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
  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. 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, 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	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
  

• 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 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 which can by installed via npm:

npm install -g insect

Note that this might fail if you run it with sudo. Instead, set up a prefix directory and call npm install as a user.

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

For Android, install Termux from Google Play or F-Droid. Install nodejs in Termux and then install insect.

pkg install nodejs-lts
npm install -g 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