this page seriously undersells the versatility and utility of the units program
how long will my laptop take to charge at its current rate of charging?
You have: (22.8 Wh - 16.8 Wh)/7.4W
You want: time
48 min + 38.918919 sec
how long will a 2000mAh 18650 cell take to discharge at 2.5 watts, using a nominal voltage of 3.7 volts?
You have: 3.7 V 2 amp hour / 2.5 watt
You want: time
2 hr + 57 min + 36 sec
what energy density is that, so i can compare it to the volume needed for other forms of energy storage?
You have: 3.7 V 2 amp hour / circlearea(half 18 mm) 65 mm
You want: MJ/ℓ
* 1.6105936
/ 0.62088909
what's the specific energy of stoichiometrically mixed oxyhydrogen fuel?
You have: 44000 J/mol / ((2 hydrogen + oxygen)g/mol)
You want: MJ/kg
* 2.4423711
/ 0.40943818
okay but how much volume? say at atmospheric pressure?
You have: 3 mol gasconstant tempC(20) / 1 atm
You want: l
* 72.165351
/ 0.013857066
so that's how much energy density?
You have: 44kJ/_
You want: J/l
* 609.71089
/ 0.0016401216
(i may be off by a factor of 2 here)
how much energy can this capacitor hold?
You have: half (10V)**2 47 uF
You want: mJ
* 2.35
/ 0.42553191
how much energy density is that?
You have: half (10V)**2 47 μF / 15mm circlearea(3mm)
You want: J/ℓ
* 5.5409499
/ 0.18047447
how thick of a cable do i need to support me in a lightweight fabric-sling chair (or, from a different point of view, to pose a risk of accidental strangulation)? suppose its tensile strength is 2.7 gigapascals
You have: 120kg gravity / 2.7 GPa
You want: mm2
* 0.43585111
/ 2.2943615
You have: _
You want: circlearea
0.00037247244 m
You have: _
You want: mm
* 0.37247244
/ 2.6847624
note that this is the radius of the cable, not its diameter!
the datasheet says this 400×240 display uses 175 μW if all the pixels flip once per second and 60 μW for a static display. how much energy is that per pixel flip?
You have: (175 uW - 50 uW) / 400 240 1 Hz
You want: nJ
* 1.3020833
/ 0.768
if i overclock it to 60 fps how much power will it use?
You have: 60 Hz 400 240 1.3nJ
You want: μW
* 7488
/ 0.00013354701
and how many pixels is its diagonal?
You have: 400**2+240**2
You want:
Definition: 217600
You have: _**.5
You want:
Definition: 466.47615
what is the visual angle subtended by the sun as seen from earth?
You have: 2 sunradius/sundist
You want: milliradians
* 9.3049358
/ 0.10746984
You have: _
You want: dms
31 arcmin + 59.280781 arcsec
okay, how does that compare to the moon?
You have: moonradius 2 / moondist
You want:
Definition: 0.0090426639
on average the moon looks a little smaller, which is why annular eclipses are so common, but we can also calculate that total eclipses are possible because sometimes the moon looks bigger
You have: moonradius 2 / moondist_min
You want:
Definition: 0.0097530864
what percentage of this copper sulfate is actual copper?
You have: copper / (copper + (sulfur + 4 oxygen))
You want: %
* 39.813395
/ 0.025117175
how fast can i write to this slc flash chip without wearing it out in 53 years, assuming perfect wear leveling and no write amplification?
You have: 100 thousand 128 MiB/53 years
You want: bytes/second
* 8024.8943
/ 0.00012461223
how much fuel will this truck need to get across the country?
You have: 4000 km / (6.5 miles/gallon)
You want: l
* 1447.4744
/ 0.00069085852
how much is that per kilogram of lettuce or sodium lauryl sulfate or whatever?
You have: _/28 tonnes
You want: ml/kg
* 51.695513
/ 0.019344039
okay, but how much energy is 52 mℓ of diesel per kg of lettuce?
You have: _ 38.6 kJ/l
You want: kJ/kg
* 1.9954468
/ 0.5011409
how much data can i transfer overnight during unmetered hours on a 2400-baud modem?
