Sheet language quick reference

Every kind of line a CivilKit Calcs sheet takes, its inputs, and the functions, constants, operators and units of the engine, on one page that prints well. Use Print and choose Save as PDF to keep a copy. The full account is in the user guide.

Open Calcs

Lines of a sheet

Line	You write	You get
Heading	`# Beam check`	A heading, level 1 to 6 with more #.
Prose	`Plain text, bold, italic, lists and tables.`	Markdown. A line that reads as a calculation but is not one can start with a backslash.
Formula in text	`The moment is $M = wL^2/8$.`	A formula typeset in the text.
Quantity	`L: 6 m \| span`	A name with a value and a unit; the text after \| is a note.
Calculation	`M: w * L^2 / 8 -> kN*m`	The working shown with the values put in, converted to kN·m.
Several on a line	`a: 1; b: 2 \| note for b`	Two quantities; the note belongs to the last.
Your own function	`f(x, y): sqrt(x^2 + y^2)`	Used as f(3, 4) in later lines and in plots.
A unit of your own	`#unit bag = 25 kg`	Then 3 bag, or -> bag.
Vector and matrix	`v: [1, 2, 3] A: [1, 2; 3, 4]`	Commas across, semicolons between rows. v.2 and A.(1, 2) pick an element.
Condition	`if u <= 1: "OK" else: "Fails"`	A block with a body uses an indented body after if, else, for, while or repeat.
Loop	`for i in 1..5: P: 10 kN * i`	for x in v, for i in 0..10 step 2, while, repeat n, break and continue also work.
Solve	`x0: solve f(x) = 4 for x in 0..5`	Root finding on a range.
Integral and slope	`A: integral of f(x) for x in 0..3 k: slope of f(x) at x = 3`	Numerical integral and derivative.
Plot	`plot sin(x) as "sine", cos(x) for x in 0..6`	Curves on one plot; as "name" adds a legend entry.
Page break	`<div style="page-break-after:always"></div>`	Starts a new page in print, PDF and Word.
Raw engine line	`>> #deg`	A line passed to the Calcpad engine as written.

Inputs (a question mark makes the value a form field)

Line	You write	You get
Number	`L: ? 6 m \| span`	A box with its unit; the value is the default.
Slider	`w: ? 12 kN/m [2 .. 30 step 0.5] \| load`	A box with a slider between the bounds.
Drop-down	`E: ? [Steel = 200 GPa, *Timber = 11 GPa]`	The name takes the value of the chosen option; * marks the default.
Radio buttons	`k: ? (Low = 1, High = 2)`	The same with round brackets.
Checkbox	`ribs: ? on`	on is 1 and off is 0.

Constants and operators

Constant	Symbol
Pi - ratio of circumference to diameter	`π`
Pi - ratio of circumference to diameter (spelled out)	`pi`
Euler's number - base of natural logarithm	`e`
Golden ratio	`φ = 1.618033988749894`
Euler-Mascheroni constant	`γ = 0.5772156649015328`
Standard gravitational acceleration	`g = 9.80665m/s^2`
Gravitational constant	`G = 6.6743010^-11(m^3/(kg*s^2))`
Earth mass	`M_E = 5.972210^24kg`
Solar mass	`M_S = 1.9884710^30kg`
Speed of light in vacuum	`c = 299792458m/s`
Planck constant	`h = 6.6260701510^-34J/Hz`
Vacuum permeability	`μ_0 = 1.2566370621210^-6N/A^2`
Vacuum permittivity	`ε_0 = 8.854187812810^-12F/m`
Coulomb constant	`k_e = 8.987551792310^9N*m^2/C^2`
Elementary charge	`e = 1.60217663410^-19C`
Electron mass	`m_e = 9.109383701510^-31kg`
Proton mass	`m_p = 1.6726219236910^-27kg`
Neutron mass	`m_n = 1.6749274980410^-27kg`
Avogadro constant	`N_A = 6.0221407610^23mol^-1`
Stefan-Boltzmann constant	`σ = 5.67037441910^-8Wm^-2K^-4`
Boltzmann constant	`k_B = 1.38064910^-23J/K`
Molar gas constant	`R = 8.31446261815324(J/(molK))`
Faraday constant	`F = 96485.33212331C/mol`
Unit weight of concrete	`γ_c = 25kN/m^3`
Unit weight of steel	`γ_s = 78.5kN/m^3`
Unit weight of aluminium	`γ_a = 27kN/m^3`
Unit weight of glass	`γ_g = 25kN/m^3`
Unit weight of water	`γ_w = 10kN/m^3`

