insect

A high precision scientific calculator with full support for physical units.

Try the web version here: https://insect.sh

Contents

• Documentation
• Reference
• Pros and cons
• FAQ
• Terminal version
• Development

Documentation

• Evaluate mathematical expressions:

  1920/16*9
  2^32
  sqrt(1.4^2 + 1.5^2) * cos(pi/3)^2
  

  • Operators: addition (+), subtraction (-), multiplication
    (*, ·, ×), division (/, ÷, per), exponentiation
    (^, **). Full list: see Reference below.

  • Mathematical functions: abs, acos, acosh, asin,
    asinh, atan, atan2, atanh, ceil, cos, cosh, exp,
    floor, fromCelsius, fromFahrenheit, gamma, ln, log,
    log10, maximum, minimum, mean, round, sin, sinh,
    sqrt, tan, tanh, toCelsius, toFahrenheit.

  • High-precision numeric type with 30 significant digits
    that can handle very large (or small) exponents like
    10^(10^10).

  • Exponential notation: 6.022e23.

• Physical units: parsing and handling, including metric prefixes:

  2 min + 30 s
  40 kg * 9.8 m/s^2 * 150 cm
  sin(30°)
  

  • Supported units: see Reference section
    below.

  • Implicit conversions: 15 km/h * 30 min evaluates to
    7.5 km.

  • Useful error messages:

    > 2 watts + 4 newton meter
    
    Conversion error:
      Cannot convert unit N·m (base units: kg·m²·s⁻²)
                  to unit W (base units: kg·m²·s⁻³)
    

• Explicit unit conversions: the -> conversion operator
  (aliases: →, ➞, to):

  60 mph -> m/s
  500 km/day -> km/h
  1 mrad -> degree
  52 weeks -> days
  5 in + 2 ft -> cm
  atan(30 cm / 2 m) -> degree
  6 Mbit/s * 1.5 h -> GB
  

• Variable assignments:

  Example: mass of the earth

  r = 6000km
  vol = 4/3 * pi * r^3
  density = 5 g/cm^3
  vol * density -> kg
  

  Example: oscillation period of a pendulum

  len = 20 cm
  2pi*sqrt(len/g0) -> ms
  

  • Predefined constants (type list to see them all): speed of
    light (c), Planck's constant (h_bar), electron mass
    (electronMass), elementary charge (elementaryCharge),
    magnetic constant (µ0), electric constant (eps0), Bohr
    magneton (µ_B), Avogadro's constant (N_A), Boltzmann
    constant (k_B), gravitational acceleration (g0), ideal gas
    constant (R), ...

  • Last result: you can use ans (answer) to refer to the
    result of the last calculation.

• User-defined functions:

  Example: kinetic energy

  kineticEnergy(mass, speed) = 0.5 * mass * speed^2 -> kJ
  
  kineticEnergy(800 kg, 120 km/h)
  

  Example: barometric formula

  P0 = 1 atm
  T0 = fromCelsius(15)
  tempGradient = 0.65 K / 100 m
  
  pressure(height) = P0 * (1 - tempGradient * height / T0)^5.255 -> hPa
  
  pressure(1500 m)
  

• Sums and products:

  Syntax:

  sum(<expression>, <index-variable>, <from>, <to>)
  product(<expression>, <index-variable>, <from>, <to>)
  

  Examples:

  # sum of the first ten squares
  sum(k^2, k, 1, 10)
  
  # the factorial of n as the product 1 × 2 × ... × n
  myFactorial(n) = product(k, k, 1, n)
  

• Unicode support:

  λ = 2 × 300 µm
  ν = c/λ → GHz
  

• And more: tab completion, command history (arrow keys,
  Ctrl+R), pretty printing, syntax highlighting, ...

Reference

• Operators (ordered by precedence: high to low), Operator, Syntax, ---------------------------, ----------------------, factorial, !, square, cube, ..., ², ³, ⁻¹, ..., exponentiation, ^, **, multiplication (implicit), whitespace, modulo, %, division, per, division, /, ÷, multiplication (explicit), *, ·, ×, subtraction, -, addition, +, unit conversion, ->, →, ➞, to, assignment, =, Note that implicit multiplication has a higher precedence than
  division, i.e. 50 cm / 2 m will be parsed as 50 cm / (2 m).

