Program Library U for RPN-67 & 97

This library is intended to hold all kinds of unclassified and user-contributed programs.

Please note:
For copyright reasons, documentation is not available for download. User's manuals in PDF format for all programs listed below
are available from The Museum of HP Calculators.

You may import cards into RPN-67 or RPN-97 – no manual conversion is required.
See section "Sharing" to learn how to load cards.
 

 
User's Library Individual Programs
00226D - Algebraic Notation This program turns the HP-67/97 into an algebraic calculator with 10 levels of parentheses and 11 pending operations.
00239D - Random Integers Given a random seed between 0 and 1, this program will generate as many as 216 pseudo-random integers without repetition.
00251D - Head Loss in Pipes
Mar 25, 2017
To move a given volume of liquid through a pipe requires a certain amount of energy. An energy or pressure difference must exist to cause the liquid to move. A portion of that energy is lost to the resistance to flow. This resistance to flow is called head loss due to friction.
00252D - LNAP (Ladder Network Analysis Program) This program will provide the transfer function (20 log magnitude and phase) of a ladder network consisting of 1 to 4 nodes and up to 8 branches. Sketch
00297D - LC-LNAP (LC Ladder Network Analysis Program) This program will provide the transfer function (20 log magnitude and phase) of a ladder network consisting of up to seven LC branches. Sketch
00301D - Second Order Active Network Pole and Zero This program will provide the coefficients of the numerator and denominator polynomials of the transfer function H(s) = N(s)/D(s) of a generalized second order active network as shown in this Sketch. Figures: Example, EE-08A.
00315D - Curve Fitting Using Cubic Splines This program will fit a cubic spline interpolating curve through 2 to 9 equally spaced points.
00648D - Arithmetic Progressions Given three quantities of an arithmetic progression, computes the remaining two quantities.
00653D - Multiplication of Two 25-Digit Numbers This program multiplies two numbers of up to 25 digits each and returns the exact result.
00680D - Gaussian Elimination for up to 12 Equations
Apr 19, 2017
This program uses Gaussian Elimination to solve a linear system of up to 12 equations and unknowns. Documentation
00761D - Complete Calendar / Julian Date Functions This program converts Julian (Old Style, OS) or Gregorian (New Style, NS) calendars to Julian Day Number (JDN) and vice versa, computes day of week (DoW), and permits interconversion of Julian and Gregorian dates.
01602D - Fast Factor Finder With Automatic Answer Accumulation Factoring of large integers.
01650D - Random Sequence of Numbers Randomly selects all of the numbers between 1 and N, without repeating any numbers.
01683D - Open Channel Design
Mar 15, 2017
This program will aid in the design of open channel sections. The flow, channel slope, and Manning's "n" are required input, and for trapezoidal and rectangular sections the side slope is also required.
Manning's "n" Coefficients
01884D - Noughts and Crosses Written by 8-year-old Zvi Schreiber, this program allows to players to play Noughts and Crosses (or Tic-Tac-Toe.)
Picture of Zvi (from HP Key Notes, 1978)
03055D - Is it prime?
Aug 2, 2016
This program tests whether an integer N, N > 2, is prime. It also finds the lowest prime number P, n ≤ P, and if desired will continue to display successive primes indefinitely.
03250D - Doppler Effect - Interchangeable Solutions This program provides interchangeable solutions for both classical and relativistic Doppler shifts.
03949D - Relativity - Interchangeable Solutions This program provides interchangeable solutions for the basic relationships of Einstein's Special Relativity. Additionally, interchangeable solutions
for e = mc2 are provided.
03952D - How Old Are You? Given the present date and a birthdate, this program computes present age, number of days to next birthday, age on next birthday.
03994D - Fast Factorial Factor Finder Given an integer n, the program produces the prime factors of n! (n factorial) and the multiplicity of each factor.
04338D - Fast Combinations, Permutations, and Factorials This program computes combinations, permutations, and factorials for positive integers up to and including 1099.
04356D - Engine Out! Try to land an aircraft with a failed engine.
50024 - Sentential Logic For Up To 9 Unknowns Given an expression F (logical puzzle, TTL circuit, Boolean equation) in n unknown propositions and Boolean operators, the program finds all solutions of F = "true" or F = "false".
