Program Library 3 for RPN-67 & 97

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.

Note to "Legendary-67" users:
A number of the programs provided below will not run correctly on "Legendary-67", the HP-67 simulator for iPhone. Some will not run at all.
This is due to implementation issues with that simulator. Programs are identical to those published by Hewlett-Packard, unmodified except where noted in the description. All of them have been verified to execute successfully on RPN-67 Pro.

Users' Library Solutions — 1. Aeronautical Engineering
AE01 - Properties of Air
Mar 27, 2017
This program computes the following properties of air at low pressures for a given temperature: specific heat ratio, specific heat at constant pressure, specific heat at constant volume, coefficient of viscosity, and absolute Rankine temperature.
AE02 - Standard Atmosphere
Mar 27, 2017
The program computes the theoretical U.S. Standard Atmosphere values for temperature and pressure at any altitude from -16,500 to 35,332 feet.
AE03 - Aircraft Flyover Acoustic Tone Doppler Shift
Mar 27, 2017
Computes Doppler shift of an aircraft flyover acoustic source frequency observed on the ground.
AE04 - Isentropic Flow for Ideal Gases
Mar 27, 2017
This card replaces isentropic flow tables for a specified specific heat ratio k. Inputs and outputs are interchangeable with the exception of k.
AE05 - Shock Parameters for Compressible Flow
Mar 27, 2017
Knowing freestream Mach number, shock angle and ratio of specific heats (Gamma); computes mach number behind shock and the ratios across the shock.
AE06 - Oblique Shock Angle for Wedge
Mar 27, 2017
Given the upstream Mach number, the flow deflection angle, and the ratio of specific heats the program determines if an oblique shock is possible and finds the shock angle for the weak shock condition if the condition is possible.
AE07 - Mach Number and True Airspeed
Mar 27, 2017
This program converts calibrated airspeed to Mach number and true airspeed.
AE08 - Take-off Run vs. Density Altitude
Mar 27, 2017
Computes actual take-off run required given sea level run at 15°C at full gross weight, pressure altitude, actual air temperature, and actual takeoff weight.
AE09 - True Air Temperature and Density Altitude
Mar 27, 2017
Converts indicated air temperature to true alr temperature accounting for the temperature rise associated with high speed flight. Once a true temperature is established the density altitude can be calculated.
AE10 - Aircraft Climb
Mar 27, 2017
This program permits one to determine the desirability of climbing from an altitude of high headwinds to an altitude with lower headwinds.

Users' Library Solutions — 2. Aircraft Operation
AC01 - Aircraft Flight Plan With Wind Simplifies flight planning.
AC02 - Flight Management Speed-Time-Distance-Fuel.
AC03 - Predicting Freezing Levels Computes theoretical freezing level.
AC04 - General Aircraft Weight and Balance Helps determine your position in the weight-balance envelope.
AC05 - Pilot Unit Conversions Common units encountered by pilots.
AC06 - Turn Performance Computes G-force, turn diameter, and stall speed.
AC07 - Rate of Climb and Descent Helps you to be sure you'll clear the mountain.
AC08 - Head Winds and Cross Winds Resolves reported winds into head-winds and cross-wind components.
AC09 - Flight Planning and Flight Verification Plan and update the plan enroute.
Computes ETA, ground speed, etc.
AC10 - Determining In-Flight Winds Computes winds from time-distance inputs.
AC11 - Standard Atmosphere Estimates atmospheric conditions from pressure altitude.
AC12 - Mach Number and True Air Speed Converts calibrated airspeed to mach number and true airspeed.
AC13 - True Air Temperature and Density Altitude Computes density altitude, accounting for compressibility effects.
AC14 - Lowest Usable Flight Level Used on flights operating above 18,000 feet.

