Entering Units on LON-CAPA

One of the features of LON-CAPA is its ability to handle units intelligently.

Many LON-CAPA problems give the student some physical quantities and ask for a physical quantity as an answer. Basically, if you are given units in a problem, usually you should respond with units.

The units are symbols consisting of one or more letters, listed in the tables below. A space is not required between the number and the units (but you can enter a space if you like).

The student has some freedom about what units to use in the response, but the units must be appropriate for the physical quantity being calculated. For example, if you are asked for a length, you may enter a number with any of the length units (ft, yd, m, cm, mi, km, and so on).

LON-CAPA will read the response with units and automatically convert the units when necessary to check if the response was equivalent to the correct answer. Thus, all of the following responses are equivalent:

24 min
.4 hr
1440 s

Similarly, these are also equivalent responses (at least to 5 significant figures):

11.111m
36.454 ft
.011111 km
437.45in
1111.1 cm
12.151 yd

You may combine any of the defined unit symbols in any way which is appropriate for physical quantity, using the * and / symbols for multiplication and division, and ^ for exponentiation.

For example, if you are asked to find a speed, you can give an answer with any units which represent length divided by time, such as the following examples:

m/s
ft/s
km/hr
mi/hr
yd/min

The asterisk * symbol used to represent multiplication is optional. If you enter two units with a space between them, multiplication is assumed. For example, "N m" is understood to be Newtons * meters, a derived unit of work (also called a Joule).

The carat ^ symbol is used to represent exponentiation. For example, an area unit like square meters could be entered "m^2", although "m*m" and "m m" also work (as described above).

While you can enter as many or few spaces as you like before or after a unit symbol, never separate the unit "word" itself by spaces. Clearly, LON-CAPA would misunderstand if you entered "m in" (which looks like meters times inches, an area) for "min" (which is a time duration).

If you enter the wrong units, you will be given a response indicating that fact, and you are NOT charged a try for that response. LON-CAPA will not "grade" a response until the units are correct.

Base Units

name	symbol	comment
meter	m	length
kilogram	kg	mass
second	s	time
ampere	A	electric current
kelvin	K	thermodynamic temperature
mole	mol	amount of substance
candela	cd	luminous intensity
decibel	dB	log of pressure amplitude

Prefixes

Prefix	symbol	factor
yotta	Y	10^{24}
zetta	Z	10^{21}
exa	E	10^{18}
peta	P	10^{15}
tera	T	10^{12}
giga	G	10^9
mega	M	10^6
kilo	k	10^3
hecto	h	10^2
deci	d	10^-1
centi	c	10^-2
milli	m	10^-3
micro	u	10^-6
nano	n	10^-9
pico	p	10^{-12}
femto	f	10^{-15}
atto	a	10^{-18}
zepto	z	10^{-21}
yocto	y	10^{-24}

Derived Units

name	symbol	equivalence	comment
gram	g	0.001 kg	mass
day	day	24.0 hr	time
year	yr	365.24 day	time
hour	hr	3600. s	time
hour	h	3600. s	time
minute	min	60 s	time
pound	lb	0.45359237 kg	mass
ounce	oz	1.77185E-3 kg	mass
inch	in	2.54 cm	length
foot	ft	12 in	length
mile	mi	5280 ft	length
yard	yd	0.9144 m	length
nautical_mile	n_mi	6080 ft	length, nautical mile (UK)
rood	rood	1210 yd^2	area, rood
acre	acre	4840 yd^2	area, acre
hertz	Hz	1/s	frequency
litre	L	10^3* cm^3	volume
newton	N	m*kg/s^2	force
pound_force	lbf	4.44822 N	force
dyne	dyn	1E-5 N	force
pascal	Pa	N/m^2	pressure, stress
bar	bar	1E5 Pa	pressure
mmHg	mmHg	1.33322E2 Pa	pressure, millimeter of mercury
torr	torr	1 mmHg	pressure
atm	atm	760 torr	standard atmosphere
joule	J	N*m	energy, work, heat
electronvolt	eV	1.6021892E-19 J	energy
calorie	cal	4.1868 J	energy
Btu	Btu	1.05506E3 J	energy
watt	W	J/s	power, radiant flux
coulomb	C	A*s	electric charge
volt	V	J/C	electric potential, electromotive force
ohm	ohm	V/A	electric resistance, use this in /ANS
ohm	ohms	V/A	electric resistance
ohm	Ohm	V/A	electric resistance
ohm	Ohms	V/A	electric resistance
siemens	S	1/Ohm	electric conductance
farad	F	C/V	electric capacitance
tesla	T	V*s/m^2	magnetic flux density
weber	Wb	V*s	magnetic flux
henry	H	V*s/A	inductance
radian	rad	m/m	plane angle
degree	deg	1.745329E-2 rad	plane angle (Pi rad=180 deg)
steradian	sr	m^2/m^2	solid angle
lumen	lm	cd*sr	luminous flux
lux	lx	cd*sr/m^2	illuminance
becquerel	Bq	1/s	activity (radioactive)
gray	Gy	J/kg	absorbed dose (of radiation)
sievert	Sv	J/kg	dose equivalent (dose equivalent index)
astroUnit	AU	1.49598E11 m	mean distance earth to sun
celcius	degC	1 K	multiplicatively OK
farenheight	degF	.5555555555 K	multiplicatively OK