 ## ANU vCalc Collaboration

The following are links to free online calculators for the use and benefit of students and faculty around the world.  These free calculators are sponsored by Olivet Nazarene University and Africa Nazarene University in collaboration with vCalc.

#### Mathematic Calculators

3D vector arithmetic functions including Cartesian, Spherical and Cylindrical coordinate transforms.

Statistics Calculator:

9 functions of quaternion arithmetic.

3×3 Matrix Characteristics: computes the determinant, trace, inverse and characteristic polynomial of a 3×3 matrixCramer’s Rule

#### Physics and Engineering Calculators

10 functions on levers, pulley and gear systems.

Light and Matter Online Physics Textbook: 36 chapters of a complete open-source to physics textbook.  This text was programmed into vCalc by the faculty and students of Africa Nazarene University.

Power: (watts, milliwatts, kilowatts, horsepower)

Potential: (volts, millivolts)

Resistance: (ohms, milliohms, kiloohms)

Current: (amps, milliamps, microamps, gilberts)

31 functions covering Kepler’s 3rd Law, the Small Angle Formula, Flux and Magnitude formulas, Telescope formulas, Mass formulas, Relative Size formulas, Wavelength formulas, Luminosity formulas and others.

Reflection, refraction and critical angle according to Snell’s Law.

#### Chemistry Calculators

Ideal Gas Law:    P • V = n • R • T

The Ideal Gas Law calculator has the formula solved for its constituent parts as follows:

Charles Law:    V1•T2 = V2•T1

The Charles’ Law Calculator has the formula solved for its constituent parts as follows:

Boyles Law:    P• V1 = P2 • V2

The Boyles’ Law Calculator has the formula solved for its constituent parts as follows:

Gay-Lussac Law:      T1 • P2 = T2 • P1

The Gay-Lussac Law Calculator has the formula solved for its constituent parts as follows:

Combined Gas Law:    P• Vi/Ti = P• Vf/Tf   = k

The Combined Gas Law Calculator has the formula solved for its constituent parts as follows:

The Bragg’s Law calculator has the formula solved for its constituent parts as follows:

The Rate Law calculator has rate of reaction functions for Zero Order, First Order and Second Order reactions as follows:

53 functions embedded functions in a free online chemistry E-Textbook. These include ChemPRIME, Concept Development Studies in Chemistry, UC Davis ChemWiki: The Dynamic Chemistry E-Textbook.

Miscellaneous Chemistry Calculators

#### Meteorology and Weather

Meteorology Calculator:

Functions on heat indices, humidity, wind chill and barometric pressure.

Microeconomics Calculator:

Microeconomics functions:

Functions related to macroeconomics including GDP, Inflation, Surplus, Producer, Consumer, Imports, Exports, Currency, Domestic and International.

67 functions (formulas) related to hotels, food services, restaurants, cost, labor, pricing, turnover, occupancy, sales, ADR, GOP-PAR, forecast, margins and more.  Hospitality calculators are in the following categories:

• Income Statement
• Ratio Analysis
• Food and Beverage Pricing
• Revenue Management for Hotels
• Managerial Accounting for Costs
• Forecasting in the Hospitality Industry
• Budgeting and Internal Controls
• Capital Investment, Leasing and Taxation

Functions on loans, interest, credit cards, cash flow, present and future value and annual growth rate (CAGR):

#### Production Calculator

The Production Calculator computes the cost in time or capital to buy, produce or consume commodities measured by number of units or by length, area, volume or weight.  It provides conversions between different units for time, length, area, volume, mass and up-to-date conversions between several international currencies.

PRICE or Production Time by UNITS

PRICE or Production Time by LENGTH

PRICE or Production Time by AREA

PRICE or Production Time by VOLUME

PRICE or Production Time by WEIGHT or MASS

Amdahl’s LawComputes the speedup factor for a total task based on the speedup factor of a portion of the task and the percent of that portion in relation to the total task.