50089 - 5th Degree Equation This program solves 5th degree equations of the type x5 + ax4 + bx3 + cx2 + dx + e = 0. Roots are displayed in rectangular or polar form.
50495 - Multiple Integrals This program computes the integral of functions of 1, 2, or 3 variables over a finite interval, a rectangular region in the plane, or a parallel-epiped in 3D-space by means of the rectangle rule.
50520 - Approximation by Legendre Polynomials up to Degree 7 A set of m+1 equally spaced data points (xi,yi) (i=0..m) is approximated by a sum of Legendre Polynomials Pk(t).
See program 50813 below to turn the result into a power series with argument x.
50653 - n-th Degree Polynomial (n ≤ 18) This program finds the roots of a polynomial of up to degree 18.
50684 - Linear Systems In Up To 7 Unknowns This program solves linear systems of up to 7 unknowns.
50685 - Determinants Up To 8x8 This program calculates a determinant of degree k (k = 2...8). Its elements have to be entered only once.
50784 - Fourier Coefficients This program will compute Fourier coefficients of a function defined on a finite interval. The function may consist of up to three parts and should not be continuous.
50812 - 5x5, 4x4, 3x3 Matrices This program calculates cofactors and the determinant (if one exists) for 5x5, 4x4, and 3x3 matrices which are entered directly or by data card.
50813 - Conversion of Legendre Polynomials into Power Series This program is an optional complement to program 50520. It converts the sum of Legendre Polynomials ŷ = ∑akPk(t) into an ordinary power series
ŷ = ∑ckxk.
50925 - Linear 2nd Order Boundary-value Problem The program computes by 4th order Runge-Kutta integration the solution of the linear differential equation y" = f(x,y,y') for boundary conditions of the third kind
α1y(a) + β1y'(a) + γ1 = 0
α2y(a) + β2y'(a) + γ2 = 0
The program thus comprises boundary conditions of the first kind (β1 = β2 = 0) and second kind (α1 = α2 = 0 ).
51352 - Chebyshev Economisation Given a polynomial p(x) = ∑ak*xk (k = 0..n) over an interval I = [xL,xR] and ε ≥ 0, this program computes another polynomial q(x) = ∑bk*xk (k = 0..m) over I with m ≤ n and ε1 := Max |p(x)-q(x)| ≤ ε
51403 - Double Precision Arithmetic For Positive Integers This 3-card program provides basic arithmetic for integers of up to 18 digits. A 4-level stack and storage registers are provided
51658 - Approximation By Summing 4 Functions This program computes the coefficients A, B, C, D of the curve fitting y = Af1(x) + Bf2(x) + Cf3(x) + Df4(x) = f(x).
51772 - Texas Simulator This program allows you to use your calculator in Algebraic Notation. You can use brackets like in algebra, e.g. (3+5)x(7+12). Up to five pending operations are supported.
51892 - Literal Derivation of Functions This program finds the derivative of functions of x. Functions may include up to 10 external constants and a number of operations such as sin, cos, ln.
52046 - Square Root to 182 Digits This program calculates up to 182 digits of the square root of any integer greater than 1 and less than 8 digits.
52112 - Palindromic Numbers The program reverses the order of the digits of an integer and checks whether the integer equals the reversed one. If not, the two integers are added and the sum is inversed again, and so on until the number becomes a palindrome.
60060 - Multiply Two Numbers Up To Twenty Digits This program multiplies two numbers of up to 20 digits each and returns the exact result. It features easy number input.
60123 - New and Full Moon Date This program finds the date of New Moon and of Full Moon for any month m and any year y between 0 and 2100.
60377 - Fourier Series - Harmonic Analysis - Discrete Domain Given n data points that are samples of a periodic function y(x), this program approximates y(x) by a Fourier series of the same period as y(x). Sketch
60453 - Elliptic Lowpass Filter Design This program helps design elliptic lowpass filters, given amin (min. stopband loss), amax (max. passband loss), fb (upper passband edge), fh (upper stopband edge). If the degree is ≤ 30, the program also finds the zeros and poles of attenuation.
60454 - Factors of a Number This program will find all prime factors of a positive integer n.
60534 - Areas, Length of Arcs This program calculates areas, length of arcs, volumes and surfaces of revolution generated by curves expressed either in rectangular or polar coordinates.
60535 - Numerical Analysis of Functions This program provides several of the most useful routines that may be found in numerical analysis for the purpose of analyzing a given function of x.
60582 - Summation of an Infinite Alternating Series This program computes the sum of alternating series of the form:
y(0) - y(1) + y(2) - y(3) +... = ∑(-1)i y(i)  for i = 0...∞.
 

