EngineeringPaper.xyz and EngineeringPaper.pro Reference Card

This is the digitally accessible version of the EngineeringPaper.xyz Quick Reference Guide (PDF). EngineeringPaper.xyz is an open source, free, and powerful web application available today at EngineeringPaper.xyz.EngineeringPaper.pro is a desktop native app with a perpetual license available for Windows, Mac, and Linux at EngineeringPaper.pro. Features exclusive to the PRO version are indicated below with [.pro].

1. Cell Types and Syntax

Math Cell

• Assignment including number with units: x = 10 [m]
• Multiple assignments: y = 2 [m], z = 5 [N]
• Query to evaluate expression: z * (x * y)^-1 = 0.25 [Pa]
• Specifying preferred units for a query result: z * (x * y)^-1 = [psi] = 3.63 x 10^-5 [psi].
• Combined assignment and query: Pressure = z * (x * y)^-1 = 0.25 [Pa]
• Predefined variables (cannot be redefined): pi = 3.14159265358979, e = 2.71828182845905, and i = sqrt(-1).
• Comment mode: Toggled with the quotation mark key (e.g., sigma=(M*y)/I “Bending stress equation”).
• Function calls: Expressions can be called as functions (e.g., sigma(M = 1 [kN*m], y = 1 [mm], I = 1 [m^4]) = 1 [Pa]).
• See the live tutorial for more information.

Documentation Cell

A documentation cell is a rich text editor that can contain images, links, and mathematical expressions.

• Text Formatting Shortcuts: Toggle bold text (Ctrl/Cmd + B), Toggle italics text (Ctrl/Cmd + I), Toggle underline text (Ctrl/Cmd + U).
• Insert Options: Insert link (Ctrl/Cmd + K), Insert formula using LaTeX notation (Ctrl/Cmd + E), Insert image (images may also be pasted).
• Editing Options Toolbar Functions: Set heading level, set text color, set text background color, insert numbered list, insert bulleted list, remove text formatting.
• Undo/Redo: Undo edit in current field (Ctrl/Cmd + Z), redo edit in current field (Ctrl + Y or Cmd + Shift + Z).

Piecewise Expression Cell

• An expression is assigned to a variable.
• Values are assigned to the variable based on specified conditions.
• Conditions are evaluated in order; the first true condition is used.
• A final fallback value is used if no condition is true (labeled Otherwise).
• The resulting variable can be used like any other expression.

Plot Cell

• Supports function definitions, scatter points definitions, function plots, scatter plots (points or lines), and parametric plots.
• Function plots can have the number of points specified by appending “with N points” (default N is 51).
• Axes can be set to log x, log y, or fixed to a 1:1 ratio.
• Plot data can be copied directly from the cell.
• See the plotting live tutorial for more information.

System Solve Cell

• Symbolic System Solve: Specify a system of equations and variables to solve for. If more than one solution exists, you can choose the desired solution.
• Numerical System Solve: Specify a system of equations, variables to solve for, and initial guesses to trigger a numerical solve (use ~ key to insert ≈). You must define all variables needed by the numerical solve cell as separate equations in the system solve cell.
• Results from both solve types are available in the rest of the sheet.
• See the equation solving live tutorial for more information.

Selector Table Cell

• The first row sets variable names, and the second row optionally sets units.
• Each column sets the value for a specific variable.
• Selecting a specific row inserts those variable values into the rest of the sheet.
• Row-specific documentation can be added by clicking the “Add Row Specific Documentation Button”.

Data Table Cell

• Input columns assign column contents to a variable (variables become vectors).
• Optional units may be specified for input columns.
• Output columns perform row-by-row calculations.
• Data can be imported from files (CSV or XLSX) and exported as CSV files, using the “Import Spreadsheet” and “Export CSV” buttons, respectively.
• Input columns can be interpolated or fit with polynomials using the “Add Interpolation” and “Add Polyfit” buttons, respectively.
• See the data table live tutorial for more information.

