vCalc Calculators

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

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

k V – scalar multiplication
V / |V| – Unit Vector
|V| – Magnitude of a vector
U + V – Vector Addition
U – V – Vector Subtraction
|U – V| – Distance between vectors
|U + V| – Magnitude of vector sum.
V • U – Dot Product of two vectors
V x U – Cross Product of two vectors
V x U • W – Mixed Product of three vectors
Vector Angle – Angle between two vectors
Vector Area – Area between two vectors
Vector Projection – Vector Projection
Vector Rotation – Result vector after rotating around an axis.
Normal to 3 Points – Vector Normal to a Plane Defined by Three Points
(ρ, θ, φ) to (x,y,z) – Spherical to Cartesian
(x,y,z) to (ρ, θ, φ) – Cartesian to Spherical
(r, θ, z) to (x,y,z) – Cylindrical to Cartesian
(x,y,z) to (r, θ, z) – Cartesian to Cylindrical
Vector Components – Magnitude, Unit Vector and angle between vector and three coordinate axes

Statistics Calculator:

Observational Statistics: Calculate observational statistics for a set including count, min, max, sum, sum of squares (Σx²), square of the sum (Σx)², mean, median, mode, range, mid-point, rand, sort up, sort down, rand, population variance, population standard deviation, the sample/experimental variance, sample/experimental standard deviation.
Frequency Distribution: Enter a set of numbers, a low and high range and a number of bins. This computes how many of the observations are in each of the bins between the high and low values designated.
Random Sample of k items in a set.
Relative Percentile of observation in a set.
Probability of a favorable Event in a total number of outcomes.
Binomial Distribution with the probability of S successes in n trials.
Binomial Coefficient derived from Pascal’s Triangle.
z SCORE of Observation in set (X)
z SCORE based on Mean and Standard Deviation.
z SCORE based on Probability or Percentile in Normal Distribution.
Percentile, probability or area under the curve of a Normal Distribution left of the z SCORE.
Percentile, probability or area under the curve of a Normal Distribution right of the z SCORE
Area under the Normal Distribution curve between z SCOREs.
Raw Score associated with a percentile in a Normal Distribution (μ,σ).
Paired Sample t-test: Computes parameters for Paired Sample t-test.
ANOVA (one way): one way analysis of variance
(χ²) Chi-Square Test: Chi-Square value for a nxm array of data
y = a + bx: Linear equation used with Linear Regression
Linear Regression: Compute the regression line (least-squares) through a set of X and Y observations, and compute the regression coefficient (r).
SDOM: standard deviation of mean

Quaternion Calculator: 9 functions of quaternion arithmetic.

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

Physics and Engineering Calculators

Simple Machine Calculator: 10 functions on levers, pulley and gear systems.

Lever Beam Length: Computes the length of a lever (beam) on one side of a fulcrum needed to lift an object based on the objects weight and the length of the beam on the other side of the fulcrum.
Leverage Lift Weight: Computes the weight that can be lifted using a lever based on the downward force and the length of the lever on either side of the fulcrum.
Fulcrum Position (x): Computes the position of the fulcrum needed in a lever to lift a weight (W) with a downward force (F) with a beam of length (L), where L = x + y.
Belt Length: Computes the length of a belt that goes around two pulleys of different diameters separated by a specific distance.
Belt Speed: Computes the speed a belt travels based on the diameter of the pulley and the RPMs.
Pulley RPMs: Computes the RPMs of a pulley based on the speed of the belt and the diameter of the pulley.
2nd Pulley RPMs: Computes the RPMs of a second pulley in a two-pulley system when the RPM and Diameter are known for one pulley and the diameter of the second pulley is also known.
2nd Pulley Diameter: Computes the diameter of a second pulley in a two-pulley system based on diameter and RPM of one pulley and the RPMs of the second.
RPM of 4th pulley on three shafts: Computes the RPMs of a fourth pulley on a three-shaft system when the RMPs of the first shaft is known and the four diameters.
2nd Gear RPM: Computes the RPMs of a second gear when the RPM and number of teeth are known for the first gear, and the number of teeth is known for the second gear.

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.

Ohm’s Law Calculator:

Power: (watts, milliwatts, kilowatts, horsepower)

o P = I • V: power (watts) from current (amps) and potential (volts).

o P = R • I²: power (watts) from current (amps) and resistance (ohms).

o P = V² / R: power (watts) from potential (volts) and resistance (ohms).