You have: 8 hours 2400 bps
You want: MB
* 8.64
/ 0.11574074
how much power does the earth receive from the sun, assuming a solar constant of 1400 W/m²?
You have: 1400 W/m**2 * circlearea(earthradius)
You want: petawatts
* 178.52313
/ 0.0056015152
what would the equilibrium temperature of an object be if it were illuminated at that brightness and had a flat emission spectrum?
You have: (1400 W/m**2 / stefanboltzmann)**(1/4)
You want: tempC
123.24583
how about here in buenos aires at the winter solstice? first, what angle is the sun at anyway? we're at 34°36’ south, and the sun's latitude at the solstice is 23°26’
You have: 34° + 36' + 23° + 26'
You want: dms
58 deg + 2 arcmin
so that reduces the peak insolation to how much? here underneath the atmosphere we only get 1kW/m²
You have: cos(_) 1000 W/m^2
You want: W/m^2
* 529.4258
/ 0.0018888388
and that would be what temperature in equilibrium?
You have: (_/stefanboltzmann)**(1/4)
You want: tempC
37.698189
(integrating the sun's angle over the course of the day as the earth rotates is sadly beyond its capacities)
how much money could a sensible heat storage reservoir of 15 kg of water save me over 16 years? say power rates go down to only 2.5¢/kWh because of solar
You have: 1500 kcal/day * 16 years * 2.5 cents/kWh
You want:
Definition: 254.69556 US$
what's the surface area of a 300mm × 400mm × 150mm backpack? like how much cloth?
You have: 2 (300mm 400mm + 400mm 150mm + 150mm 300mm)
You want:
Definition: 0.45 m^2
okay but in cm²
You have: _
You want: cm2
* 4500
/ 0.00022222222
what's the electrical impedance of a 1000 μF cap at an audio highpass frequency of 20Hz?
You have: 1/(2 pi 20 Hz 1000 uF)
You want: ohms
* 7.9577472
/ 0.12566371
what's the time constant of 100 pF (roughly the smallest capacitance you can get in a macroscopic circuit with any degree of precision) and 1 MΩ?
You have: 100 pF 1 megohm
You want: ms
* 0.1
/ 10
okay. so how long will an 0.1μF cap take to discharge through a 100kΩ resistor from 5 volts down to a 1.3 volt threshold?
You have: ln(5V/1.3V) .1 uF 100kilohm
You want: ms
* 13.470736
/ 0.074234991
how many bits of precision does a linear adc need to be able to measure a difference of 1.8 millivolts if 1.5 volts is full-scale?
You have: log(1.8mV/1.5V)/log(2)
You want:
Definition: -9.7027499
if this oxygen absorber contains 7 grams of iron which oxidizes to Fe₂O₃, how much air can it remove all the oxygen from? air is 21% oxygen by volume (and roughly by mass) and weighs 1.2 grams per liter
You have: 3 oxygen / 2 iron * 7 g
You want: g
* 3.0082138
/ 0.33242318
You have: _/21%/(1.2g/ℓ)
You want: ℓ
* 11.937356
/ 0.083770641
i've lost 7 kg over the last two months; how much of a caloric deficit does that represent in my diet?
You have: 7 kg 3500kcal/pound / 2 months
You want: kcal/day
* 887.30034
/ 0.0011270141
if you were to spread the moon evenly over russia, how deep would it be?
You have: spherevol(moonradius) / area_russia
You want:
Definition: 1286134.4 m
how big is nigeria compared to massachusetts?
You have: area_nigeria/area_massachusetts
You want:
Definition: 33.793093
how many ounces of platinum is a ton of oil worth at 40 dollars per megawatt hour?
You have: tonoil 40 dollars/MWh
You want: platinumounce
* 0.58368883
/ 1.7132416
or in grams?