Users' Library Solutions — 6. Avigation
AV01 - Great Circle Plotting Computes points on a great circle.
AV02 - Rhumb Line Navigation Computes rhumb line heading and distance.
AV03 - Great Circle Navigation Computes great-circle distance and initial heading.
AV04 - Position Given Heading, Speed, and Time A dead reckoning program.
AC05 - Line of Sight Distance A transmitter-aircraft geometry problem.
AV06 - Position and/or Navigation by Two VOR's Simplifies the geometry of VOR's and aircraft.
AV07 - Position by One VOR Computes distance from a VOR station.
AV08 - DME Speed Correction Calculates ground speed from DME even when not headed directly towards a DME station.
AV09 - Average Wind Vector Approximates an average wind. Wind Pattern
AV10 - Course Correction Helps get an aircraft back on course. Sketch
AV11 - Time of Sunrise and/or Sunset Gives approximate times of these important phenomena.
AV12 - Azimuth of Sunrise and/or Sunset Computes azimuth of rising or setting Sun.

Users' Library Solutions — 9. Biology
BI04 - Niche Breadth and Overlap / Shannon's H and Horn's R0 Computes niche breadths from Simpson's diversity index, niche overlap from Pianka's overlap index, Shannon's information theoretic index of diversity for two communities, and Horn's overlap index.
BI07 - Crossover: Location/Products Computes the number and location of crossovers which must occur to produce a given progeny chromatid and also the progeny chromatid resulting from single or multiple crossovers of the given parental chromatid.
Sketch 1 Sketch 2
BI08 - Chromosome Cleavage Simulates chromosomal cleavage to analyze chromosome models.
BI09 - Recessive Gene Frequency After Selection, Mutation, and Inbreeding Two models: one computes recessive gene frequency after selection and mutation; the other computes recessive gene frequency after selection, mutation, and inbreeding.

Users' Library Solutions — 10. Calendars
CL01 - Calendar Date to Julian Date Conversion Converts between Gregorian and Julian calendars.
CL02 - Days to Dates and Dates to Days; Day of Week Computes days between two dates, day of the week, and the date a specified number of days from a date.
CL03 - Day of Year - Day of Week Calculates day of year and day of week.
CL04 - Number of Weekdays Between Two Dates Calculates the number of weekdays between any two dates in history.
CL05 - In What Year Is a Given Date an M-Day? User specifies a year, a date, and a day-of-week--program computes what years from the specified year have the specified date falling on the specified day.
CL06 - Number of M-Days Between Two Dates and The nth M-Day of the Month User speclfies a day-of-week and two dates; the program gives the number of times that day occurs between the given dates. User specifies a year, a month, a day-of week - and a number N; the program computes the N-th occurrence of the specified day in the given month.
CL07 - Holidays Calculates the date of Mother's day, Father's day, Election Day, Thanksgiving Day, Washington's Birthday, Labor Day, Columbus Day, and Veterans' Day.
CL08 - Easter-Ash Wednesday-Religious Holidays Computes the dates of various religious holidays.
CL10 - Mohammedan (Islam) - Gregorian Calendar Conversion Converts between Mohammedan and Gregorian calendar.

Users' Library Solutions — 12. Chemistry
CH01 - pH of Weak Acid/Base Solutions A program for calculating the pH of weak acid or base solutions using the Newton-Raphson iteration method. The program also performs a number of interconversions of pH, pOH, Ka, Kb, (H+), (OH-) etc.
CH02 - Acid-Base Equilibrium (Diprotic) The program determines H3O+ concentration or pH for solutions of a dibasic acid and its salts. Useful for calculation of buffer solution.
CH03 - Weak Acid/Base Titration Curve A powerful program for calculating the pH of weak acid or base solutions with up to 4 dissociation constants. Provides data for plots of pH versus volume of titrant.
CH04 - Equations of State Provides both ideal gas and Redlich/Kwong equation of state calculations for gases. Tables
CH05 - Van der Waals Gas Law Performs calculations for gases obeying Van der Waals equation, given the Van der Waal constants. Also calculates critical temperature, pressure and molar volume of the gas.
CH06 - Beer's Law and Absorbtivity Calculations A program for colorimetry calculations using Beer's law. Aborbtivitiy is calculated by the least squares method.
CH07 - Activity Coefficients From Potentiometric Data Calculates the Standard Electrode Potential and activity coefficients given concentration and EMF.
CH08 - Kinetics Using Lineweaver-Burk or Hofstee Plots Fits experimental data to a line and calculates Vmax and Km for enzyme reactions. Calculates constants for competitive inhibitor reactions.
CH09 - Polynomial Evaluation Solves cubic and quadratic equations and evaluates up to third degree polynomials for arbitrary real values of x.
CH10 - Mixture Viscosities The program provides estimates of the Viscosity of a mixture of gases at low pressures.
CH11 - Vapor Pressure, Bubble and Dew Point Calculation Coefficients for the Antoine equation are calculated from 2 points of vapor pressure vs temperature. Bubble and dew points of the mixture may also be calculated.
CH12 - Single-Stage Equilibrium Calculation The program calculates the compositions of liquid and vapor streams from a flash vessel for mixtures of up to 10 components.

