press CONST (f-4) ... recall saved constant
SCOTT is capable to save 10 user defined function keys for fast access to intrinsic commands. Get the appropriate number for the desired command from the following table:
NR ASC COMMAND NR ASC COMMAND NR ASC COMMAND
------------------ ------------------ ------------------
00 0-9 Numbers
01 : DOT 21 N nop 41 b COSH
02 ; CLX 22 O SQRT 42 c TANH
03 < EE 23 P POW(y^x) 43 d ASINH
04 = ENTER 24 Q INV(1/x) 44 e ACOSH
05 > CHS 25 R EXP 45 f ATANH
06 ? BATT 26 S LN 46 g SETCONST
07 @ RCL 27 T GAMMA(!) 47 h SETCMD
08 A STO 28 U R2P 48 i CONTR
09 B SUB(-) 29 V P2R 49 j REC1
10 C nop 30 W PV 50 k REC2
11 D CMD(user) 31 X ND 51 l REC3
12 E MULT(*) 32 Y STAT 52 m PLAY1
13 F MENU 33 Z SETCMD 53 n PLAY2
14 G nop 34 [ SIN 54 o PLAY3
15 H DIV(/) 35 \ COS 55 p SUM1
16 I SWAP 36 ] TAN 56 q SUM2STACK
17 J SLEEP 37 ^ ASIN 57 r SHADOWSAVE
18 K RORup 38 _ ACOS 58 s SHADOWLOAD1
19 L ADD(+) 39 ` ATAN 59 t SHADOWLOAD2
20 M ROT 40 a SINH 60 u ENTER3
Example to save the function SIN to slot 4:
1 Enter 34 ENTER ... enter number for function SIN (34)
2 Press 4 ... enter desired slot (number 4)
3 MENU (f-7) ... enter MENU
4 Press 8xDOWN ... goto menu line 9 (alternatively press 3xUP)
5 Press 8 (F2) ... set CMD
Example to execute command stored in slot 4:
1 Press 4 ... enter desired slot (number 4)
2 Press CMD (f-5) ... recall saved command
SCOTT is able to record 3 user defined sequences of keypresses (up to 146 each) and "replay" them by selecting the appropriate user menu entry. These user defined key sequences or formulas are stored to the EEPROM memory permanently.
Example to record temperature conversion (Fahrenheit -> Celsius):
1 MENU (f-7) ... enter MENU
2 Press 2xUP ... goto menu line 9 (record keys)
3 Press 7 (F1) ... enter recording slot 1 (record indicator is displayed)
4 32 - 1.8 / ... convert to celsius
5 Press C ... stop recording
Convert Fahrenheit to Celsius:
1 50 ... enter value to convert
2 MENU (f-7) ... enter MENU
3 Press UP ... goto last menu line (play keys)
4 Press 7 (F1) ... enter playing slot 1
5 X=10 ... 50 Fahrenheit are 10 Celsius
As SCOTT is supplied with battery power a severe power management is essential. After 10 seconds without pressing a key the display brightness will be reduced to a minimum. After 10 more seconds the display will be deactivated. Till now every further keypress will be interpreted as normal keypress for calculations.
After 10 more seconds without pressing a key SCOTT falls into a deep sleep mode. Only a pin change (pressing any key in the upper part of the keyboard) wakes SCOTT up, but this keypress will not be interpreted as normal keypress for calculations.
If demanded the user can enter the sleep mode by pressing SHIFT and C. Additionally SCOTT saves the stack and brightness values to the EEPROM. By pressing SHIFT and 0 the battery voltage will be shown. The default brightness of the display can be set by entering a value (0...255) followed CMD from the MENU (SHIFT and 7).
Running on a single battery (CR2032) SCOTT draws a current of 10 mA (bright display with a lot of "8s"). With a battery capacity of at least 200 mAh SCOTT can calculate approximately 20 hours. After dimming the current falls to 5.5 mA, after deactivating the display 1.1 mA are needed.
