1(1) insect - scientific calculator (1)
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6 insect - interactive scientific calculator
7
9 insect [EXPR]
10
12 insect is a high-precision scientific calculator with full support for
13 physical units.
14 It can be used in interactive mode by simply calling insect. This mode
16 can also be used to read from a file, by simply piping the file con‐
17 tents via insect < my-calculation.ins. If you want to evaluate just a
18 single expression, pass it as an argument: insect '70mph to km/h'.
19 Documentation
21 · Evaluate mathematical expressions:
22 1920/16*9
24 2^32
25 sqrt(1.4^2 + 1.5^2) * cos(pi/3)^2
26 · Operators: addition (+), subtraction (-), multiplication (*, ·, ×),
28 division (/, ÷, per), exponentiation (^, **). Full list: see Ref‐
29 erence below.
30 · Mathematical functions: acos, acosh, asin, asinh, atan, atan2,
32 atanh, ceil, cos, cosh, exp, floor, fromCelsius, fromFahrenheit,
33 gamma, ln, log, log10, round, sin, sinh, sqrt, tan, tanh, toCel‐
34 sius, toFahrenheit.
35 · High-precision numeric type with 30 significant digits that can
37 handle very large (or small) exponents like 10^(10^10).
38 · Exponential notation: 6.022e23.
40 · Physical units: parsing and handling, including metric prefixes:
42 2 min + 30 s
44 40 kg * 9.8 m/s^2 * 150 cm
45 sin(30°)
46 · Supported units: see Reference section below.
48 · Implicit conversions: 15 km/h * 30 min evaluates to 7.5 km.
50 · Useful error messages:
52 > 2 watts + 4 newton meter
54 Unification error:
56 Cannot convert unit N·m (base units: kg·m²·s⁻²)
57 to unit W (base units: kg·m²·s⁻³)
58 · Explicit unit conversions: the -> conversion operator (aliases: →, ➞,
60 to):
61 60 mph -> m/s
63 500 km/day -> km/h
64 1 mrad -> degree
65 52 weeks -> days
66 5 in + 2 ft -> cm
67 atan(30 cm / 2 m) -> degree
68 6 Mbit/s * 1.5 h -> GB
69 · Variable assignments:
71 Example: mass of the earth
73 r = 6000km
75 vol = 4/3 * pi * r^3
76 density = 5 g/cm^3
77 vol * density -> kg
78 Example: oscillation period of a pendulum
80 len = 20 cm
82 2pi*sqrt(len/g0) -> ms
83 · Predefined constants (type list to see them all): speed of light
85 (c), Planck's constant (h_bar), electron mass (electronMass), ele‐
86 mentary charge (elementaryCharge), magnetic constant (µ0), electric
87 constant (eps0), Bohr magneton (µ_B), Avogadro's constant (N_A),
88 Boltzmann constant (k_B), gravitational acceleration (g0), ...
89 · Last result: you can use ans (answer) to refer to the result of the
91 last calculation.
92 · User-defined functions:
94 Example: kinetic energy
96 kineticEnergy(mass, speed) = 0.5 * mass * speed^2 -> kJ
98 kineticEnergy(800 kg, 120 km/h)
100 Example: barometric formula
102 P0 = 1 atm
104 T0 = fromCelsius(15)
105 tempGradient = 0.65 K / 100 m
106 pressure(height) = P0 * (1 - tempGradient * height / T0)^5.255 -> hPa
108 pressure(1500 m)
110 · Sums and products:
112 Syntax:
114 sum(<expression>, <index-variable>, <from>, <to>)
116 product(<expression>, <index-variable>, <from>, <to>)
117 Examples:
119 # sum of the first ten squares
121 sum(k^2, k, 1, 10)
122 # the factorial of n as the product 1 × 2 × ... × n
124 myFactorial(n) = product(k, k, 1, n)
125 · Unicode support:
127 λ = 2 × 300 µm
129 ν = c/λ → GHz
130 · And more: tab completion, command history (arrow keys, Ctrl+R), pret‐
132 ty printing, syntax highlighting, ...
133 Reference
135 · Operators (ordered by precedence: high to low)
136 Operator Syntax
138 ──────────────────────────────────────────
139 factorial !
140 square, cube, ... ², ³, ⁻¹, ...
141 exponentiation ^, **
142 multiplication (implicit) whitespace
143 modulo %
144 division /, ÷, per
145 multiplication (explicit) *, ·, ×
146 subtraction -
147 addition +
148 unit conversion ->, →, ➞, to
149 assignment =
150 Note that implicit multiplication has a higher precedence than divi‐
152 sion, i.e. 50 cm / 2 m will be parsed as 50 cm / (2 m).
153 · Commands
155 Command Syntax
157 ─────────────────────────────────
158 help text help, ?
159 list of variables list, ls, ll
160 reset environment reset
161 clear screen clear, cls
162 quit (CLI) quit, exit
163 FAQ
165 · Why are Celsius and Fahrenheit not supported?
166 Compared to the SI unit Kelvin (https://en.wikipedia.org/wiki/Kelvin)
168 and in contrast to all other units, Celsius and Fahrenheit require an
169 additive offset when converting into and from other temperature
170 units. This additive offset leads to all kinds of ambiguities when
171 performing calculations in these units. Adding two temperatures in
172 Celsius, for example, is only meaningful if one of them is seen as an
173 offset value (rather than an absolute temperature). Insect is pri‐
174 marily a scientific calculator (as opposed to a unit conversion tool)
175 and therefore focuses on getting physical calculations right.
176 Even though °C and °F are not supported as built-in units, there are
178 helper functions to convert to and from Celsius (and Fahrenheit):
179 · fromCelsius takes a scalar value that represents a temperature in
181 Celsius and returns a corresponding temperature in Kelvin:
182 > fromCelsius(0)
184 = 273.15 K
186 > k_B * fromCelsius(23) to meV
188 = 25.5202 meV
190 · toCelsius takes a temperature in Kelvin and returns a scalar value
192 that represents the corresponding temperature in Celsius:
193 > toCelsius(70 K)
195 = -203.15
197 > toCelsius(25 meV / k_B)
199 = 16.963
201 · Why is 1/2 x parsed as 1/(2x)?
203 Implicit multiplication (without an explicit multiplication sign) has
205 a higher precedence than division (see operator precedence rules).
206 This is by design, in order to parse inputs like 50 cm / 2 m as
207 (50 cm) / (2 m). If you meant ½ · x, write 1/2 * x.
208 · What is the internal numerical precision?
210 By default, Insect shows 6 significant digits in the result of the
212 calculation. However, the internal numerical precision is much high‐
213 er (30 digits).
214 · How does the conversion operator work?
216 The conversion operator -> attempts to convert the physical quantity
218 on its left hand side to the unit of the expression on its right hand
219 side. This means that you can write an arbitrary expression on the
220 right hand side (but only the unit part will be extracted). For ex‐
221 ample:
222 > x1 = 50 km / h
224 > x2 = 3 m/s -> x1
226 x2 = 10.8 km/h
228
230 Written by David Peter <mail@david-peter.de>.
231
233 Please report bugs on GitHub: <https://github.com/sharkdp/insect>.
234
236 insect is MIT-licensed. For details, see
237 <https://github.com/sharkdp/insect>.
238
240 · Full documentation at <https://github.com/sharkdp/insect>.
241 · Web-version at <https://insect.sh>.
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