Users' Library Solutions — 16. EE (Lab)
EL01 - Wire Table Calculates useful wire parameters.
EL02 - Ohm's Law Calculates the missing two values among E, I, R, and P.
EL03 - Reactance Chart Interchangeable solution among f, L, C, XC and XL.
EL04 - Coil Calculations Calculates self-inductance of four types of inductors. Sketch
EL05 - Complex Impedance Calculator - AC Circuit Calculator Gives your calculator a complex stack.
EL06 - WYE•Delta and Delta•WYE Transformations Given one, it computes the other.
EL07 - RC Timing Interchangeable solution among R, C, Vl, V2, Vi, and t.
EL08 - Series R-L-C Circuit Analysis Program Determines the characteristics and performance of the series R-L-C circuit.
EL09 - Passive High and Low Pass Filter Design Computes component values for a prototype "T" or "PI", high or lowpass filter. Given "m", computes component values for an m-derived filter section. Sketch
EL10 - "L" Attenuator Computes resistor values needed to realize desired pads.
EL11 - 1% Resistor Value Subroutine Subroutine to find the nearest available 1% resistance.
EL12 - Wheatstone Bridge Computes the missing impedance.

Users' Library Solutions — 21. Geometry
GM01 - Sine Plate Solutions Coordinates of a point, position and slope of an inclined hole.
This program, with the aid of commonly available dowel pins, measuring tools, (in the case of the sine plate, obviously a sine plate and height blocks), will aid in accurately finding angles, including holes and coordinates of points.
GM02 - V Notches and Long Radii This program, together with commonly available dowel pins and height gages, will accurately determine the position and angles of "V" grooves or notches. With the same tools, long radii are accurately measured.
GM04 - Points of Tangency With Circles and Arcs These programs will accurately locate points of tangency between straight lines and arcs, between straight lines and a circle, and between two circles and a straight line.
GM09 - Tangent Circle to Two Straight Lines With a Given Radius This program calculates the X and Y coordinates of the circle with a given radius. This circle being tangent to two given straight lines. In the more general case, there are four center solutions to this problem.
GM10 - Distance Between Lines In Space Given two lines, each defined by any two points, program calculates shortest distance between the two lines. {This program was written to determine the clearance between electrical distribution circuits and guy wires or supporting structures.}