In sleep mode SCOTT consumes less than 0.25 mA. With a battery capacity of at least 200 mAh SCOTT lasts more than a month in sleep mode.
Example to calculate the present value of a $1 5 year return with an
interest rate of 8%:
1 .08 ENTER 5 ... interest rate and periods
1 MENU (f-7) ... enter MENU
2 Press 2xDOWN ... goto menu line 3
4 Press 9 (F3) ... enter PV
2 X=3.99 ... 5 years $1 each are equal to ~$4 invested with 8%
y
^
|
1 ------------------------
| +++++++ CDF (Cumulative Distribution Function)
| +
| + (x) .
|+ CDF = integral(PDF) = 1/(1+exp(-0.07*x^3-1.6*x))
+ (-inf)
**+**
** +| **
+ | * PDF = 1/sqrt(2*PI)*exp(-x*x/2)
** + | **
+*+*+*+ | ***** PDF (Probability Density Function)
---------------+------------------------> x
Example to calculate PDF and CDF at x=0:
1 0 ND (MENU - 3xDOWN - 7(F1))
2 PDF=0.3989=1/sqrt(2*PI)
3 SWAP
4 CDF=0.5
y
^ /
| Ypredict(x=1.5)=4
4 - <----------- /
| /
| / ^
| / |
| /
3 - [*] P2=(1|3)
| /
| / ^
| / |
| /
2 - [*] P1=(0.5|2)
| /
|_ / ^
| /| |
|/ | |
1 - | |
/| | |
/ | | |
/ | | Xpredict(y=1.5)=0.25
| v |
----+----+----|----+----|-> x
0 | 1 2
|
Xmean=0.75
| |
->|--|<- Standard Deviation S=0.354
Example to calculate mean value and standard deviation:
1 0.5 SUM 1 SUM ... enter X-data (SUM+ ... f-8)
2 STA (MENU - 3xDOWN - 8(F2))
3 Xmean=0.75 (mean value)
4 SWAP
5 S=0.354 (standard deviation)
Example to calculate the line of best fit (LR ... linear regression):
1 2 ENTER 0.5 SUM ... enter YX-data of first node (SUM+ ... f-8)
2 3 ENTER 1 SUM ... enter YX-data of second node (SUM+ ... f-8)
3 LR (MENU - 3xDOWN - 9(F3))
4 X=2 ... slope of best-fit-line
5 SWAP
6 Y=1 ... y-axis-intercept (y = 2x + 1)
| CONTRAST | STACK | CMD | CONST | REC1 | REC2 | REC3 | EOREC | EOEE
0 1 21 31 71 217 363 509 511
| +1 | +20 | +10 | +40 | +146 | +146 | +146 | +2 |
_____
Analog0/Reset D5 S0 H1|* U |H8 S7 Vcc
Analog2 D3 S1 H2| |H7 S6 D2 SCK/Analog1
Analog3 D4 S2 H3| |H6 S5 D1 PWM1/MISO
GND S3 H4|_____|H5 S4 D0 PWM0/AREF/SDA/MOSI
H...Hardware pin
S...Software pin
D...Digispark pin
____ _________
|* |--Vcc Vcc--| DISPLAY |
+---D3--| AT |--SCK-------SCK--| SSD1306 |
| |TINY| GND--| 128x32 |
| GND--|_85_|--SDA-------SDA--|__OLED___|
|
|
| ONE WIRE KEYBOARD ____
| Vcc--X----------X----------X----------X--|_Ra_|--+
| | | | | | ____
| X----------X----------X----------X----------+--|_Rb_|--+
| | | | | | ____
| X----------X----------X----------X---------------------+--|_Rc_|--+
| | | | | |
| X----------X----------X----------X--------------------------------+
| | | | |
| | ____ | ____ | ____ | R = 10k
+-------+--|_R1_|--+--|_R2_|--+--|_R3_|--+ R1 = R2 = R3 = 820
| ____ Ra = Rb = Rc = 3k3
+--|_R__|---GND
Approximate keycode with quadratic function: keyvalue = 2 * keynr^2 + 470
- 8192 bytes of flash memory (stores program code)
- 512 bytes of SRAM (holding variables)
- 512 bytes or EEPROM (stores settings and user data permanently)
- 128x32 pixels
- I2C communication (occupies two pins of the microcontroller only)
- Controlled by SSD1306
- 16 keys
- Analog keypad (occupies only one pin of the microcontroller)
- Needs 7 resistors
- 1 x CR2032 battery (3V)
To save flash memory a lot of functions are calculated with SCOTT itself (and not with libraries). Every command of SCOTT can be dispatched with one character (one byte command - see chapter COMMANDS). So a sequence of commands can be represented and "played" with a sequence of characters in a string.