Operator	Symbol
Factorial	`!`
Exponent (power)	`^`
Division	`/`
Division bar (inline) / slash (pro mode)	`÷`
Integer division	`\`
Modulo (remainder)	`⦼`
Multiplication	`*`
Subtraction / Negation	`-`
Addition	`+`
Equal to	`≡`
Not equal to	`≠`
Less than	`<`
Greater than	`>`
Less than or equal	`≤`
Greater than or equal	`≥`
Logical AND	`∧`
Logical OR	`∨`
Logical XOR	`⊕`
Phasor angle operator A∠φ	`∠`
Assignment	`=`
Outer scope assignment	`←`

In a sheet: + - * / ^ %, < > <= >= == !=, and or, and the forms ≤ ≥ ≠ ∧ ∨ × · ÷. ² and ³ after a name or unit mean ^2 and ^3.

Functions

Arguments are separated by commas in a sheet (the engine's semicolon also works inside brackets). A function written with a unit-bearing argument returns its result with the right unit.

Functions of numbers

Trigonometric

sin(x) cos(x) tan(x) csc(x) sec(x) cot(x)

Inverse Trigonometric

asin(x) acos(x) atan(x) atan2(x; y) acsc(x) asec(x) acot(x)

Hyperbolic

sinh(x) cosh(x) tanh(x) csch(x) sech(x) coth(x)

Inverse Hyperbolic

asinh(x) acosh(x) atanh(x) acsch(x) asech(x) acoth(x)

Logarithmic, Exponential and Roots

log(x) ln(x) log_2(x) exp(x) sqr(x) sqrt(x) cbrt(x) root(x; n)

Rounding

round(x) floor(x) ceiling(x) trunc(x)

Integer

mod(x; y) gcd(values; …) lcm(values; …) fact(n)

Complex

re(z) im(z) abs(z) phase(z) conj(z)

Aggregate and Interpolation

min(v₁; v₂; ...) min(v) min(M) max(v₁; v₂; ...) max(v) max(M) sum(v₁; v₂; ...) sum(v) sum(M) sumsq(v₁; v₂; ...) sumsq(v) sumsq(M) srss(v₁; v₂; ...) srss(v) srss(M) average(v₁; v₂; ...) average(v) average(M) product(v₁; v₂; ...) product(v) product(M) mean(v₁; v₂; ...) mean(v) mean(M) median(v₁; v₂; ...) stdev(v₁; v₂; ...) stdevp(v₁; v₂; ...) var(v₁; v₂; ...) varp(v₁; v₂; ...) take(n; values) take(n; v) take(n; m) line(x; data) line(x; xData; yData) line(x; m) spline(x; data) spline(x; xData; yData) spline(x; m)

Conditional and Logical

if(cond; value-if-true; value-if-false) switch(c₁; v₁; c₂; v₂; …; def) not(x) and(values; …) or(values; …) xor(values; …)

Other

sign(x) random(x) getunits(x) setunits(x; u) clrunits(x) hp(x) ishp(x) timer(x) mandelbrot(x; y)

Vector functions

Creational

vector(n) vector_hp(n) range(x1; xn; s) range_hp(x1; xn; s) linspace(a; b; n)

Structural

len(v) size(v) resize(v; n) fill(v; x) join(items) slice(v; i1; i2) first(v; n) last(v; n) extract(v; i)

Data

sort(v) rsort(v) order(v) revorder(v) reverse(v) count(v; x; i) search(v; x; i) find(v; x; i) find_eq(v; x; i) find_ne(v; x; i) find_lt(v; x; i) find_le(v; x; i) find_gt(v; x; i) find_ge(v; x; i) lookup(a; b; x) lookup_eq(a; b; x) lookup_ne(a; b; x) lookup_lt(a; b; x) lookup_le(a; b; x) lookup_gt(a; b; x) lookup_ge(a; b; x) polyfit(x; y; n) interp(x; xs; ys) linterp(x; xs; ys)

