Useful (Approximate) Data for Physical Calculations
Approximate values of some constants, & approximately constants, that
are useful for order-of-magnitude calculations.
Sections: Motion, Geological & Astrophysical,
Electric & Magnetic,
Radiation Dosage, Thermodynamics, Materials,
Optics, Periodic Table
Mnemonics, SI Prefixes, Conversions, Imperial
Units, Quantum Mechanics,
Numerical Shortcuts,
Small Value Approximations.
Motion Data
| Speed of sound in |
air |
1/3 km/s |
| water |
1.5 km/s |
| iron |
5 km/s |
| Acoustic 0 dB |
10-12 W/m2 |
| Coefficient of Friction |
steel on steel |
static 4/5, sliding 2/5 |
| glass on glass |
static 19/20, sliding 2/5 |
| PTFE on PTFE |
1/20 |
| steel on oiled steel |
<= 1/4 |
Geological & Astrophysical Data
| Gravitational constant = G |
6.66x10-11 N m2/kg2 |
| Gravitational acceleration at earth's
surface = g |
9.81 m/s2
(~10 m/s2 |
| Radius of the earth's orbit
(= 1 AU) |
150 million km |
| Radius of the earth |
6350 km |
| Year (tropical) |
365.24 days |
| 1 parsec |
3 1/4 ly |
| Sun & moon angular diameter from earth |
1/2 ° |
| Moon / earth |
diameter |
a bit over 1/4 |
| mass |
1/80 |
| Distance to Andromeda galaxy |
2 million ly |
| Equatorial solar power on earth |
incident |
1.5 kW/m2 |
| max. at ground |
1 kW/m2 |
| Axial tilt of earth |
23.5 ° |
| Earth surface land fraction |
2/5 |
| Ocean depth |
2 to 4 km |
Electrical & Magnetic Data
| Fundamental constants |
ε0 |
8.9x10-12 F/m |
| μ0 |
4πx10-7 H/m |
| e (electron charge) |
1.6x10-19 C |
| c |
3.00x108 m/s |
| Relative electrical permittivity |
gasses & vacuum |
1 |
| water |
80 |
| oily stuff |
2 to 5 |
| ethanol |
25 |
| normal solid stuff (stones, glass, etc.) |
2 to 10 |
| Relative magnetic permeability for magnetically
soft materials |
~103 to ~106 |
| Air breakdown electric field strength |
3 MV/m |
| Resistivity |
iron |
10x10-8 Ωm |
| mild steel |
50x10-8 Ωm |
| stainless steel |
6x10-8 Ωm |
| copper |
1.7x10-8 Ωm |
Radiation Dosage
| 5 Sv |
50 % immediate death |
| 1 Sv |
5 % lethal tumours |
| 1/5 Sv |
0.5 % gross genetic birth defect |
| 20 mSv |
Max. occupational average yearly dose |
| 1 mSv |
Max. public average yearly dose |
| 2 mSv |
Natural background yearly dose |
Thermodynamic Data
| Fundamental(ish) constants |
k |
1.38x10-23 J/K |
| NA |
6.0x1023 mol-1 |
| σ |
6x10-8 W m-2K-4 |
| b |
3 mm K |
| Boiling point |
Helium |
4 K |
| Hydrogen |
20 K |
| Nitrogen |
77 K |
| Oxygen |
90 K |
| Sulphur |
444 °C |
| Subliming point |
CO2 |
-78.5 °C |
| Melting point |
lead |
600 K |
| aluminium |
900 K |
| iron |
1800 K |
| tungsten |
3600 K |
| Volume 1 mol gas |
STP |
22.5 dm3 |
| room temp. |
24 dm3 |
| Thermal conductivity |
copper |
400 W m/K |
| glass |
1 W m/K |
| cork |
1/20 W m/K |
| Specific heat capacity |
metals |
0.1 to 1 kJ/K/kg |
| typical solids |
1/2 to 3 kJ/K/kg |
| water |
4.2 kJ/kg/K |
| Latent heat of fusion |
typical |
1/10 to 2 MJ/kg |
| water |
3.8 MJ/kg |
| Latent heat of vap' |
typical |
0.2 to 0.4 MJ/kg |
| alcohol |
0.9 MJ/kg |
| water |
2.3 MJ/kg |
Material Data
| Density |
the earth |
5 Mg/m-3 |
| the sun |
1.5 Mg/m-3 |
| air |
1 kg/m-3 |
| water |
1 Mg/m-3 |
| building stuff (stone, brick, concrete etc.) |
2 to 3 Mg/m-3 |
| normal metals (iron, copper etc.) |
7 to 9 Mg/m-3 |
| lead |
11 Mg/m-3 |
| gold |
20 Mg/m-3 |
| uranium |
27 Mg/m-3 |
| Viscosity (20 °C) |
water (halves by 50 °C) |
1/1000 Nsm-2 |
| cooking oil |
1/10 Nsm-2 |
| glycerol |
1 Nsm-2 |
| atmosphere |
15 μNsm-2 |
| Young's modulus |
iron (wrought) |
20 x1010 Pa |
| wood |
1010 Pa |
| rubber |
1/20 x1010 Pa |
| Surface tension |
mercury |
1/2 N/m |
| water |
0.07 N/m |
| Expansion coefficients |
typical solids |
1 to 100 MK-1 |
Optics Data
Wavelength boundaries:
| γ |
|
X |
|
UV |
|
violet to red |
|
IR |
|
μ |
|
radio |
|
10-11 m |
|
10-8 m |
|
400 μm |
|
700 μm |
|
1/10 mm |
|
1 m |
|
Periodic Table Mnemonics
| At the top |
H He |
|
| Period I |