After playing a string the result(s) is/are shown in the register(s) X and/or Y. Other parts of the stack (including mem) will be restored from a "shadow stack".
COMMANDS (5): 90 + SIN
Converts 4 mem - to: -
stack[] --------- -----
(incl. 3 t - - cos(x) = sqrt(1 - sin(x)*sin(x))
mem) 2 z - -
from: 1 y - -
0 x x cos(x)
COMMANDS (9): SIN ENTER ENTER * CHS 1 + SQRT /
Converts 4 mem - to: -
stack[] --------- ----- sin(x) sin(x)
(incl. 3 t - - tan(x) = ------ = -----------------------
mem) 2 z - - cos(x) sqrt(1 - sin(x)*sin(x))
from: 1 y - -
0 x x tan(x)
COMMANDS (4): ASIN CHS 90 +
Converts 4 mem - to: -
stack[] --------- ------
(incl. 3 t - - acos(x) = 90 - asin(x)
mem) 2 z - -
from: 1 y - -
0 x x acos(x)
COMMANDS (10): ENTER ENTER ENTER * 1 + SQRT INV * ASIN
Converts 4 mem - to: -
stack[] --------- ------ x
(incl. 3 t - - atan(x) = asin( ------------- )
mem) 2 z - - sqrt(1 + x*x)
from: 1 y - -
0 x x atan(x)
COMMANDS (14): CHS SWAP ENTER 1 + SWAP ROT SWAP PWR CHS 1 + ROTup /
Converts 4 mem - to: -
stack[] --------- ------- 1 - (1+i)^-n
(incl. 3 t - - PV(i,n) = ------------
mem) 2 z - - i
from: 1 y i -
0 x n PV(i,n)
COMMANDS (33): 1 + ENTER ENTER ENTER 12 * SWAP 10 * INV - INV +
1 EXP / SWAP PWR 2.506628 ROTup SQRT / *
Converts 4 mem - to: -
stack[] --------- --- x + 1/(12*x - 1/10/x)
(incl. 3 t - - (x-1)! = sqrt(2*PI/x)* (----------------------)^x
mem) 2 z - - e
from: 1 y - -
0 x x x!
