HP 67 Collection: October 2026

HP 67 Collection: October 2026

All examples are done in FIX 4. (DSP 4)

Earth's Gravity at a Specific Latitude

The true earth gravity force depends on several factors, such as latitude and altitude. This estimation takes the latitude (north/south), in degrees-minutes-seconds, and latitude, in kilometers, into account.

The constant 9.80665 m/s^2 is an accepted average, the true force varies.

g_s = 9.806 – 0.026 * cos(2 * φ)

g_h = g_s * (6378.1 / (6378.1 + h))

HP 67 Code:

LBL A: 001 31, 25, 11

DEG: 002 35, 41

H←: 003 31, 74

2 : 004 02

× : 005 71

COS: 006 31, 63

. : 007 83

0 : 008 00

2 : 009 02

6 : 010 06

× : 011 71

9 : 012 09

. : 013 83

8 : 014 08

0 : 015 00

6 : 016 06

x<>y: 017 35, 52

- : 018 51

x<>y: 019 35, 52

6 : 020 06

3 : 021 03

7 : 022 07

8 : 023 08

. : 024 83

1 : 025 01

+ : 026 61

LST x: 027 35, 82

x<>y: 028 35, 52

÷ : 029 81

× : 030 71

RTN : 031 35, 22

Inputs:

Y: h

X: φ

Examples:

Inputs: h = 0, φ = 2°33’: g ≈ 9.7801

Inputs: h = 0.762, φ = 52°17’: g ≈ 9.8114

Source 

Grainger Engineering Office of Marketing and Communications. (answer written by Rebecca H.) (2016, November 21). “How gravitational force varies at different locations on Earth.” Illinois. https://van.physics.illinois.edu/ask/listing/64061. Retrieved March 10, 2026.

Triangulation

With angles α and ß:

base = dist * (1/tan α + 1/tan ß)

dist = base ÷ (1/tan α + 1/tan ß)

Labels:

LBL A: Enter angles α and ß in the current angle mode. Returns 1/tan α + 1/tan ß.

LBL B: Base. When a number is entered prior to pressing [ B ], the number is stored as a base. Otherwise, the program solves for a base.

LBL C: Distance (of a line that bisects the base). When a number is entered prior to pressing [ C ], the number is stored as a base. Otherwise, the program solves for a base.

HP 67 Code:

LBL A: 001 31, 25, 11 (enter the angles)

TAN: 002 31, 64

1/x: 003 35, 62

x<>y: 004 35, 52

TAN: 005 31, 64

1/x: 006 35, 62

+: 007 61

STO 5: 008 33, 05

RTN: 009 35, 22

LBL B: 010 31, 25, 12 (base)

STO 3: 011 33, 03

F? 3: 012 35, 71, 03

RTN: 013 35, 22

RCL 4: 014 34, 04

RCL 5: 015 34, 05

× : 016 71

STO 3: 017 33, 03

RTN: 018 35, 22

LBL C: 019 31, 25, 13 (distance)

STO 4: 020 33, 04

F? 3: 021 35, 71, 03

RTN: 022 35, 22

RCL 3: 023 34, 03

RCL 5: 024 34, 05

÷ : 025 81

STO 4: 026 33, 04

RTN: 027 35, 22

Examples:

α = 30°, ß = 65°

Set degree mode. 30 [ ENTER ] 65 [ A ]. Result: 2.1984

Distance = 24, solve for base. 24 [ C ] [ B ]. Result: 52.7606

Base = 24, solve for distance. 24 [ B ] [ C ]. Result: 10.9172

Source:

“Triangulation (surveying)” Wikipedia. https://en.wikipedia.org/wiki/Triangulation_(surveying) (last edited October 24, 2025). Retried March 17, 2026

Time of Runoff on Turf

t = 2.5 * (L / (S * I^2))^(1/3)

t: time of runoff (rain off) in minutes

2.5: turf constant

L: distance from remote area in feet

S: slope of the terrain

I: rain intensity in inches per hour

Input Stack:

Z: L

Y: S

X: I

Output Stack:

X: t

HP 67 Code:

LBL A: 001 31, 25, 11

x² : 002 32, 54

× : 003 71

÷ : 004 81

3 : 005 03

1/x: 006 35, 62

y^x: 007 35, 63

2 : 008 02

. : 009 83

5 : 010 05

× : 011 71

RTN: 012 35, 22

Examples:

Inputs: Z: 900 ft, Y: 0.11, X: 4 in/hr. Result: 19.9917 min

Inputs: Z: 650 ft, Y: 0.33, X: 0.06 in/hr. Result: 204.4744 min

Source

Texas Instruments. Slide Rule Calculator SR-50A Manual. 1975. Manual from datamath.org: http://www.datamath.net/Manuals/SR-50A_US.pdf pg. 59

Beamwidth of a Radio Telescope

This program calculates the beam width of a radio telescope in degree-minutes-seconds.

Θ = 67625 ÷ (D * f)

Θ = beam width

D = the diameter of a circular telescope in feet

f = observing frequency in MHz (megahertz)

Inputs:

Y: D

X: f

Outputs:

X: Θ

HP 67 Code:

LBL B: 001 31, 25, 12

× : 002 71

1/x : 003 35, 62

6 : 004 06

7 : 005 07

6 : 006 06

2 : 007 02

5 : 008 05

× : 009 71

→H.MS: 10 32, 74

RTN: 11 35, 22

Examples:

Inputs: X: 1980 MHz, Y: 106 ft. Output: Θ: 0.1920 (19’20”)

Inputs: X: 1665 MHz, Y: 84 ft. Output: Θ: 0.2901 (29’01”)

Source

Ball, John A. Algorithms for RPN Calculators John Wiley & Sons: New York, NY. 1978. ISBN 0-471-03078-8. pg. 259

Fan Laws

p2 = (rpm2 ÷ rpm1)^n * p1

(p1 and p2 stand for various parameters, see the input syntax below)

Inputs:

1^st law: (cfm: cubic feet per minute, rpm: revolutions per minute)

Calculate cfm2:

T: cfm1

Z: rpm2

Y: rpm1

X: 1

2^nd Law: (sp: static pressure, rpm: revolutions per minute)

Calculate sp2:

T: sp1

Z: rpm2

Y: rpm1

X: 2

3^rd Law: (hp: horsepower, rpm: revolutions per minute)

Calculate hp2:

T: hp1

Z: rpm2

Y: rpm1

X: 3

HP 67 Code:

LBL B: 001 31, 25, 12

R↓ : 002 35, 53

÷ : 003 81

R↑ : 004 35, 54

y^x: 005 35, 63

× : 006 71

RTN: 007 35, 22

Examples

1^st Law: T: cfm1 = 2000, Z: rpm2 = 1100, Y: rpm1 = 950, X: n = 1

Result: cfm2 ≈ 2315.7895

2^nd Law: T: sp1 = 0.5, Z: rpm2 = 1100, Y: rpm1 = 950, X: n = 2

Result: sp2 ≈ 0.6704

3^rd Law: T: hp1 = 1.5, Z: rpm2 = 1100, Y: rpm1 = 950, X: n = 3

Result: hp2 ≈ 2.3286

Source

Gladstone, John. Air Conditioning Testing and Balancing: A Field Practice Manual A Van Nostrand Reinhhold Book. August 1976. pp. 24-32

More HP 67 goodness to come in November,

Eddie

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.