High precision scientific calculator with support for physical units
npm install insectyou can read more about why Insect has been rewritten from scratch here.
A high-precision scientific calculator with full support for physical units.
Contents
--------
- Documentation
- Reference
- Pros and cons
- FAQ
- Terminal version
- Development
- Maintainers
- 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(
product(
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, ...
- 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 |
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.
- 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
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 withsudo. 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
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:
`` Dockerfile
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