COMMANDS (7): EXP ENTER INV CHS + 2 /
Converts 4 mem - to: -
stack[] --------- ------- exp(x) - exp(-x)
(incl. 3 t - - sinh(x) = ----------------
mem) 2 z - - 2
from: 1 y - -
0 x x sinh(x)
COMMANDS (6): EXP ENTER INV + 2 /
Converts 4 mem - to: -
stack[] --------- ------- exp(x) + exp(-x)
(incl. 3 t - - cosh(x) = ----------------
mem) 2 z - - 2
from: 1 y - -
0 x x cosh(x)
COMMANDS (9): 2 * EXP 1 - ENTER 2 + /
Converts 4 mem - to: -
stack[] --------- ------- exp(x) - exp(-x)
(incl. 3 t - - tanh(x) = ----------------
mem) 2 z - - exp(x) + exp(-x)
from: 1 y - -
0 x x tanh(x)
COMMANDS (8): ENTER ENTER * 1 + SQRT + LN
Converts 4 mem - to: -
stack[] --------- --------
(incl. 3 t - - asinh(x) = ln(x + sqrt(x*x + 1))
mem) 2 z - -
from: 1 y - -
0 x x asinh(x)
COMMANDS (8): ENTER ENTER * 1 - SQRT + LN
Converts 4 mem - to: -
stack[] --------- --------
(incl. 3 t - - acosh(x) = ln(x + sqrt(x*x - 1))
mem) 2 z - -
from: 1 y - -
0 x x acosh(x)
COMMANDS (11): ENTER ENTER 1 + SWAP CHS 1 + / SQRT LN
Converts 4 mem - to: -
stack[] --------- -------- 1 + x
(incl. 3 t - - atanh(x) = ln(sqrt(-----))
mem) 2 z - - 1 - x
from: 1 y - -
0 x x atanh(x)
COMMANDS (12): 1 STO ROT ENTER ENTER * ROT * ROT SWAP SQRT SUM1
Converts 4 mem - to: 1 and where
stack[] --------- --- SUM1 adds
(incl. 3 t - x*y stack[i]
mem) 2 z - x*x to
from: 1 y y y sum[i]
0 x x x
COMMANDS (37): ENTER ENTER ENTER * * .07 * CHS SWAP 1.6 * - EXP 1 + INV
SWAP ENTER * CHS 2 / EXP 0.3989423 *
Converts 4 mem - to: - (x)
stack[] --------- --- CDF = integral(PDF) = 1/(1 + exp(-0.07*x^3 - 1.6*x))
(incl. 3 t - - (-inf)
mem) 2 z - -
from: 1 y - CDF PDF = 1/sqrt(2*PI) * exp(-x*x/2)
0 x x PDF
COMMANDS (14): ENTER * SWAP ENTER ENTER ROT * + SQRT ENTER ROT / ASIN ROTup
Converts 4 mem - to: -
stack[] --------- --- r = sqrt(x*x + y*y)
(incl. 3 t - -
mem) 2 z - - y
from: 1 y y a a = atan(---)
0 x x r x
COMMANDS (15): SWAP SIN ENTER ENTER * CHS 1 + SQRT ROT * ROT * SWAP ROT
Converts 4 mem - to: -
stack[] --------- --- y = r * sin(a)
(incl. 3 t - -
mem) 2 z - -
from: 1 y a y x = r * cos(a)
0 x r x
COMMANDS (16): SWAP ROT ENTER RCL / ENTER ROT * CHS + RCL 1 - / SQRT SWAP
Converts 4 mem n to: - XX - X^2 / n
stack[] --------- --- d = sqrt(--------------)
(incl. 3 t XY - n - 1
mem) 2 z XX -
from: 1 y Y d m = X / n
0 x X m
COMMANDS (25): SWAP 2 / CHS ENTER ENTER * SWAP ROT SWAP - SQRT ROT ROT
ENTER ROTup ENTER ROT SWAP ROT - ROT + SWAP ROT
Converts 4 mem - to: -
stack[] --------- --- y = x*x + p *x + q
(incl. 3 t - -
mem) 2 z - - x1 = -p/2 + sqrt((p/2)^2 - q)
from: 1 y p x2
0 x q x1 x2 = -p/2 - sqrt((p/2)^2 - q)
COMMANDS (33): SUM2STACK * SWAP RCL * ROTup RCL * ROTup SHADOWSAVE
SUM2STACK ENTER * SHADOWLOAD1
SWAP ROT - ROT - ROTup / ENTER ENTER ENTER SHADOWSAVE
SUM2STACK SHADOWLOAD2 ROTup * - RCL / SWAP
Converts 4 mem n to: -
stack[] --------- --- y = a * x + b
(incl. 3 t XY -
mem) 2 z XX - a = (XY*n - X*Y) / (XX*n - X*X)
from: 1 y Y b
0 x X a b = (Y - X*a) / n
HI LO | 0 1 2 3 4 5 6 7 8 9 a b c d e f
--------------------------------------------------------
0 0000 | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 0010 | 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
2 0010 | 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
3 0011 | 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
4 0100 | 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
5 0101 | 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
6 0110 | 96 97 98 99 0 1 2 3 4 5 6 7 8 9 10 11
7 0111 | 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
8 1000 | 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
9 1001 | 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
A 1010 | 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
B 1011 | 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
C 1100 | 92 93 94 95 96 97 98 99 0 1 2 3 4 5 6 7
D 1101 | 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
E 1110 | 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
F 1111 | 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55
DEC | 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
HEX | 0 1 2 3 4 5 6 7 8 9 a b c d e f
------------------------------------------
032 20 | ! " # $ % & ' ( ) * + , - . /
048 30 | 0 1 2 3 4 5 6 7 8 9 : ; < = > ?