 
Electronics

These programs were written by Stefan Vorkoetter. Please visit http://www.stefanv.com/vintage-calculators for full documentation.
Low-Sensitivity Sallen-Key Filter Design This program addresses the problem of designing second order single op-amp low- and high-pass filters using the Sallen-Key topology.
Op-Amp Gain and Offset Stage Design This program is for designing offset-and-gain stages using a single operational amplifier.
Op-Amp Oscillator Design This program selects component values for an op-amp based relaxation oscillator, given the desired frequency and output wave form peak voltages.
Resistor Networks of 1 or 2 Nodes This program can find node voltages in networks of one or two nodes, with up to five resistors and/or constant current sources per node.
 

 
Games
Pinball Wizard
Mar 15, 2017
This program will duplicate the play of a standard pinball machine. For details refer to this article from BYTE magazine, June 1978.
 

 
Math
Jean-Michel Muller's Recurrence
rev. Feb 8, 2014
Demonstrates Muller's Recurrence formula, as discussed on HP Forum.
Accurate Normal Distribution
rev. Mar 23, 2017
This program evaluates various functions of the Standard Normal distribution with high accuracy.
For details see this thread on The Museum of HP Calculators.
Extended Precision Multiplication
Mar 8, 2019
This program computes the product of any two numbers if their total combined digits does not exceed 210.
Author: Ron Knapp, PPC Journal, June 1978, p.24-25
Extended Precision Division
Mar 9, 2019
This program computes the quotient of any two positive integers up to 90 digits in length. The number of digits in the answer which the program outputs is unlimited. If the quotient is a terminating decimal then the program will stop execution after it has output all of the significant digits.
Includes a data card with sample dividend/divisor.
Author: John Kennedy, PPC Journal, July 1978, p.7-8
Extended Precision Squares
Mar 13, 2019
This program calculates the square of any number up to 230 digits. The result can be the exact square carried out completely, or the square of an approximation, carried out to the same number of digits as the input.
Original program fixed to make it work.
Author: Ron Knapp, PPC Journal, June 1978, p.24 & 27
Large Factorials to 8 Places
Mar 11, 2019
This program calculates the first eight digits and the 10's exponent of the factorial of very large numbers.
Author: Bill Barnett, PPC Journal, June 1978, p.10
Large Powers and Exact Factorial
Mar 11, 2019
This program may be used to compute large powers, mⁿ, where m and n are integers, m has 5 or less digits and n has 3 or less digits.
The program may also be used to compute n! exactly where 14 ≤ n ≤ 99.
Slightly extended and therefore should not be run in vintage mode.
Author: John Kennedy, PPC Journal, July 1978, p.9
SIN or COS to 20 Places
Mar 13, 2019
This program computes the COS of any angle 0° ≤ A ≤ 90°. When SIN is desired, the angle is subtracted from 90° and then the COS is computed.
Modified in order to eliminate data card and therefore not compatible with vintage mode.
Author: Ron Knapp, PPC Journal, June 1978, p.28
SIN or COS to 105 Places
Mar 30, 2019
This remarkable program computes the SIN or COS to 105 digits. Three cards requiring two merge operations are involved. Original runtime was about 7 hours.
The included data card is only needed if "Enhancements" are "Off" in Settings.
Author: Ron Knapp, PPC Journal, June 1978, p.26–27. Download original article.
Pi to 50 Places
Mar 30, 2019
This program computes Pi to 50 digits (last digit is inaccurate). Original runtime on HP-67 was about 1 hour.
Author: Ron Knapp, PPC Journal, June 1978, p.29.
Pi to 120 Places
Mar 30, 2019
This program computes Pi to 120 decimal digits. Original runtime on HP-67 was about 5 hours and 45 minutes.
Author: Ron Knapp, PPC Journal, June 1978, p.29–30.
Successive Bisections
Mar 31, 2019
This program solves equations of the form f(x) = 0, where f(x) represents a general function, by the method of successive bisections.
Author: John Kennedy, PPC Journal, Sep/Oct 1978, p.19–21. Download original article.
Quartic Equation
July 26, 2019
This program solves the quartic equation ax⁴ + bx³ + cx² + dx + e = 0.
It makes use of the built-in Extra Function #106 ("Quartic Function") and therefore must be run with "Enhancements" turned on.
Three examples are included.
Roots of a Quartic Equation
July 28, 2019
This program solves the quartic equation x⁴ + a₃x³ + a₂x² + a₁x + a₀ = 0.
Compatible with vintage mode.
Ref.: "NASA Technical Memorandum 78678", Nov 1978, p.38–42 & 53. Download document.
 