Price Comparison Calculator

#### Psychology Calculators

Psychology and Statistics Calculator

The Psychology and Statistics Calculator contains useful tools for Psychology Students.  The psychology statistics functions include the following:

• Wilcoxon Signed Rank Test: Enter two sets, whether it’s a one or two tail test and an alpha value to see the Wilcoxon statistic and the critical value.
• Bayes’ Theorem for Disease Testing: Enter a base rate probability, probability of false positives and the probability of correct positives to see a ratio of people with the disease, approximate number of false and true positives and the theorem’s percent likelihood of a having the disease if tested positive.
• chi-square for 3×2: Enter a 3×2 matrix to see the expected values matrix with row and column totals, degrees of freedom and the chi-square value.
• Rescorla-Wagner Formula (alpha and beta version): Enter salience for conditional stimuli, rate of unconditional stimuli, maximum conditioning for unconditioned stimuli and the total associative strength of all stimuli present to see the change in strength between conditional and unconditional stimuli.
• Rescorla-Wagner Formula (k version):  Enter Maximum conditioning possible for the unconditioned stimuli, total associative strength of all stimuli present, combined salience of the conditioned and unconditioned stimuli, and number of trials to see the change in strength associated with the trials.
• Ricco’s Law: Enter the area of visually unresolved target and constant of background luminance when eyes are adapted to see Ricco’s Law factor.
• Ricco’s Law (K variable): Enter the scotopic vision constant, background luminance and photopic vision constant.
• Stevens’ Power Law: Enter proportionality constant, magnitude of stimulation, type of stimulation exponent to see magnitude of sensation.
• Weber Fraction: Enter just-noticeable difference for intensity and stimulus intensity to see the weber fraction.
• Weber-Fechner’s Law: Enter just-noticeable difference for intensity, instantaneous stimulus, stimulus intensity and the threshold to see the factor.
• Observational Statistics (aka Simple Stats): Observational statistics on a set including: count, min, max, mean, median, mode, mid-point, range, population and sample variance and standard deviation, mean absolute deviation, standard deviation of mean, sum of values, sum of squared values, square of the sum, and the sorted set.
• Frequency Distribution: Frequency distribution of a set of observations in uniformly sized bins between a minimum and maximum.
• Least-squares Trend Line (aka Linear Regression): Linear regression line on a set of paired numbers (correlation coefficient, number of observations, means, sums (ΣX, ΣY, Σ(X⋅Y), ΣX2, ΣY2), y intercept, and (b) slope of regression line.
• Single-Sample t-test: t-Test parameters including alpha level, population mean and whether it’s one or two tailed and see the degrees of freedom, critical t-value, t score and the standard error.
• Paired Sample t-test: Test of two sets of values with an alpha level and whether it’s one or two tailed and see the number of observations, mean and standard deviation for both sets, the degrees of freedom, critical t-value, t-score and the Standard Error value.
• Effect Size (r-squared): Degrees of freedom to see r2 for t-test result.
• Effect Size (Cohen’s d): Estimated standard deviation to see the effective size.
• Analysis of Variance (one way): ANOVA for numeric observations of three groups. Computes the F Score, Numerator: degrees of freedom Between, Denominator: degrees of freedom Within, mean of each group, grand mean, total sum of squares, sum of square within and between, and variance within and between.
• Random Integer: Random integer between a lower and upper bound.

Biology and Ecology Calculators

Population Growth Calculator

• Logistic Growth: computes the logistic growth based on the per capita growth rate of population, population size and carrying capacity
• Malthusian Growth Model: computes the estimated future size of a population (P) based on the current population (P0), a growth exponential factor (r) and the  period of time (t).
• Organism Count (Logistic Growth): computes the number of cells/organisms undergoing exponential growth as a population.
• Biotic Potential: computes the maximum population growth based on the per capita growth rate of population and the population size
• Max Potential Growth Rate (biotic potential)
• How Many Ancestors: computes the total number of ancestors a person or sexual reproducing animal has base on the number of generations going back.  It also estimates the approximate time span associated with those ancestors.
• SIS Epidemic Model: computes the basic reproduction number and the portion of the population susceptible.
• SIR Epidemic Model: provides information on the increase or decrease of an epidemic based on the infection rate, recovery rate, total population, initial susceptible population, initial infected population and the initial recovered population.

Medicine and Nursing

Body Surface Area Calculator:

Epworth Sleepiness Scale: computes potential of medical condition associated with tiredness (e.g., sleep apnea)

The Metabolic Health calculator has formulas for metabolism and calories burned:

#### Sports and Fitness

Body Building and Weight Lifting

Functions related to weight lifting and body building.

Calories Burned Calculator

Functions on calories burned over time doing various activities and exercises.