064 40 | @ A B C D E F G H I J K L M N O
080 50 | P Q R S T U V W X Y Z [ \ ] ^ _
096 60 | ` a b c d e f g h i j k l m n o
112 70 | p q r s t u v w x y z { | } ~
Constant ID Name
---recommended:-------------------------------------------
3.141593 PI Number PI
0.01745329 RpD Radians per Degrees
---from WP34S-Manual:-------------------------------------
365.2425 A Gregorian year
5.291772E-11 Ao Bohr radius
384.4E6 Am Semi-major axis of the Moon's orbit
1.495979E11 Ae Semi-major axis of the Earth's orbit
2.997942E8 c Speed of light
3.741772E-16 C1 First radiation constant
0.01438777 C2 Second radiation constant
1.602177E-19 e Electron charge
96485.34 F Faraday constant
2.502908 Fa Feigenbaum's alpha
4.669202 Fd Feigenbaum's delta
9.80665 g Standard earth accelleration
6.674083E-11 G Newtonian constant of gravitation
7.748092E-5 Go Conductance quantum
0.9159656 Gc Catalan's constant
-2.002232 Ge Lande's electron g-factor
6.626069E-34 h Planck constant
1.38065E-23 k Boltzmann constant
4.835979E14 Kj Josephson constant
1.616199 lP Planck length
9.109383E-31 me Electron mass
7.349E22 mM Mass of the Moon
1.674927E-27 mn Neutron mass
1.672622E-27 mp Proton mass
2.17651E-8 mP Planck mass
1.660539E-27 mu Atomic mass unit
1.492417E-10 Muc Energy equivalent of atomic mass unit
1.883541E-28 mm Muon mass
1.9891E30 mS Mass of the Sun
5.9736E24 mE Mass of the Earth
6.022141E23 NA Avogadro's number
101325 po Standard atmospheric pressure
1.875546E-18 qP Planck charge
8.314472 R Molar gas constant
2.81794E-15 re Electron radius
25812.81 RK Von Klitzing constant
1.73753E6 RM Mean radius of the Moon
1.097373E7 Ryd Rydberg constant
6.96E8 rS Mean radius of the Sun
6.37101E6 rE Mean radius of the Earth
273.15 To Standard temperature
5.39106E-44 tP Planck time
1.416833E-32 TP- Planck temperature
0.02241397 Vm Molar volume of an ideal gas
376.7303 Zo Impedance of vacuum
7.297353E-3 _A Fine structure constant
0.5772157 _GE Euler-Mascheroni constant
2.675222E8 _GP Proton gyromagnetic ratio
8.854188E-12 _Eo Electric constant or vacuum permitivity
2.42631E-12 _Le Compton wavelength of the electron
1.319591E-15 _Ln Compton wavelength of the neutron
1.32141E-15 _Lp Compton wavelength of the proton
1.256673E-6 _mo Magnetic constant or vacuum permeability
9.274009E-24 _mB Bohr's magneton
-9.284764E-24 _me Electron magnetic moment
-9.662364E-27 _mn Neutron magnetic moment
1.410607E-26 _mp Proton magnetic moment
5.050783E-27 _mu Nuclear magneton
-4.490448E-26 _mm Muon magnetic moment
5.670373E-8 _SB Stefan-Boltzmann constant
1.618034 _P Golden ratio
2.067834E-15 _Po Magnetic flux quantum