Math

norm(v) norm_1(v) norm_2(v) norm_e(v) norm_p(v; p) norm_i(v) unit(v) cumsum(v) convolve(a; b) dot(a; b) cross(a; b)

Matrix functions

Creational

matrix(m; n) identity(n) diagonal(n; d) column(m; c) utriang(n) ltriang(n) symmetric(n) matrix_hp(m; n) identity_hp(n) diagonal_hp(n; d) column_hp(m; c) utriang_hp(n) ltriang_hp(n) symmetric_hp(n) vec2diag(v) vec2row(v) vec2col(v) join_cols(columns; …) join_rows(rows; …) augment(matrices; …) stack(matrices; …)

Structural

n_rows(M) n_cols(M) mresize(M; m; n) mfill(M; x) fill_row(M; i; x) fill_col(M; j; x) copy(A; B; i; j) add(A; B; i; j) row(M; i) col(M; j) extract_rows(M; i) extract_cols(M; j) diag2vec(M) submatrix(M; i1; i2; j1; j2)

Data

sort_cols(M; i) rsort_cols(M; i) sort_rows(M; j) rsort_rows(M; j) order_cols(M; i) revorder_cols(M; i) order_rows(M; j) revorder_rows(M; j) mcount(M; x) msearch(M; x; i; j) mfind(M; x) mfind_eq(M; x) mfind_ne(M; x) mfind_lt(M; x) mfind_le(M; x) mfind_gt(M; x) mfind_ge(M; x) hlookup(M; x; i1; i2) hlookup_eq(M; x; i1; i2) hlookup_ne(M; x; i1; i2) hlookup_lt(M; x; i1; i2) hlookup_le(M; x; i1; i2) hlookup_gt(M; x; i1; i2) hlookup_ge(M; x; i1; i2) vlookup(M; x; j1; j2) vlookup_eq(M; x; j1; j2) vlookup_ne(M; x; j1; j2) vlookup_lt(M; x; j1; j2) vlookup_le(M; x; j1; j2) vlookup_gt(M; x; j1; j2) vlookup_ge(M; x; j1; j2)

Math

hprod(A; B) fprod(A; B) kprod(A; B) mnorm(M) mnorm_1(M) mnorm_2(M) mnorm_e(M) mnorm_i(M) cond(M) cond_1(M) cond_2(M) cond_e(M) cond_i(M) det(M) rank(M) trace(M) transp(M) adj(M) cofactor(M) polyroots(v) eigenvals(M; ne) eigenvecs(M; ne) eigen(M; ne) ceigenvals(M) ceigenvecs(M) cholesky(M) lu(M) qr(M) svd(M) inverse(M) lsolve(A; b) clsolve(A; b) slsolve(A; b) msolve(A; B) cmsolve(A; B) smsolve(A; B) fft(M) ift(M) take(x; y; M) line(x; y; M) spline(x; y; M)

Units

Write a unit after a number (300 MPa, 9.81 m/s², 5 kN*m). The engine combines and checks them, so a unit error is a mistake caught. Prefixes (k, M, G, m, µ, n and the rest of the SI set) apply to the metric units. Convert a result with -> unit, show a ratio as a percentage with -> %, and show a result in SI base units with -> base. Point at a unit for its meaning.

Dimensionless

% ‰ ‱ pcm ppm ppb ppt ppq

Angles

° ′ ″ deg rad grad rev

Metric: Mass

g dag hg kg t kt Mt Gt dg cg mg μg ng pg Da u

Metric: Length

m km dm cm mm μm nm pm AU ly

Metric: Area

a daa ha

Metric: Volume

L daL hL dL cL mL μL nL pL

Time

s ms μs ns ps min h d w y

Frequency

Hz kHz MHz GHz THz mHz μHz nHz pHz rpm

Speed

kmh

Temperature

°C Δ°C K

Metric: Force

N daN hN kN MN GN TN gf kgf tf dyn

Metric: Moment

Nm kNm

Metric: Pressure

Pa daPa hPa kPa MPa GPa TPa dPa cPa mPa μPa nPa pPa bar mbar μbar atm at Torr mmHg

