High precision scientific calculator with support for physical units
A high precision scientific calculator with full support for physical units.
Try the web version here: https://insect.sh
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, ...
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 |
Gregorian year | years , year |
Julian year | julianYears , julianYear |
Reasons to use Insect
Reasons to choose an alternative
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
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.
For Arch Linux, there is a package on AUR:
yaourt -S insect
For macOS, there is a Homebrew package:
brew install insect
For Android, install Termux from
F-Droid. Install Node.js in
Termux and then install insect
.
pkg install nodejs-lts
npm install -g insect
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