Users' Library Solutions — 22. High-level Math
HM01 - Eigenvalues for 3rd Order System Program calculates the eigenvalues of a 3rd order system described by Ax =  λx.
HM02 - Eigenvalues/Vectors of 3rd Order System For a given 3rd order matrix with distinct eigenvalues, the program calculates the eigenvalues and eigenvectors. The first (largest) eigenvalue and eigenvector are calculated by power method, while the 2nd and 3rd are calculated by deflation method.
HM03 - Matrix Algebra For two matrices X and Y, each with dimensions less than or equal to three, the program will calculate X*Y, X+Y, X-Y, aX, and bY where a and b are scalars. Non-square matrices X and Y are allowed.
HM04 - Characteristic Equation of a 3x3 Matrix This program automatically loads data by telling user when to input, and calculates the characteristic equation of a 4 by 4 matrix.
HM05 - 5x5 Matrix Determinant and Inverse
Aug 17, 2016
Program calculates the determinant and inverse of a general real 5 by 5 matrix, on one card and with data entered only once. Expansion by minors is used to attain this advantage, although some accuracy is lost by not using pivots. The matrix data is left intact.
HM06 - Simultaneous Equations In Six Unknowns Finds the solution for six simultaneous linear equations in six unknowns, using Crout's method. This two-card program will also compute the inverse and determinant of the coefficient matrix.
HM07 - Roots of Polynomials Finds real and/or complex roots of polynomials up to degree 14 with real coefficients. When a real (complex) root is found, the polynomial is depressed by the corresponding linear (quadratic) factor, until all roots are found. Newtons method is used, with a modification to prevent diverging iterations.
HM08 - Miscellaneous Special Functions A Computes Gamma function, Gaussian hypergeometric function, Jacobian polynomial, Legendre polynomial, Gegenbauer polynomial, and first and second Chebychev polynomials. Works for positive or zero subscripts and superscripts, but for large subscripts can be slow. Gamma function for 0 < x < 70.95.
HM09 - Miscellaneous Special Functions B Using a recursion relation to compute the Gegenbauer, Laguerre, Hermite, Legendre, and Chebychev (both first and second kind) polynomials. A special key enables one, by inputting alternate starting values, to compute polynomials with non-integer subscripts. Starting values can be computed for non-integer subscripts by using Miscellaneous Special Functions A.
HM10 - Incomplete Gamma Function Γ(a,x) The upper-tail of the incomplete Gamma function is computed by continued fractions. Practical considerations restrict x to lie between 1 and 200.
HM11 - Incomplete Beta Function The complete Beta function is computed by continued fractions. Valid for arguments A and B greater than 0 and x between zero and one. Accuracy table included.
HM12 - Incomplete Elliptic Integrals This program will compute incomplete elliptic integrals of the first or second kind as well as any linear combination of them.

Users' Library Solutions — 27. Medical Practitioner
MP01 - Blood Pressure Averages and Mean Arterial Pressure This program calculates the mean arterial pressure of a given blood pressure reading and the averages of systolic, diastolic and mean arterial pressure for a group of readings.
MP03 - Blood Alcohol The program calculates the approximate percent of alcohol concentration in the blood when the person's weight, amount of alcoholic beverage and time are known.
MP07 - Estimating Obesity, Body Fat, Surface Area and Total Body Water From body height and weight the program calculates whether or not the subject is obese. Body fat, body surface area and total body water can also be calculated.

Users' Library Solutions — 29. Options/Technical Stock Analysis
OP01 - Put & Call Option Fair Values (Black-Scholes) This program computes the theoretical value of a put or call option based on the valuation formulas published by Black and Scholes.
OP02 - Call Option Evaluation This program computes call option values using the Black-Scholes model. It also computes the implied empirical variance (variability) when the actual market value is entered.
OP03 - Routines for Option Writers In addition to calculating the fair option value (Black-Scholes) with consideration for dividends, the program calculates the maximum yield, cash flow yield, and high and low breakeven points.
OP04 - Empirical CBOE Call Pricing Using the Clasing empirical formulas, this program calculates a fair call option price.
OP05 - Warrant & Option Hedging This program calculates cross return and high and low breakeven points for various short sale ratios.
OP06 - Bull Spread Option Strategy For various bull (vertical) spreads, this program calculates the upper and lower breakeven points and the percent movement necessary to reach them.
OP07 - Butterfly Options This program calculates the maximum profit, maximum loss, and the upside and downside breakeven points for various butterfly option strategies..
OP08 - Stock Price 30-Week Moving Average With Data Storage This program allows both the data and the program for calculating a 30-unit moving average to be stored on a single program card.
OP09 - Exponential Smoothing Exponential smoothing is a geometrically weighted moving average which can be used to locate and project significant trends in securities and commodities prices.
OP10 - Multiple Linear Regression This program can be used to search for leading indicators of stock and commodities movements by analyzing past data for possible linear relationships.
OP11 - Curve Fitting, Selecting Best Function Four different mathematical functions are evaluated to determine the function which best represents the data; linear, power, exponential, and logarithmic. Program makes projections based on curve fit selected.