• Commands, Command, Syntax, -------------------, --------------------, help text, help, ?, list of variables, list, ls, ll, reset environment, reset, clear screen, clear, cls, quit (CLI), quit, exit, - Supported units (remember that you can use tab completion).

  All SI-accepted units support metric prefixes. In addition, binary
  prefixes (MiB,
  GiB, ...) are also supported., Unit, Syntax, ------------------------------------------------------------------------------, -----------------------------------------------------------------------------, Ampere, amperes, ampere, A, Ångström, angstrom, Å, Astronomical unit, AU, au, astronomicalunits, astronomicalunit, Atmosphere, atm, Bar, bar, Barn, barn, Becquerel, becquerel, Bq, Bel, bel, Bit, bits, bit, Bits per second, bps, British thermal unit, BTU, Byte, Bytes, bytes, Byte, byte, B, Octets, octets, Octet, octet, Calorie, calories, calorie, cal, Candela, candela, cd, Coulomb, coulomb, C, Cup, cups, cup, DPI, dpi, Day, days, day, d, Degree, degrees, degree, deg, °, Dot, dots, dot, Electronvolt, electronvolt, eV, Euro, euros, euro, EUR, €, Farad, farad, F, Fluid ounce, fluidounces, fluidounce, floz, Foot, feet, foot, ft, Fortnight, fortnights, fortnight, Frame, frames, frame, Frames per second, fps, Furlong, furlongs, furlong, Gallon, gallons, gallon, gal, Gauss, gauss, Gram, grams, gram, grammes, gramme, g, Gray, gray, Gy, Hectare, hectare, ha, Henry, henrys, henries, henry, H, Hertz, hertz, Hz, Hogshead, hogsheads, hogshead, Hour, hours, hour, h, Inch, inches, inch, in, Joule, joules, joule, J, Katal, katal, kat, Kelvin, kelvin, K, Light-year, lightyears, lightyear, ly, Liter, liters, liter, litres, litre, L, l, Lumen, lumen, lm, Lux, lux, lx, Meter, meters, meter, metres, metre, m, Mile, miles, mile, Miles per hour, mph, Millimeter of mercury, mmHg, Minute, minutes, minute, min, Mole, mole, mol, Month, months, month, Newton, newton, N, Ohm, ohms, ohm, Ω, Ounce, ounces, ounce, oz, PPI, ppi, Parsec, parsecs, parsec, pc, Parts-per-million, ppm, Parts-per-billion, ppb, Parts-per-trillion, ppt, Parts-per-quadrillion, ppq, Pascal, pascal, Pa, Percent, percent, pct, Person, persons, person, people, Piece, pieces, piece, Pint, pints, pint, Pixel, pixels, pixel, px, Pound-force, pound_force, lbf, Pound, pounds, pound, lb, Psi, psi, RPM, RPM, rpm, Radian, radians, radian, rad, Rod, rods, rod, Second, seconds, second, sec, s, Siemens, siemens, S, Sievert, sievert, Sv, Tablespoon, tablespoons, tablespoon, tbsp, Teaspoon, teaspoons, teaspoon, tsp, Tesla, tesla, T, Thou, thou, Tonne, tonnes, tonne, tons, ton, t, US Dollar, dollars, dollar, USD, $, Volt, volts, volt, V, Watt-hour, Wh, Watt, watts, watt, W, Weber, weber, Wb, Week, weeks, week, Yard, yards, yard, yd, Year, years, year, Pros and cons

Reasons to use Insect

• Insect is open source.
• There is a web version that requires no
  installation.
• With both browser and terminal versions available, insect is truly
  cross-platform.
• Insect has first-class support for physical units, including
  metric and binary prefixes. While evaluating your calculation,
  Insect ensures that you did not accidentally make any mistakes in
  combining the physical quantities.
• Insect supports an
  interactive style with its
  readline-based interface. There is a saved history that can be
  browsed by pressing up- and down keys. The history is also
  searchable via Ctrl-R.
• The syntax of Insect is rather strict. The parser does not try to be
  "smart" on syntactically incorrect input, so there shouldn't be any
  surprises - and you can trust the result of your calculation. The
  parsed user input is always pretty-printed for a quick double-check.
• Insect is written in PureScript and
  therefore benefits from all the safety-guarantees that a
  strictly-typed functional programming language gives you.
• The source code of
  purescript-quantities
  (the underlying library for physical units) as well as the code of
  Insect itself is extensively tested.

