HP 67 Collection: November 2026

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.

Casio fx-6500P Program Library 2025

Casio fx-6500P Program Library 2025

Last birthday, I reviewed the rare classic, the Casio fx-6500G:

https://edspi31415.blogspot.com/2024/03/spotlight-casio-fx-6500g.html

Parabola Area and Maximum Point: Program P1: Steps 114

Area Under a Parabola set up by the equation:

y = -((x – a)*(x – b)) = -x^2 + p*x – q

p = a + b

q = a * b

Cls

“-((X-A)×(X-B))”

“A”? →A

“B”? → B

A+B → P

AB → Q

-B^3 ÷ 3 + B² P ÷ 2 – Q B + A^3 ÷ 3 - A² P ÷ 2 + Q A → R

“AREA:”

R ◢

“MAX PT:”

P ÷ 2 →X ◢

-((X-A)×(X-B)) → Y

The caret symbol ^ stands for [x^y].

Example:

y = -((x + 4) * (x – 2)) = -x^2 – 2*x + 8

A = -4, B = 2

Area: 36

Maximum Point: (-1, 9)

Circular Sector: Arc Length and Sector Area: Program: P2: Steps: 59

“RADIUS”? →R

“ANG(°)”? → T

RTπ÷180 →L

RL÷2 →A

“ARC LENGTH:”

L ◢

“AREA:”

A

The degree character is generated by the [° ‘ “] key.

Example:

R = 10.5, T (angle) = 120°

Results: Arc length = 21.99114858, Area = 115.45353

Integer Division: Program: P3: Steps: 51

“INT÷”

“X>0”? →X

“M>0”? →M

Int(X÷M)→Q

X-M×Q→R

Q ◢

“REM”

R

Examples:

43 Int÷ 11 = 3 Rem 10

7263 Int÷ 1849 = 3 Rem 1716

Hint: To find out the number of steps in a single program? Simply scroll down the last character and hold down the [ MDisp ] key. Kind of neat because this works outside of programming mode. I think this key was available on most Casio graphing calculators well into the fx-7700G (single G) and fx-9700Gα (E,M,H) series in mid 1990’s.

95% Population Proportion: Program P4: Steps: 96

X successes out of population N

“95 PRCT PROP”

“X”? → X

“N”? → N

X ÷ N → P

√(P(1-P))→ M

1.959963984 M ÷ √N → H

P – H → L

L + 2H → H

“LOW:”

L ◢

“HIGH:”

H

Example:

X = 850, N = 1176

Interval:

LOW: 0.6972058859

HIGH: 0.7483723454

Interval:

Source: HP 21S Stat/Math Calculator: Owner’s Manual. Hewlett Packard. 3^rd Edition. June 1990.

Power Generated by a Wind Turbine: Program P5: Steps: 82

“WIND PWR”

“RADIUS (M)”? →R

“SPEED (M÷S)”? → V

“DENSITY”? →P

π × R² × P × V^3 ÷ 2 → W

“POWER:”

W

Example:

R = 8.18 m, V = 4.48 m/s, P = 1.2 kg/m³

Result: 11340.74989 W

Source: Sharp Electronics Corporation Conquering The Sciences: Applications for the SHARP Scientific Calculator EL-506A Sharp Corporation. Osaka, Japan. 1986. pp.75-77

Round to Nearest Integer (display only): Program P6: Steps: 11

?→N

Fix 0

Rnd

Norm

Examples:

N = 19.273 → 19

N = 44.8273 → 45

N = -2.82 → -3

That’s it. I wish you all a wonderful day. Thank you,

Eddie

All original content copyright, © 2011-2025. 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.

Circular Sector: Finding the Radius and Angle

 Circular Sector: Finding the Radius and Angle

Here is the problem:

We are given the area of the circular segment, A, and the arc length of the segment, s. What is the radius, r, and the angle, θ?

The arc length is calculated as: s = θ * r

The area is calculated as: A = ½ * θ * r^2

We have the system of equations:

A = ½ * θ * r^2

s = θ * r

Divide A by s:

A / s= (½ * θ * r^2) / (θ * r)

A / s = r / 2

2 * A / s = r

Then

s = r * θ

θ = s / r = s^2 / (2 * A)

In summary:

r = 2 * A / s

θ = s / r = s^2 / (2 * A)

Note that the angle is in radians.

Example

Example 1:

s = 4, A = 30

r = (2 * 30) / 4 = 15

θ = 4 / 15 ≈ 0.266666667

Example 2:

s = 10.5, A = 31.8

r = (2 * 30) / 4 = 212/35 ≈ 6.057142857

θ = 10.5 / (212/35) = 735/424 ≈ 1.733490566

Eddie

All original content copyright, © 2011-2024. 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.