Metric: Viscosity

P cP St cSt

Metric: Energy

J kJ MJ GJ TJ mJ μJ nJ pJ Wh kWh MWh GWh TWh mWh μWh nWh pWh VAh kVAh MVAh GVAh VARh kVARh MVARh GVARh eV keV MeV GeV TeV PeV EeV cal kcal erg

Metric: Power

W kW MW GW TW mW μW nW pW VA kVA MVA GVA TVA mVA μVA nVA pVA VAR kVAR MVAR GVAR TVAR mVAR μVAR nVAR pVAR

Electrical: Current

A kA MA GA TA mA μA nA pA

Electrical: Charge

C kC MC GC TC mC μC nC pC Ah mAh

Electrical: Potential

V kV MV GV TV mV μV nV pV

Electrical: Capacitance

F kF MF GF TF mF μF nF pF

Electrical: Resistance

Ω kΩ MΩ GΩ TΩ mΩ μΩ nΩ pΩ

Electrical: Conductance

S kS MS GS TS mS μS nS pS ℧ k℧ M℧ G℧ T℧ m℧ μ℧ n℧ p℧

Electrical: Magnetic Flux

Wb kWb MWb GWb TWb mWb μWb nWb pWb

Electrical: Magnetic Flux Density

T kT MT GT TT mT μT nT pT

Electrical: Inductance

H kH MH GH TH mH μH nH pH

Luminous

cd lm lx

Radioactivity

Bq kBq MBq GBq TBq mBq μBq nBq pBq Ci Rd

Dose: Absorbed

Gy kGy MGy GGy TGy mGy μGy nGy pGy

Dose: Equivalent

Sv kSv MSv GSv TSv mSv μSv nSv pSv

Catalytic Activity

kat

Amount of Substance

mol

Imperial: Mass

gr dr oz lb lbm lb_m kipm kip_m klb st qr cwt cwt_US cwt_UK ton ton_US ton_UK slug

Imperial: Length

th in ft yd ch fur mi ftm ftm_UK ftm_US cable cable_UK cable_US nmi li rod pole perch lea

Imperial: Speed

mph knot

Imperial: Temperature

°F Δ°F °R

Imperial: Area

rood ac

Imperial: Volume

fl_dr_UK fl_dr_US fl_oz fl_oz_UK fl_oz_US gi gi_UK gi_US pt pt_UK pt_US pt_dry qt qt_UK qt_US qt_dry gal gal_UK gal_US gal_dry bbl bbl_UK bbl_US bbl_dry pk_UK pk_US bu_UK bu_US

Imperial: Force

ozf oz_f lbf lb_f kip kipf kip_f tonf tonf_US tonf_UK pdl

Imperial: Pressure

osi osf psi psf ksi ksf tsi tsf inHg

Imperial: Energy

BTU therm therm_US therm_UK quad

Imperial: Power

hp hp_E hp_S hp_M ks

The user guide, with a chapter for each of these.
Calculators and guides: ready-made templates that open as forms.
Source on GitHub (MIT licence).

Sheet language quick reference

Lines of a sheet

Inputs (a question mark makes the value a form field)

Constants and operators

Functions

Functions of numbers

Trigonometric

Inverse Trigonometric

Hyperbolic

Inverse Hyperbolic

Logarithmic, Exponential and Roots

Rounding

Integer

Complex

Aggregate and Interpolation

Conditional and Logical

Other

Vector functions

Creational

Structural

Data

Math

Matrix functions

Creational

Structural

Data

Math

Units

Dimensionless

Angles

Metric: Mass

Metric: Length

Metric: Area

Metric: Volume

Time

Frequency

Speed

Temperature

Metric: Force

Metric: Moment

Metric: Pressure

Metric: Viscosity

Metric: Energy

Metric: Power

Electrical: Current

Electrical: Charge

Electrical: Potential

Electrical: Capacitance

Electrical: Resistance

Electrical: Conductance

Electrical: Magnetic Flux

Electrical: Magnetic Flux Density

Electrical: Inductance

Luminous

Radioactivity

Dose: Absorbed

Dose: Equivalent

Catalytic Activity

Amount of Substance

Imperial: Mass

Imperial: Length

Imperial: Speed

Imperial: Temperature

Imperial: Area

Imperial: Volume

Imperial: Force

Imperial: Pressure

Imperial: Energy

Imperial: Power

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