HP 67 Collection: November 2026
All examples are done in FIX 4. (DSP 4)
Circular Sector – Degrees
R: radius
Θ°: angle in degrees
Arc Length: A = π * Θ° * R ÷ 180
Chord Length: L = 2 * R * sin(Θ° ÷ 2)
Input Stack:
Y: Θ°
X: R
Code:
LBL A : 001 31, 25, 11
ENTER : 002 41
ENTER : 003 41
CLx : 004 44
- : 005 51
R↓ : 006 35, 53
x<>y : 007 35, 52
R↓ : 008 35, 53
DEG : 009 35, 41
→R : 010 35, 73
× : 011 71
-x- : 012 31, 84 (show arc length)
R↓ : 013 35, 53
R↓ : 014 35, 53
2 : 015 02
÷ : 016 81
SIN : 017 31, 62
× : 018 71
RTN: 019 35, 22 (show chord length)
Examples
Inputs: Y: Θ = 45°, X: R = 8.36
Outputs: Arc Length: 6.5659, Chord Length: 17.2208
Inputs: Y: Θ = 30°, X: R = 7.92
Outputs: Arc Length: 4.1469, Chord Length: 7.7646
Inputs: Y: Θ = 120°, X: R = 10
Outputs: Arc Length: 20.9440, Chord Length: 103.9230
Capacitor Voltage Across an RC Circuit
Vc = Vi * (1 – e^(-t ÷ (R * C))
Inputs:
T: Vi: step voltage (Volts, V)
Z: t: time elapsed (Seconds)
Y: R: resistance (Ohms, Ω)
X: C: capacity (Farads, F)
Output:
Vc: voltage across the RC circuit (Volts)
Code:
LBL B : 001 31 25 12
× : 002 71
÷ : 003 81
CHS: 004 42
e^x : 005 32, 52
1 : 006 01
x<>y : 007 35, 52
- : 008 51
× : 009 71
RTN : 010 35, 22
Examples
Inputs:
T: Vi: 18 V
Z: Time: 250 * 10^-3 sec
Y: Resistance: 3300 Ω
X: Capacitance: 47 * 10^-6 F
Output: 14.4087 V
Inputs:
T: Vi: 30 V
Z: Time: 0.5 sec
Y: Resistance: 2000 Ω
X: Capacitance: 53 * 10^-6 F
Output: 29.7317 V
Source
Texas Instruments. Slide Rule Calculator SR-50A Manual. 1975. Manual from datamath.org: http://www.datamath.net/Manuals/SR-50A_US.pdf pg. 61
Ideal Thermal Voltage and Shockley Diode Equation
Thermal Voltage:
Vt = k * T ÷ q * 10^3 (mV)
Constant used (values taken from a Casio fx-9910CW):
k: Boltzmann Constant: 1.380649 * 10^-23 J/K
q (e): Electron Charge: 1.602176634 * 10^-19 C
k/q ≈ 1 / 11604.51812
The equation can be simplified to (SI units):
Vt ≈ (T°C + 273.15) ÷ 11604.51812
Shockley Diode Equation:
Id = Is * (exp(vD ÷ (n * vt)) – 1)
Ideal: n = 1
Then:
Id = Is * (exp(vD ÷ vt – 1)
Input Stack:
Z: Is: reverse bias saturation current (in milliamps)
Y: Vd: voltage across the diode (millivolts)
X: T°C: temperature in Celsius (°C)
Outputs:
Vt: thermal voltage (millivolts) – stored in memory register 1
Id: diode current (milliamps) – stored in memory register 2
Code:
LBL C : 001 31 25 13
ENTER: 002 41
2 : 003 02
7 : 004 07
3 : 005 03
. : 006 83
1 : 007 01
5 : 008 05
+ : 009 61
1 : 010 01
1 : 011 01
6 : 012 06
0 : 013 00
4 : 014 04
. : 015 83
5 : 016 05
1 : 017 01
8 : 018 08
1 : 019 01
2 : 020 02
÷ : 021 81
3 : 022 03
10^x : 023 32, 53
× : 024 71
STO 1 : 025 33 01
-x- : 026 31 84 (show Vt)
÷ : 027 81
e^x : 028 32 52
1 : 029 01
- : 030 51
× : 031 71
STO 2 : 032 33 02 (show Id)
RTN : 033 35 22
Examples:
Inputs:
Z: Is: 35 mA
Y: Vd: 40 mV
X: T°C: 27 °C
Outputs:
Vt: 25.8649 mV
Id: 129.3246 mA
Inputs:
Z: Is: 35 mA
Y: Vd: 40 mV
X: T°C: 33 °C
Outputs:
Vt: 26.3820 mV
Id: 124.4189 mA
Inputs:
Z: Is: 35 mA
Y: Vd: 10 mV
X: T°C: 33 °C
Outputs:
Vt: 26.3820 mV
Id: 16.1312 mA
Source:
“Shockley Diode Equation” Wikipedia. Last Edited November 13, 2025.
https://en.wikipedia.org/wiki/Shockley_diode_equation
Retrieved June 19, 2026.
Angle of a Banked Turn
Determine the angle of a banked turn, which is a turn which a vehicle includes towards the inside of a turn. The slope is usually sloped down towards the center of the curve. In this equation, friction is not considered.
The banked turn in degrees, not considering friction:
Θ° = arctan( v² ÷ (r * g)) * 180 ÷ π
v: velocity of the vehicle
r: radius of the curve
g: gravitational constant.
Θ: banked angle
Note: We can apply elevation and latitude if desired:
g_ø, h ≈ (9.806 – 0.026 * cos(ø°)) * (6378.1 ÷ (6378.1 + ø))
(ø is latitude (North/South) in degrees, h is elevation in kilometers)
In this program, the standard Earth’s gravity constant is used (g = 9.80665 m/s²). The program switches angle modes: first to radians then to degrees.
Input Stack:
Y: radius (in meters)
X: velocity (in meters per second)
Output: banked angle in degrees
Code:
LBL A : 001 31 25 11
RAD : 002 35 42
x² : 003 32 54
x<>y : 004 35 52
9 : 005 09
. : 006 83
8 : 007 08
0 : 008 00
6 : 009 06
6 : 010 06
5 : 011 05
× : 012 71
÷ : 013 81
TAN^-1 : 014 32 64
D← : 015 31 73
DEG : 016 35 41
RTN : 017 35 22
Example:
Input:
Y: r: 1280 m
X: v: 16 m/s
Output:
Θ: 1.1683°
Source
The Engineering ToolBox (2012). Banked Turn. [online] Available at: https://www.engineeringtoolbox.com/banked-turn-d_1844.html Accessed June 24, 2026
Another day with one of my favorite calculators. Until next time,
Eddie
HHC Conference Videos
Please check out the Youtube page hpcalc.org at https://www.youtube.com/@hpcalc .
Videos and talks from HP Calculator conferences until HCC 2025 are posted. Look out for talks from HCC 2026 to posted there soon. Disclaimer: I do not run this account.
All original content copyright, © 2011-2026. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.