Quick unit-aware calculator

Question

I want to be able to press a keyboard combination, start typing a mathematical expression that includes units and slightly advanced math (not just a four-function calculator), and get a result immediately, in units that I specify, that I can copy and paste.

• Currently I open Firefox and press Ctrl+K, type in the search box, and it usually gives me a result in the drop-down from Google Calculator. It doesn't always, though, so I press "=" at the end, wait for a result, remove the equals, wait for a result, realize it doesn't understand the way I typed a unit, open the result in a new tab, etc. it sucks.
• Wolfram Alpha is smarter, but very much slower, and the output is all images, not text, and I don't have a quick widget for it, if such a thing could even exist.
• GNU units has a ton of units, which is great, and I can define my own units, which is great, but they have to be written in specific, unintuitive ways, it doesn't handle much advanced math, and I'd need to open a terminal, start units, etc. I hate the command line.
• I wasted a lot of time trying to make front-ends for units in Deskbar and Launchy, but I'm not a real coder and I don't use either of those anymore.

Any other solutions or enhancements of these?

(Cross-platform is best)

The ideal unit-aware calculator would be able to handle all of these:

• 7 nV/sqrt(Hz) ⋅ sqrt(20000 Hz - 20 Hz) → μV = 0.99 μV
• sqrt(4*k*25 °C * 1 kΩ * (20 kHz - 20 Hz)) = 0.57357 μV
• 3.5 billion kilowatt-hours per year = 399.5 MW
• 60 billion kWh per year = 6.849 GW
• 1/sqrt(2 mH * 2 nF) = 500 kHz
• 1/(2*pi*10 kΩ * 22 µF) = 0.7234 Hz
• 1/(2·π·100 Hz·30pF) → ohm = 53.05 MΩ
• −10 dBV + 4 dB + 10 dB − 12 dB → dBu = -5.782 dBu
• 94 dBSPL → Pa = 1.00237 Pa
• 54 inches + 2 feet → cm = 198.1 cm
• 12 V ÷ 141.5 µA = 84.8 kΩ
• 16 bit * 44.1 kHz * 2 → kbit/s = 1411 kbit/s
• 1 hundred V / 5 ohms = 20 A
• furlong per fortnight → cm/minute = 0.9979
• attoparsec/microfortnight → in/second = 1.004
• 1 ft / speed of sound = 0.89576 ms

Answer 1

I'm very impressed with Qalculate!.

Answer 2

insect has both web- and terminal-based versions. It does support parsing, handling and conversion of physical units, for example:

>>> 2min + 30s

   = 2.5min

>>> 40000km / speedOfLight -> ms

   = 133.426ms

>>> 6Mbit/s * 1.5h -> GB

   = 4.05GB

>>> 2J·s + 3W

  Unification error:

    Cannot unify unit W (base units: kg·m²·s⁻³)
            with unit J·s (base units: kg·m²·s⁻¹)

Answer 3

For a easily scriptable solution you might want to have a look a the sympy python module.

$ cat conv.py

#!/usr/bin/env python
import sys
from sympy.physics.units import *
from sympy.printing.pretty.pretty import pprint
from sympy.abc import x, y, z
from sympy import *

# adding extra units is easy
parsec = 3.26163626*ly

if __name__ == '__main__':
  s_input = sys.argv[1]
  s_unit  = sys.argv[2]
  input = eval(s_input)  # input string
  unit  = eval(s_unit)   # output unit

  print 'Converting:'
  pprint(input)
  print
  print str((input/unit).evalf()) +' '+ s_unit

which gives e.g. for some moderately ugly expression converted to mm:

$./conv.py 'tanh(3*m/(2*m))*sinh(60*deg)*1*parsec' 'mm'


Converting:
                           /π\
3.08574615554565e+16*m*sinh|--|*tanh(3/2)
                           \3 /

3.48955431541888e+19 mm

Of course this is really studpid code that does no checking thet unit compatibility of the input and output, so you might end up extra units in the result.

$./conv.py 'c' 'parsec'

Converting:
299792458*m
-----------
     s

9.71539598165644e-9/s parsec

Answer 4

I mostly share your ideas about an ideal calculator and the disadvantages of using GNU Units and Wolfram and rolled my own online calculator which I put online at PhyCalc.com. It does its own unit algebra for SI units and uses GNU Units for conversion to other units, or as a fallback when the expression itself contains non-SI units.

Its aims to interpret Unicode input where it makes sense. And tries to be smart about guessing the exact quantity and corresponding unit. It automatically inserts SI-prefixes. (much like my trusty old Casio pocket calculator does in "ENG" mode)

Some comments about your "ideal calculator" inputs and responses:

sqrt(4*k*25 °C * 1 kΩ * (20 kHz - 20 Hz)) = 0.57357 μV

Its not exactly accurate to automatically assume °C to be an absolute temperature. Also k is not exactly an unambiguous symbol for the Boltzmann constant. However this should give you the required answer:

sqrt(4*1.38064852e-23J/K*(273.15K+25 °C) * 1 kΩ * (20 kHz - 20 Hz)) in μV

These fail in GNU Units:

3.5 billion kilowatt-hours per year

1 ft / speed of sound

GNU Units alternatives could be:

3.5 billion kWh per year
1 ft / mach in ms

1/(2·π·100 Hz·30pF) → ohm

You can leave out the "→ ohm" part. That is what I meant with "being smart about guessing the quantity" :-).

−10 dBV + 4 dB + 10 dB − 12 dB → dBu

GNU Units has some dB conversion, but it is defined as 10^(x/10) which is a scalar that it will not add to a voltage, where you assume that the calculator should recognize that it should be scaling Voltage instead of Power and should apply scaling of 10^(x/20) instead. That would be very cool, but is a bridge too far for gnu units I'm afraid. This will at least give you the correct answer using GNU Units:

 1V*dB(-10)^0.5*dB(4)^0.5*dB(10)^0.5*dB(-12)^0.5 → dBu

But I can see why you may find that un-intuitive.

Otherwise I think PhyCalc.com may come pretty close to your ideal calculator.

To have fast access to it, I map my dedicated calculator keyboard key to it by adding to the following string (REG_SZ) name/value pair in the Windows registry:

[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\AppKey\18]
"ShellExecute"="http://phycalc.com"

Answer 5

Wolfram Alpha is capable of crunching math and doesn't require you to download or install anything.

Check here for how to use its math functions.