Li Na K Rb Cs Fr |
Light infantry never attacked King Kong - Rupert
Bear can surely fire rockets. |
| Period II |
Be Mg Ca Sr Ba Ra |
Bad eggs make gungey cakes and smell really
bleedin' awful repeated again. |
| Period III |
B Al Ga In Tl |
Brass bears and lilac gorillas are incredibly
nauseating to look-at. |
| Period IV |
C Si Ge Sn Pb |
Canoes can sink in gelatinous effluent; several
now plummet bottomwards. |
| Period V |
N P As Sb Bi |
No new pork pies are slightly slimy because
butter's included. |
| Period VI |
O S Se Te Po |
Odd old Simon saw several elephant's trunks
expertly picking oranges. |
| Period VII |
F Cl Br I At |
(This period is easy to remember from their
distinctive & progressive chemistry.) |
| Transition Row I |
Sc Ti V Mn Fe Co Ni Cu Zn |
Some chemists try igniting very volatile
chemicals rapidly making noxious fumes. Extremely careful operators never
ignite chemicals up zebras' nostrils. |
SI Prefixes
| 10? |
+24 |
+21 |
+18 |
+15 |
+12 |
+9 |
+6 |
+3 |
+2 |
+1 |
0 |
-1 |
-2 |
-3 |
-6 |
-9 |
-12 |
-15 |
-18 |
-21 |
-24 |
|
Y |
Z |
E |
P |
T |
G |
M |
k |
h |
da |
|
d |
c |
m |
μ |
n |
p |
f |
a |
z |
y |
Mnemonics: "μ,n,p,f,a"="my nan picked from 'at",
"G,T,P,E"="gigantic terrapin eggs".
Conversions
| Angle |
1 rad |
57.2958° |
| Quasi-SI |
l |
dm3 |
| μ |
μm |
| fermi |
fm |
| Å |
10-10 m |
| Barn=b |
10-28 m2 |
| tonne=t |
Mg |
| Imperial |
inch=in |
25.4 mm |
| lb |
1/2.2 kg |
| mile |
~8/5 km |
| CGS |
dyne (force) |
g/cm/s2 |
| erg (energy) |
g/cm2/s2 |
| poise (viscosity) |
g/cm/s |
| Other CGI units like SI but uses cm & g
instead of m & kg. |
| Pressure |
1 atm |
~105Pa |
| 1 bar |
| 15 lb/sq.in |
| 750 mmHg at 0 °C |
| Temperature |
°C to K |
+ 273.15 |
| °C to °F |
x 9/5 then + 32 |
| Energy |
eV |
1.6x10-19 J |
| Cal |
1 kcal |
| cal |
4.2 J |
| Radiation |
rad |
1/100 Gy |
| rem |
1/100 Sv |
| Ci |
37 GBq |
| radiation from 1 g radium |
Imperial Units
| Length |
1000 thou = inch =in,
12 in = foot = ft,
3 ft = yard = yd,
2 yd = fathom,
11 fathoms = chain,
10 chains = furlong,
8 furlong = 1 mile
|
| Volume (UK) |
fluid = fl.oz,
5 fl.oz = gill,
4 gill = pint = pt,
2 pt = quart = qt,
4 qt = gallon = gal (= 10 lb mass if water)
|
| Volume (USA) |
fluid = fl.oz,
4 fl.oz = US gill,
2 US gill = US cup,
2 US cup = US pint (= 1 lb mass if water)
|
| Mass |
16 oz = pound = lb,
14 lb =stone = st,
2 st = quarter,
4 quarters = hundredweight = cwt,
20 cwt = ton
|
| Area |
chain x furlong = acre = 1/640 sq. mile
|
| Force (weight) |
weight of 1 lb = pound-force = lbf
|
| Force (consistent) |
1 lb ft s-2 = poundal = pdl
|
Quantum Mechanics
| Planck constant=h |
6.6x10-34 J s |
| proton mass / electron mass |
2000 |
| proton mass |
~1 GeV |
| typical atom diameter |
~1 Å |
| typical nucleus diameter |
~1 fermi |
Numerical Shortcuts
| year |
~3x107 s |
| light-year |
~1016 m |
| g |
~10 m/s2 |
| 4 in |
~10 cm |
| π2 |
~10 |
| e3 |
~20 |
| 72 |
~50 |
| rad |
~60° |
| 1/sqrt(2), ln(2) |
~0.7 |
| sin(0°) |
0 |
| sin(30°) |
1/2 |
| sin(45°) |
1/sqrt(2) |
| sin(60°) |
sqrt(3)/2 |
| sin(90°) |
1 |
| for other trig' |
cos(x)=sin(90-x) & tan(x)=sin(x)/cos(x) |
| n! |
~sqrt(2 n)nne-n |
| (x+1)(x-1) |
x2-1 |
Small Value Approximations
For x<<1:
| (1+x)a |
-> 1+ax |
| sin(x), sinh(x), tan(x), tanh(x) |
-> x |
| cos(x) |
-> 1-x2/2 -> 1 |
| cosh(x) |
-> 1+x2/2 -> 1 |
| ln(1+x) |
-> x |
| exp(x) |
-> 1+x |
Origin
I originally assembled this list (on paper) to memorise for doing quick
calculations for S.T.E.P. Physics exams (optional extra UK exams at A' Level
time using mainly A' Level syllabus but with less predictable questions) but
found them useful for general rough-estimate calculations afterwards. Many more
approximate constants can be derived from these with a little elementary maths
& physics.
There are probably typos in the this document so verify the data before
using for vital work (and tell me of any mistakes you find so that I can
correct them).