Potential: (volts, millivolts)

o V = I • R : potential (volts) from current (amps) and resistance (ohms).

o V = P / I: potential (volts) from power (watts) and current (amps).

o V = √(P • R) : potential (volts) from power (watts) and resistance (ohms).

Resistance: (ohms, milliohms, kiloohms)

o R = V²/P: resistance (ohms) from potential (volts) and power (watts).

o R = P / I²: resistance (ohms) from power (watts) and current (amps).

o R = V / I: resistance (ohms) from potential (volts) and current (amps).

Current: (amps, milliamps, microamps, gilberts)

o I = V / R: current (amps) from potential (volts) and resistance (ohms).

o I = P / V: current (amps) from power (watts) and the potential (volts).

o I = √(P/R): current (amps) from power (watts) and the resistance (ohms).

Astronomy Calculator: 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.

Angles of Reflection and Refraction Calculator: 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:

(P) pressure (atmospheres, pascals, bar, Torr, inches of mercury, psi, N/m²)
(V) volume (liters, mL, cc, gallons)
(n) number of moles (moles)
(R) Universal Gas Constant
(T) temperature (Kelvin, Celsius, Fahrenheit)

Charles Law: V₁•T₂ = V₂•T₁

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

Boyles Law: P₁• V₁ = P₂ • V₂

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

(P₁ = P₂ • V₂/V₁) Initial Pressure
(V₁ = P₂ • V₂/P₁) Initial Volume
(P₂ = P₁ • V₁/V₂) Final Pressure
(V₂ = P₁ • V₁/P₂) Final Volume

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_i• V_i/T_i = P_f• V_f/T_f= k

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

(P) Pressure from volume, temperature and the combined gas constant.
(V) Volume from pressure, temperature and the combined gas constant.
(T) Temperature from pressure, volume and the combined gas constant.
k gas constant
(P_f) Final Pressure from initial and final temperature and volume and initial pressure.
(T_f) Final Temperature based on an initial and final pressure and volume and an initial temperature.
(V_f) Final Volume based on an initial and final pressure and temperature and an initial volume.

Bragg’s Law: n · λ = 2d·sinθ

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

(d) distance between layers of atoms
(n) order of diffraction
(λ) wavelength of x-ray
(θ) the angle of incidence of the incoming x-ray

Rate Law

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

Chemistry 106 Collection

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

Hess’ Law: ΔH⁰_rxn=ΔH⁰_a+ΔH⁰_b+ΔH⁰_c+ΔH⁰_d
Internal Energy (heat + work) : ΔU=q+ w
Activation Energy: E_a = (R*T₁⋅T₂)/(T₁ – T₂) ⋅ ln(k₁/k₂)
Arrhenius Equation: k = Ae^E_a^/(RT)
Clausius-Clapeyron Equation: ln(P₂/P₁) = (ΔH_vap)/R * (1/T₁ – 1/T₂)
Compressibility Factor: Z = (p*V_m)/(R*T)
Peng-Robinson Equation of State: p = (R*T)/(V_m – b) – (a*α)/(V_m² + 2*b*V_m – b²)
Reduced Specific Volume: v_r = v/(R* T_cr/P_c)
Van’t Hoff Equation: ΔH⁰ = R * ( -ln(K₂/K₁))/ (1/T₁ – 1/T₂)

Meteorology and Weather

Meteorology Calculator:

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

Business and Economics

Microeconomics Calculator:

Microeconomics functions:

Price Elasticity of Demand (Midpoint Method)
Average Fixed Cost
Average Variable Cost
Average Total Cost
Unit Cost / Average Total Cost
Profit as a function of revenue and expense.
Profit (v.2) as a function of unit price, cost and quantity produced.
Economic Profit
Cross-Price Elasticity of Demand
Income Elasticity of Demand
Price Elasticity of Demand
Price Elasticity of Supply
Consumer Surplus
Producer Surplus
Total Surplus
Accounting Profit

Macroeconomics Calculator

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

Hospitality Industry Calculator

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

Personal Finance Calculator

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

Time for Units: Computes time to process a number of units.
Units over Time: Computes number of units processed over a period of time.
Total Cost of Units: Computes total cost based on the number of units and the cost of a single unit.
Unit Cost: Computes the Average Unit Cost.

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 Law: Computes 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

The Price Comparison Calculator compares prices for products with different amounts and prices.

Various Business and Economics Calculators:

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.