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:

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) 20 fl.oz = pint = pt, 2 pt = quart = qt, 4 qt = gallon = gal (= 10 lb mass if water)
Volume (USA) 16 fl.oz = US pint
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°
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).