 
Mechanical Engineering
Max Rope Tension A simple program to calculate rope tension, based on load, friction, number of parts and number of deflected pulley/sheaves. Sketch
Provided as HP-35s program by Jean-Marc Biram on HP Forum (12/8/13).
 

 
Miscellaneous
Radar Detection
Mil
June 4, 2020
This set of 8 programs provides the user with commonly used radar-detection performance data. Both fixed threshold and adaptive threshold CFAR detection with noncoherent integration are covered. Recursive programs for the general chi-squared target fluctuation distribution are treated as well as faster running recursive programs for the Swerling target Cases I – IV. Also included are fast programs for the required detection signal-to-noise ratio based on the simplified algorithms of Barton.
Documentation (PDF)
Nuclear Blast
Mil
May 21, 2020
This program has been designed to solve the blast wave from a nuclear detonation. It comes in two versions: (1) for the troposphere (36,000 ft and less), (2) for the stratosphere (36,000 to 82,000 feet).
Documentation (PDF)
II – Active Sonar Acquisition
Mil
July 3, 2020
This program helps determining the acquisition range of a sonar at a depth SD with various geometries and acoustic parameters when a target is located at a depth TD at a slant range r'.
Documentation (PDF, page 3)
III – P-3: Three Engine Available Range
Mil
May 20, 2020
This program allows a pilot or copilot to rapidly and efficiently provide a quick estimate of available range remaining in an emergency situation (three engine flight).
Documentation (PDF, page 25)
IV – P-3: Mission Planning
Mil
May 20, 2020
This program allows the pilot or flight engineer to enter P3-B aircraft's altitude and gross weight and find the indicated airspeed (IAS) to fly most efficiently.
Documentation (PDF, page 33)
V – P-3: Approach and Landing
Mil
May 20, 2020
This program is a time-step simulation of the final five miles of a precision approach for a Lockheed P-3 ORION aircraft.
Documentation (PDF, page 41)
IX – Normal Mode Theory
Mil
May 30, 2020
This program determines the number of normal modes that will propagate in a given ocean model. The ocean model must have either a rigid bottom or pressure release bottom..
Documentation (PDF, page 111)
X – Normal Mode Transmission Losses
Mil
May 30, 2020
This program shows that – as an alternative to Ray Theory – the use of Normal Mode Theory provides a more exact approach to the solution of transmission loss models.
Documentation (PDF, page 123)
XI – Golden Section Search
Mil
May 20, 2020
This program finds the minimum value of a unimodal function of one variable, f(x), for a specified interval by utilizing Golden Section Search Techniques.
Documentation (PDF, page 137)
RPN Shopping
Apr 5, 2018
A little shopping app which will give you a paper tape of the prices paid, a total of the prices, total taxes paid, and a grand total. Also handles taxes.
 