Fluid Properties Cell

• Allows users to select a fluid, select an output, and select 0, 2, or 3 inputs (0 for constant, 3 for humid air).
• Requires a function or constant name to be used in the sheet, a function name will be automatically assigned.
• This function is called similarly to a built-in function.
• A toggle labeled “Use Sheet Fluid” can be used to lock all fluid cells in the sheet to the same fluid.
• See the fluid properties live tutorial for more information.

Insert Sheet Command

• Click the insert sheet button to insert an existing sheet.
• Select the "Link Sheet" option to link to one or more external sheet files [.pro].
• Linked sheets are connected by relative file paths and the link will be preserved as long as the files are kept together [.pro].

Code Cell

• Code cells run Python and must contain a function named calculate.
• Scalar Example: You define the name of the function, units for inputs (converted before the function call), and units for the output. The function can be called like built-in functions, and print outputs appear below the code.
• Matrix Example: Use [any] for inputs that can have any units. Use [none] to indicate an input or output will be unitless.
• SymPy Mode: A toggle labeled “Use SymPy Mode” treats inputs and outputs as SymPy objects instead of standard floats.
• Custom Units: If [any] is used for output units, a custom_dims function is required to compute the output units based on the function inputs. custom_dims inputs are always SymPy objects.
• See the code cell live tutorial for more information.

2. Keyboard Shortcuts

Global Keyboard Shortcuts

Math Field Keyboard Shortcuts

• Ctrl/Cmd + ^ : Add exponent.
• Ctrl/Cmd + _ : Add subscript.
• * : Multiply.
• / : Divide.
• Ctrl/Cmd + E : Insert scientific notation.
• Tab : Move out of exponent or subscript.
• " : Toggle comment mode.
• Type sqrt : Insert square root.
• < then = : Inserts ≤.
• > then = : Inserts ≥.
• Navigation: Use the left, right, up, or down arrow keys to navigate within the math field.

Greek Characters & Math Symbols

• Spell out a Greek character to insert it (may be preceded by \ to insert immediately): alpha, beta, gamma, delta, epsilon, zeta, eta, theta, iota, kappa, lambda, mu, nu, xi, pi, rho, sigma, tau, phi, chi, psi, omega, Gamma, Delta, Theta, Lambda, Xi, Pi, Sigma, Upsilon, Phi, Psi, and Omega.
• Type \int : Insert integral.
• Type \der : Insert derivative.
• Type \dder : Insert double derivative.
• Type \tder : Insert triple derivative.
• Type \sum : Insert summation notation.
• Type \prod : Insert product notation.
• Type \hat : Add hat accent to variable name.
• Type \bar : Add bar accent to variable name.
• Type \vec : Add vector accent to variable name.
• Type \dot : Add dot accent to variable name.
• Type \ddot : Add double dot accent to variable name.
• ' (Apostrophe) : Add prime to variable name.

3. Built-in Functions

General Math

• Square root: sqrt(x) (type sqrt to insert).
• Exponent: x^y (press ^ to insert).
• Natural logarithm (base e): ln(x).
• Base 10 logarithm: log(x).
• Base b logarithm: log_b(x) (type log then press _).
• Absolute value: abs(x).
• Round to nearest integer: round(x).
• Round up to nearest integer: ceil(x).
• Round down to nearest integer: floor(x).
• Factorial: n!.
• Calculus operators: See function toolbar, f(x), for calculus operators.

Trigonometry

• Sine: sin(x) (input unitless or angle).
• Cosine: cos(x) (input unitless or angle).
• Tangent: tan(x) (input unitless or angle).
• Secant: sec(x) (input unitless or angle).
• Cosecant: csc(x) (input unitless or angle).
• Cotangent: cot(x) (input unitless or angle).
• Inverse sine: arcsin(x) (input unitless, output angle).
• Inverse cosine: arccos(x) (input unitless, output angle).
• Inverse tangent: arctan(x) (input unitless, output angle).
• Hyperbolic sine: sinh(x) (unitless input/output).
• Hyperbolic cosine: cosh(x) (unitless input/output).
• Hyperbolic tangent: tanh(x) (unitless input/output).

