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
• Maintainers

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, acot/arccotangent, acoth/archypcotangent, acsc/arccosecant, acsch/archypcosecant, arcsecant, asech/archypsecant, asin, asinh, atan2, atan, atanh, ceil, cos, cosh, cot/cotangent, coth/hypcotangent, csc/cosecant, csch/hypcosecant, exp, floor, fromCelsius, fromFahrenheit, gamma, ln, log10, log, maximum, mean, minimum, round, secant, sech/hypsecant, 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.

  • Hexadecimal, octal and binary number input:

    0xFFFF
    0b1011
    0o32
    0x2.F
    0o5p3
    

• 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) or _ 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
  copy result to clipboard	copy, cp
  quit (CLI)	quit, exit

• Supported units (remember that you can use tab completion).

  All SI-accepted units support metric prefixes and binary prefixes (MiB, GiB, ...).

  Unit	Syntax
  Ampere	amperes, ampere, A
  Ångström	angstroms, angstrom, Å
  Astronomical unit	AU, au, astronomicalunits, astronomicalunit
  Atmosphere	atm
  Bar	bars, bar
  Barn	barns, barn
  Becquerel	becquerels, becquerel, Bq
  Bel	bels, 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	candelas, candela, cd
  Coulomb	coulombs, coulomb, C
  Cup	cups, cup
  DPI	dpi
  Day	days, day, d
  Degree	degrees, degree, deg, °
  Dot	dots, dot
  Electronvolt	electronvolts, electronvolt, eV
  Euro	euros, euro, EUR, €
  Farad	farads, 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	grays, gray, Gy
  Hectare	hectares, hectare, ha
  Henry	henrys, henries, henry, H
  Hertz	hertz, Hz
  Hogshead	hogsheads, hogshead
  Hour	hours, hour, hr, h
  Inch	inches, inch, in
  Joule	joules, joule, J
  Katal	katals, katal, kat
  Knot	knots, knot, kn, kt
  Kelvin	kelvins, kelvin, K
  Light-year	lightyears, lightyear, ly
  Liter	liters, liter, litres, litre, L, l
  Lumen	lumens, 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
  Molal	molals, molal
  Molar	molars, molar
  Mole	moles, mole, mol
  Month	months, month
  Nautical mile	M, NM, nmi
  Newton	newtons, 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	pascals, 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	sieverts, sievert, Sv
  Tablespoon	tablespoons, tablespoon, tbsp
  Teaspoon	teaspoons, teaspoon, tsp
  Tesla	teslas, tesla, T
  Thou	thou, mils, mil
  Tonne	tonnes, tonne, tons, ton, t
  US Dollar	dollars, dollar, USD, $
  Volt	volts, volt, V
  Watt-hour	Wh
  Watt	watts, watt, W
  Weber	webers, weber, Wb
  Week	weeks, week
  Yard	yards, yard, yd
  Gregorian year	years, year
  Julian year	julianYears, julianYear

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-like interface. There is a saved history that can be browsed by pressing the up and down arrow keys. The history is also searchable via Ctrl-R.
• Insect's syntax 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 non-SI 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, octal, or binary numbers (yet), though it does support inputting them.

FAQ

• Why are Celsius and Fahrenheit not supported?

  In contrast to the SI unit of temperature, the Kelvin, and to all other units, Celsius and Fahrenheit both 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 as 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
  

• What is the relation between the units RPM, rad/s, deg/s and Hz?

  The unit RPM (revolutions per minute) is defined via 1 RPM = 1 / minute where the 1 on the right hand side symbolizes "1 revolution".

  As the base unit is the same (1 / second), RPM can be converted to rad / s, deg / s or Hz. Note, however, that 1 RPM does not equal 2π rad / min or 360° / min or 1 Hz, as some might expect. If you're interested in computing the traversed angle of something that rotates with a given number of revolutions per minute, you need to multiply by 2π rad or 360° because:

  1 RPM · (360°/revolution) = (1 revolution / minute) · (360° / revolution) = 360° / minute
  

Terminal version

In addition to the web interface, there is also a command-line version (supporting Node.js 10 and later) which can by installed via npm:

npm install -g insect

Note that you should almost always never run this as root or with sudo. If the command fails due to permission issues, set up a prefix directory and call npm install as a user instead.

For Arch Linux, there is an AUR package:

yaourt -S insect

For macOS, there is a Homebrew formula:

brew install insect

For Android, install Termux from F-Droid. Install Node.js in Termux and then install insect from npm:

pkg install nodejs-lts
npm install -g insect

Development

Insect is written in PureScript (see the Getting Started guide). First, install all dependencies:

npm install

To start the web version:

npm start

To build a bundled JavaScript file that you can run from the terminal (note that this builds the web version too):

npm run build

To run the index.cjs file which the previous command creates:

node index.cjs
# Or simply on Un*x
./index.cjs

Note that it's not possible to just move this file anywhere and then run it there, since it depends on packages in node_modules.

Insect comes with a comprehensive set of unit tests. To run them:

npm test

Note that Node.js 12 or above is required to work on/build Insect (despite Insect itself requiring only Node.js 10 or later to run). If you don't have or want to install Node.js 12 or later, you can use the following Dockerfile to build or run Insect on Node.js 18:

FROM node:18

WORKDIR /usr/src/insect

COPY . .

RUN npm install && \
    npm run build

CMD ["node", "index.cjs"]

After creating the image (docker build -t sharkdp/insect .), you can create the container and copy out the build artifacts:

docker create sharkdp/insect:latest
# copy SHA (e.g. 71f0797703e8)
docker cp 71f0797703e8:/usr/src/insect/index.cjs .
docker cp -r 71f0797703e8:/usr/src/insect/node_modules .

To directly run Insect inside Docker (paying a heavy startup time penalty), you can use:

docker run -it --rm -v ~/.local/share/insect-history:/root/.local/share/insect-history sharkdp/insect:latest

Maintainers

• sharkdp
• mhmdanas