 
Navigation
MPP of a Vessel
Navigation
Apr 26, 2017
After obtaining several lines of position (LOP) from celestial observation, navigator is faced with one more challenge – combine all those lines into a single point, so-called most probable position of his vessel, or MPP.
Position with Loran-C
Navigation
May 28, 2020
This program executes position determination with Loran-C chains. Operational data cards are prepared in advance for Loran-C triplets. Position determination is performed using a single program card and an appropriate onerational data card. A sample data card is included.
Documentation (PDF)
Course, Speed, Position
Mil
May 26, 2020
This program provides a procedure for estimating a contact's course, speed and position based on bearings-only data from two moving sensors.
Documentation (PDF)
 

 
RPN-67/97 only

These programs make use of the extended features of RPN-67/97. They must be run with setting "Enhancements" set to Max.
00251XT - Head Loss in Pipes
Mar 25, 2017
This extended version handles both imperial/US and metric units.
To move a given volume of liquid through a pipe requires a certain amount of energy. An energy or pressure difference must exist to cause the liquid to move. A portion of that energy is lost to the resistance to flow. This resistance to flow is called head loss due to friction.
01683XT - Open Channel Design (Extended)
Mar 15, 2017
This extended version handles both imperial/US and metric units.
This program will aid in the design of open channel sections. The flow, channel slope, and Manning's "n" are required input, and for trapezoidal and rectangular sections the side slope is also required.
Manning's "n" Coefficients
3D Rotations
Math
Jun 27, 2020
This program rotates a point in 3D space about a fixed coordinate system or it can rotate the coordinate system about a point.
Updated for a much improved user interface making use of inline texts introduced in v4.3.
Written by Don Phillips.
Accounting
Accounting
Jun 9, 2020
This is a simple program to handle debits and credits.
Updated to show total credits and debits when computing average credits and debits.
Written by Don Phillips.
Analysis of Variance (One-Way)
Statistics
July 15, 2020
The one-way analysis of variance is used to test if observed differences among k sample means can be attributed to chance. Output is fully annotated on the paper tape.
A sample session is included in the instructions.
Written by Don Phillips.
Analysis of Variance (Two-Way)
Statistics
July 15, 2020
The two-way analysis of variance tests the row effects and the column effects independently. This program will generate the ANOVA table for the case such that (1) each cell only has one observation and (2) the row and column effects do not interact.
A sample session is included in the instructions.
This is an enhanced version of the program in HP Stat Pac 1.
Written by Don Phillips.
ANOVA Factorial Experiments
Statistics
Oct 2, 2020
This program is a two-factor analysis of variance with interactions and replications.
The example used in the instructions is from Factorial Designs worked example #1 attached to this program.
The program requires RPN-67/97 v6.3 or later.
Written by Don Phillips.
Astronomical Coordinate Conversions
Astronomy
Apr 5, 2018
This program will convert from any of the five coordinate systems to any other system.
Written by Don Phillips.
Basic Interest Functions
Finance
Jun 23, 2022
Unlike many TVM programs, this program will compute the value of an annuity on any date, or of a deferred annuity, or of a perpetuity starting on any future date.
Written by Don Phillips.
Bayes' Theorem
Statistics
Feb 13, 2019
This program computes posterior probabilities from prior probabilities.
Instructions show three examples.
Written by Don Phillips.
Chi-Square Statistics
Statistics
Jul 10, 2020
This 800-steps program computes the probability P(χ²) of a given χ² and degrees of freedom (df), as well as the χ² of a given P(χ²) and degrees of freedom (df). Input values and results are clearly annotated on the paper tape printer.
Written by Don Phillips.
Chi-Square Goodness-of-Fit Test
Statistics
Jul 8, 2020
With this program you can input a 2x2 up to a 7x9 contingency table and compute the expected values, the χ² statistic, and the probability of the lower and upper tails of the χ² distribution.
Written by Don Phillips.
Clinical Trial Analysis
Math
Dec 9, 2021
This program allows you to explore the three ways to present the benefits of a clinical trial with a treatment group and a placebo group, namely (1) Absolute risk reduction [ARR], (2) Relative risk reduction [RRR], and (3) Number needed to treat (NNT). Inputs are the total number of people in both the treatment and the placebo group, as well as the number of cases in each group.