You have: tonoil 40 dollars/MWh / platinumprice
You want: g
* 18.154752
/ 0.055081997
Trying your examples, especially considering that the elliptical orbit of the earth likewise causes the Sun's angular diameter change depending on where our orbit is, I found that Units current has a buggy definition of moondist_min and moondist_max. It's defined in the definitions file as 356.371 km and 406.720 km respectively. These should be Mm! (Or remove the period, either will work)
Just to work around the bug, you can use a local definitions file to correct it:
cat > ~/.units <<EOF
moondist_min 356.371 Mm
moondist_max 406.720 Mm
EOF
interesting, looks like an effort to improve the precision resulted in a factor of 1000 error! `help moondist_max` shows me considerably less precise values:
sundist 1.0000010178 au # mean earth-sun distance
moondist 3.844e8 m # mean earth-moon distance
sundist_near 1.471e11 m # earth-sun distance at perihelion
sundist_far 1.521e11 m # earth-sun distance at aphelion
moondist_min 3.564e8 m # approximate least distance at
# perigee 1901-2300
moondist_max 4.067e8 m # approximate greatest distance at
# apogee 1901-2300
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waive all rights associated with it to the maximum extent possible
under applicable law. where applicable, i abandon its copyright to
the public domain. i wrote and published this comment in argentina in 02023
how long will my laptop take to charge at its current rate of charging?
how long will a 2000mAh 18650 cell take to discharge at 2.5 watts, using a nominal voltage of 3.7 volts? what energy density is that, so i can compare it to the volume needed for other forms of energy storage? what's the specific energy of stoichiometrically mixed oxyhydrogen fuel? okay but how much volume? say at atmospheric pressure? so that's how much energy density? (i may be off by a factor of 2 here)how much energy can this capacitor hold?
how much energy density is that? how thick of a cable do i need to support me in a lightweight fabric-sling chair (or, from a different point of view, to pose a risk of accidental strangulation)? suppose its tensile strength is 2.7 gigapascals note that this is the radius of the cable, not its diameter!the datasheet says this 400×240 display uses 175 μW if all the pixels flip once per second and 60 μW for a static display. how much energy is that per pixel flip?
if i overclock it to 60 fps how much power will it use? and how many pixels is its diagonal? what is the visual angle subtended by the sun as seen from earth? okay, how does that compare to the moon? on average the moon looks a little smaller, which is why annular eclipses are so common, but we can also calculate that total eclipses are possible because sometimes the moon looks bigger what percentage of this copper sulfate is actual copper? how fast can i write to this slc flash chip without wearing it out in 53 years, assuming perfect wear leveling and no write amplification? how much fuel will this truck need to get across the country? how much is that per kilogram of lettuce or sodium lauryl sulfate or whatever? okay, but how much energy is 52 mℓ of diesel per kg of lettuce? how much data can i transfer overnight during unmetered hours on a 2400-baud modem? how much power does the earth receive from the sun, assuming a solar constant of 1400 W/m²? what would the equilibrium temperature of an object be if it were illuminated at that brightness and had a flat emission spectrum? how about here in buenos aires at the winter solstice? first, what angle is the sun at anyway? we're at 34°36’ south, and the sun's latitude at the solstice is 23°26’ so that reduces the peak insolation to how much? here underneath the atmosphere we only get 1kW/m² and that would be what temperature in equilibrium? (integrating the sun's angle over the course of the day as the earth rotates is sadly beyond its capacities)how much money could a sensible heat storage reservoir of 15 kg of water save me over 16 years? say power rates go down to only 2.5¢/kWh because of solar
what's the surface area of a 300mm × 400mm × 150mm backpack? like how much cloth? okay but in cm² what's the electrical impedance of a 1000 μF cap at an audio highpass frequency of 20Hz? what's the time constant of 100 pF (roughly the smallest capacitance you can get in a macroscopic circuit with any degree of precision) and 1 MΩ? okay. so how long will an 0.1μF cap take to discharge through a 100kΩ resistor from 5 volts down to a 1.3 volt threshold? how many bits of precision does a linear adc need to be able to measure a difference of 1.8 millivolts if 1.5 volts is full-scale? if this oxygen absorber contains 7 grams of iron which oxidizes to Fe₂O₃, how much air can it remove all the oxygen from? air is 21% oxygen by volume (and roughly by mass) and weighs 1.2 grams per liter i've lost 7 kg over the last two months; how much of a caloric deficit does that represent in my diet? if you were to spread the moon evenly over russia, how deep would it be? how big is nigeria compared to massachusetts? how many ounces of platinum is a ton of oil worth at 40 dollars per megawatt hour? or in grams?