Users' Library Solutions — 31. Physics
PH01 - Black Body Thermal Radiation Calculates the wavelength of maximum emissive power for a given temperature.
PH02 - Black Hole Characteristics Computes temperature, Schwarzschild radius, and lifetime of a black hole.
PH03 - Special Relativity Conversions Provides relativistic conversions between rest mass, velocity, energy, and momentum.
PH04 - Three Dimensional Special Relativity Computes intervals, dilation factors, and Lorentz transformations.
PH05 - Einstein's Twin Paradox Calculate real and relative time and age differential based on the Lorentz transform.
PH06 - Delta-V–Orbit Simulator Computes orbit parameters from initial position and velocity data.
PH07 - Equations of Particle Motion Compute two unknown values based on the known values of the variables distance, time, V-final, V-initial, and acceleration.
PH08 - Ballistics Trajectory Computations Computes range, velocity, energy, time of flight, rise, and drop of a bullet.
PH09 - Isotope Overlap Corrections Corrects for spillover between channels in a liquid scintillation spectrometer.
PH10 - Critical Reactor Code Estimates the parameters of a reactor.
PH11 - Semi-Empirical Nuclear Mass Formula Calculates approximate binding energies and mass excess for any nucleus.
PH12 - Clebsch-Gordon Coefficients and 3J Symbols Evaluation Uses Racah formula to evaluate coupling two states of angular momentum.
PH13 - 32-P Remaining On MM.DDYYYY Given MCI On Earlier MM.DDYYYY Given millicuries of 32-P on date 1, this program calculates the decays per minute and counts per minute on date 2 as well as the number of days between date 1 and date 2.

Users' Library Solutions — 39. Test Statistics
TS01 - One Sample Test Stat for the Mean
Mar 25, 2017
Computes the z statistic for testing the mean if the variance is known.
TS02 - Test Statistic for Correlation Coefficient
Mar 25, 2017
The t statistic can be used to test if the true correlation coefficient is zero. The z statistic, which can be used to test if the correlation coefficient equals a given number (usually non-zero) is also computed.
TS03 - Differences Among Proportions
Mar 25, 2017
This program computes the chi-square statistic for testing if several independent binomial distributions have equal means.
TS04 - Behrens-Fisher Statistic
Mar 25, 2017
Given random samples from two independent normal populations with unequal variances (unknown), this program computes the Behren-Fisher statistic for testing the means.
TS05 - Kruskal-Wallis Statistic
Mar 25, 2017
The Kruskal-Wallis statistic can be used to test if the independent random samples come from identical continuous populations.
TS06 - Mean-Square Successive Difference
Mar 25, 2017
When test and estimation techniques are used, the method of drawing the sample from the population is specified to be random in most cases. If observations are chosen in sequence x₁, x₂, ... , xn , the mean-square successive difference η can be used to test for randomness.
TS07 - The Run Test for Randomness
Mar 25, 2017
For a given sequence, the z statistic is computed for testing the randomness of the sequence.
TS08 - Intraclass Correlation Coefficient
Mar 25, 2017
The intraclass correlation coefficient rI measures the degree of association among individuals within classes or groups.
TS09 - Fisher's Exact Test for a 2x2 Contingency Table
Mar 25, 2017
Fisher's exact probability test is used for analyzing a 2 x 2 contingency table when the two independent samples are small in size.
TS10 - Bartlett's Chi-Square Statistic
Mar 25, 2017
This chi-square statistic can be used to test the homogeneity of variances. Error corrector for erroneous input data is provided.
TS11 - Mann-Whitney Statistic
Mar 25, 2017
This program computes the Mann-Whitney test statistic U on two independent samples of equal or unequal sizes. Table
TS12 - Kendall's Coefficient of Concordance
Mar 25, 2017
This program calculates Kendall's coefficient of concordance to test agreement between rankings. Error corrector for erroneous input data is provided.

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