Written by Don Phillips.
Easter Years
Mar 8, 2017
This program can be used to determine all years in which Easter falls on a given date in the Western/Gregorian calendar.
The range of years is 1583…4099.
Ellipse and Ellipsoid
Math
Jul 5, 2021
This program computes high-precision properties of ellipses and ellipsoids by evaluating elliptic integrals where appropriate.
Based on a program by Pedro Leiva.
F & t Distributions
Statistics
Jan 27, 2020
This program evaluates the CDF of the F & t distributions, as well as their upper-tail probabilities. Output is fully annotated on the paper tape.
A sample session is included in the instructions.
Written by Don Phillips.
Gregorian & Julian Date Calculations
Calendars
Mar 23, 2024
This program provides various date calculations involving Julian and Gregorian calendars. Both B.C. and A.D. eras are covered.
Make sure the switch "With Regs" is set to ON when loading the card.
Written by Matt Agananjan.
Julian Day Numbers
Astronomy
Apr 13, 2021
This program determines the Julian Day Number from a given date and time.
Sample calculations are included in the instructions.
Written by Don Phillips.
Latin Square Analysis of Variance
Statistics
Sep 15, 2020
This program calculates the ANOVA table for a special three factor design known as Latin Squares.
A sample session is included in the instructions.
The program requires RPN-67/97 v6.3 or later. For older versions click here.
Written by Don Phillips.
Multiple Regression
Statistics
Aug 24, 2019
This program handles multiple regression with three independent variables. Output is fully annotated on the paper tape.
A sample session is included in the instructions.
Written by Don Phillips.
Normal Distribution 2
Statistics
Jan 16, 2019
This program expands on the "Accurate Normal Distribution" program (above) by making it easier to use in real-world scenarios.
The program card is accompanied by a data card containing texts and constants.
Written by Don Phillips.
Tukey's and LSD Range Tests
Statistics
Aug 5, 2020
After doing an Analysis of Variance (One Way or Two Way) on a number of treatments and blocks, and having an F-value(s) indicating a significant difference between the means of the samples or treatments and/or blocks, you do not know which means are really statistically different. This program uses Tukey's Range Test and the Modified Least Significance Difference Test to test the difference between pairs of means.
A sample session is included in the instructions.
Written by Don Phillips and Pedro Daniel Leiva.
Linear Equations in 9 Unknowns
Math
Apr 19, 2017
Using Gaussian elimination, this program solves any system of linear equations in up to 9 unknowns. Input data may be entered manually, prompted by a loop, or by providing a data card. Instructions as PDF.
Maximum Box Volume
Math
Aug 1, 2019
Given a sheet of paper of length L and width W, this program determines how to fold the sheet to length L' and width W' in order to create an open box of maximum volume. Details
The program may be used to find minima and maxima of arbitrary functions.
Random to Numerical Order
65 Notes / PPC Journal
Aug 18, 2016
This program sorts registers 1..n, where n < 25.
Ascending sort is done using regular HP-67 commands. Descending sorting uses the extended command OP SORT EXT.
Original version written by Terry Mickelson (PPC Journal, V5N1P27.)
Sudoku Solver
Tests & Demos
Dec 30, 2018
This program uses a backtracking algorithm to find the solution to a Sudoku puzzle. Top: 67/97 Pro, bottom: optimised for 67SD
Running time is in the order of minutes.


Time
Astronomy
Jul 19, 2017
This program converts – given one of LT (local time), UT (universal time), GST (Greenwich mean sidereal time), or LST (local sidereal time) – to the others.
Written by Don Phillips.
Triangle Solutions
Math
Nov 17, 2018
This is a re-write of the HP Standard Pac program "Triangle Solutions". The main goal was to make the program more intuitive to use.
Written by Don Phillips.
Time Value of Money
Finance
May 18, 2022
This program handles the number of compounding periods that can be different from the number of payment periods. It also handles annuities immediate and due. Discount rates may be used by entering CP/YR (compounding periods per year) as a negative value.
Output is printed fully annotated on paper tape.
Written by Don Phillips.
Wind Chill Factor
Feb 26, 2018
This program calculates the wind chill index.
Inputs are the air temperature (in °C or °F) and the wind velocity (in km/h, m/s, mph, or knots.)
Outputs are the wind chill index (in °C or °F) and the surface power dissipation (in W/cm².)
 

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