Complex Numbers

• Real part: real(x).
• Imaginary part: imag(x).
• Angle: angle(x).
• Complex conjugate: conj(x).

Matrices and Vectors

• Number of rows or columns: numrows(A) or numcols(A).
• Min or max: min(x) or max(x) (for list or vector).
• Number of entries: count(x) (for matrix/vector).
• Sum of values: sum(x) (for list or matrix/vector).
• Average of values: average(x) (for list or matrix/vector).
• Standard deviation: stdev(x) (sample) or stdevp(x) (population).
• Return vector of integers 1 to n: range(n).
• Return vector of integers m to n: range(m, n).
• Return vector of integers m to n, step s: range(m, n, s).
• Euclidean norm: ||A|| or norm(A).
• Determinant: det(A).
• Dot product: dot(v1, v2).
• Cross product: v1 x v2 (for 3 by 1 or 1 by 3, type @).
• Matrix transpose: A^T (use Ctrl/Cmd + T).
• Matrix inverse: A^-1.
• Matrix indexing examples: A_3,4 or A_1:end,4:2:12.
• See the matrices and vectors live tutorial for more information.

4. Built-in Units

Units can be used in their long and short forms. Most units support long prefixes in their long form and short prefixes in their short form (e.g., kilogram or kg). Long form units generally support their singular and plural forms (e.g., meter or meters). Units may be combined as needed using exponents, multiplication, and division, as in: [kg/m^3] or [kg*m^-3]

Supported Base Units

• Length: meter (m), inch (in), foot (ft), yard (yd), mile (mi), link (li), rod (rd), chain (ch), angstrom, mil.
• Surface area: m2, sqin, sqft, sqyd, sqmi, sqrd, sqch, sqmil, acre, hectare.
• Volume: m3, litre (l, L, lt, liter), cc, cuin, cuft, cuyd, teaspoon, tablespoon.
• Liquid volume: minim, fluiddram (fldr), fluidounce (floz), gill (gi), cup (cp), pint (pt), quart (qt), gallon (gal), beerbarrel (bbl), oilbarrel (obl), hogshead, drop (gtt).
• Angles: rad (radian), deg (degree), grad (gradian), cycle, arcsec (arcsecond), arcmin (arcminute).
• Time: second (s, secs, seconds), minute (min, mins, minutes), hour (h, hr, hrs, hours), day (days), week (weeks), month (months), year (years), decade (decades), century (centuries), millennium (millennia).
• Frequency: hertz (Hz).
• Mass: gram (g), tonne, ton, grain (gr), dram (dr), ounce (oz), poundmass (lbm, lb, lbs), hundredweight (cwt), stick, stone.
• Electric current: ampere (A).
• Temperature: kelvin (K), celsius (degC), fahrenheit (degF), rankine (degR).
• Amount of substance: mole (mol).
• Luminous intensity: candela (cd).
• Force: newton (N), dyne (dyn), poundforce (lbf), kip, kilogramforce (kgf), gramforce (gf).
• Energy: joule (J), erg, Wh, BTU (Btu), electronvolt (eV).
• Power: watt (W), hp, tonrefrigeration (TR, RT, TOR, toncooling), boilerhp (BHP), MBH, MMBH.
• Pressure: Pa, psi, atm, torr, bar, mmHg, mmH2O, cmH2O, inHg, inH2O, ftH2O, kpsi (ksi), Mpsi.
• Electricity and magnetism: ampere (A), coulomb (C), watt (W), volt (V), ohm, farad (F), weber (Wb), tesla (T), henry (H), siemens (S), electronvolt (eV).
• Viscosity: poise (P), reyn, ureyn, stokes (St).
• Binary: bits (b), bytes (B).

Supported Unit Prefixes