Reasons to choose an alternative

• Insect is a scientific calculator. It's not a computer algebra
  system that solves differential equations or computes integrals. Try
  WolframAlpha instead.
• There is no graphical user interface with buttons for each action
  (x², 1/x, DEG/RAD, etc.).
  Qalculate! is a fantastic tool that
  supports both text- as well as graphical input.
• Insect supports a huge range of physical units: all SI
  units,
  all units that are accepted by SI as well as most units of the
  imperial and US customary systems (and many more). However, if you
  need something even more comprehensive, try GNU
  units.
• Insect is not a general-purpose programming language. You could try
  Frink.
• Insect does not have a special mode for hexadecimal or binary
  numbers (yet).

FAQ

• Why are Celsius and Fahrenheit not supported?

  Compared to the SI unit
  Kelvin and in contrast to
  all other units, Celsius and Fahrenheit require an additive offset
  when converting into and from other temperature units. This additive
  offset leads to all kinds of ambiguities when performing
  calculations in these units. Adding two temperatures in Celsius, for
  example, is only meaningful if one of them is seen as an offset
  value (rather than an absolute temperature). Insect is primarily a
  scientific calculator (as opposed to a unit conversion tool) and
  therefore focuses on getting physical calculations right.

  Even though °C and °F are not supported as built-in units, there
  are helper functions to convert to and from Celsius (and
  Fahrenheit):

  • fromCelsius takes a scalar value that represents a
    temperature in Celsius and returns a corresponding temperature
    in Kelvin:

    > fromCelsius(0)
    
       = 273.15 K
    
    > k_B * fromCelsius(23) to meV
    
       = 25.5202 meV
    

  • toCelsius takes a temperature in Kelvin and returns a
    scalar value that represents the corresponding temperature
    in Celsius:

    > toCelsius(70 K)
    
       = -203.15
    
    > toCelsius(25 meV / k_B)
    
       = 16.963
    

• Why is 1/2 x parsed as 1/(2x)?

  Implicit multiplication (without an explicit multiplication sign)
  has a higher precedence than division (see operator precedence
  rules). This is by design, in order to parse inputs
  like 50 cm / 2 m as (50 cm) / (2 m). If you meant ½ · x, write
  1/2 * x.

• What is the internal numerical precision?

  By default, Insect shows 6 significant digits in the result of the
  calculation. However, the internal numerical precision is much
  higher (30 digits).

• How does the conversion operator work?

  The conversion operator -> attempts to convert the physical
  quantity on its left hand side to the unit of the expression on
  its right hand side. This means that you can write an arbitrary
  expression on the right hand side (but only the unit part will be
  extracted). For example:

  # simple unit conversion:
  > 120 km/h -> mph
  
    = 74.5645 mi/h
  
  # expression on the right hand side:
  > 120 m^3 -> km * m^2
  
    = 0.12 m²·km
  
  # convert x1 to the same unit as x2:
  > x1 = 50 km / h
  > x2 = 3 m/s -> x1
  
    x2 = 10.8 km/h
  

Terminal version

In addition to the web interface, there is also a command line version
which can by installed via npm:

npm install -g insect

If you prefer not to install nodejs and npm, you can use one of the
standalone binaries on the release
page.

For Arch Linux, there is a package on
AUR:

yaourt -S insect

On Fedora 28+, you can install insect from the official sources:

sudo dnf install insect

For Fedora versions 26 and 27, you need to enable this copr
repository:

sudo dnf copr enable fnux/insect

For macOS, there is a Homebrew
package:

brew install insect

Development

Insect is written in PureScript (see Getting
Started
guide). You can install all dependencies and build the whole project by
running:

npm install
npm start

Open web/index.html in your browser.

Insect comes with a comprehensive set of unit tests.
You can run them by calling

npm test