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Fundamental Physical and Technical Terms
1.1 Units of physical quantities
1.1.1 The International System of Units (Sl)
The statutory units of measurement are
1)
1. the basic units of the International System of Units (Sl units) for the basic quantities
length, mass, time, electric current, thermodynamic temperature and luminous intensity,
2. the units defined for the atomic quantities of quantity of substance, atomic mass and
energy,
3. the derived units obtained as products of powers of the basic units and atomic units
through multiplication with a defined numerical factor,
4. the decimal multiples and sub-multiples of the units stated under 1-3.
Table 1-2
Decimals
Multiples and sub-multiples of units
Decimal power Prefix Symbol
10
12 Tera T 10–2 Zenti c
10
9 Giga G 10–3 Milli m
10
6 Mega M 10–6 Mikro μ
10
3 Kilo k 10–9 Nano n
10
2 Hekto h 10–12 Piko p
10
1 Deka da 10–15 Femto f
10
–1 Dezi d 10–18 Atto a
Table 1-1
Basic SI units
Quantity Units Units
Symbol Name
Length m metre
Mass kg kilogramme
Time s second
Electric current A ampere
Thermodynamic temperature K kelvin
Luminous intensity cd candela
Atomic units
Quantity of substance mol mole
1)
DIN 1301
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Table 1-3
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
1 Length, area, volume
1.1 Length metre m see Note to No. 1.1
1.2 Area square metre m
2
are a 1 a = 10
2 m2 for land measurement
hectare ha 1 ha = 10
4 m2 only
1.3 Volume cubic metre m
3
litre l 1 l = 1 dm
3 = 10–3 m3
1.4 Reciprocal reciprocal metre 1/m
length
dioptre dpt 1 dpt = 1/m
1.5 Elongation metre per m/m
metre
1)
See also notes to columns 3 and 4 and to column 7 on page 15.
(
continued)
Numerical value of
elongation often expressed in
per cent
only for refractive index of
optical systems
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1
Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
2 Angle
2.1 Plane angle radian rad
(angle) 1 rad = 1 m/m
full angle 1 full angle = 2
π rad
π
right angle v 1 v = — rad
2
π
degree ° 1 ° = —— rad
180
minute ' 1' = 1°/60
second " 1" = 1’/60
π
gon gon 1 gon = —— rad
200
2.2 Solid angle steradian sr 1 sr = 1m
2/m2 see DIN 1315
1)
See also notes to columns 3 and 4 and to column 7 on page 15.
(
continued)
see DIN 1315
In calculation the unit rad as
a factor can be replaced by
numerical 1.
⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭
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Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
3 Mass
3.1 Mass kilogramme kg
gramme g 1 g = 10
–3 kg
tonne t 1 t = 10
3 kg
atomic u 1 u = 1.66053 · 10
–27 kg
mass unit
metric carat Kt 1 Kt = 0.2 · 10
–3 kg
3.2 Mass per unit kilogramme kg/m
length per metre
Tex tex 1 tex = 10
–6 kg/m
= 1 g/km
1)
See also notes to columns 3 and 4 and to column 7 on page 15.
(
continued)
Units of weight used as
terms for mass in
expressing quantities of
goods are the units of
mass, see DIN 1305
At the present state of
measuring technology the
3-fold standard deviation for
the relationship for u given
in col. 7 is ± 3 · 10
–32 kg.
only for gems
only for textile fibres and
yarns, see DIN 60905
Sheet1
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1
Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
3.3 Density kilogramme kg/m
3 see DIN 1306
per
cubic metre
3.4 Specific cubic metre m
3/kg see DIN 1306
volume per
kilogramme
3.5 Moment of kilogramme- kg m
2
inertia square metre
1)
See also notes to columns 3 and 4 and to column 7 on page 15.
(
continued)
see DIN 5497 and
Note to No. 3.5
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Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
4
Time
4.1 Time second s minute min 1 min = 60 s
hour h 1 h = 60 min
day d 1 d = 24 h
year a
4.2 Frequency hertz Hz 1 Hz = 1/s
4.3 Revolutions reciprocal 1/s
per second second reciprocal
minute 1/min 1/min = 1/(60 s)
1)
See also notes to columns 3 and 4 and to column 7 on page 15.
(
continued)
see DIN 1355
In the power industry a year
is taken as 8760 hours.
See also Note to No. 4.1.
If it is defined as the
reciprocal of the time of
revolution, see DIN 1355.
1 hertz is equal to the
frequency of a periodic event
having a duration of 1 s.
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1
Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
4.4 Cyclic reciprocal 1/s
frequency second
4.5 Velocity metre per m/s
second 1
kilometre km/h 1 km/h = —— m/s
per hour 3.6
4.6 Acceleration metre per m/s
2
second squared
4.7 Angular radian per rad/s
velocity second
4.8 Angular radian per rad/s
2
acceleration second squared
1)
See also notes to columns 3 and 4 and to column 7 on page 15.
(
continued)
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Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
5 Force, energy, power
5.1 Force newton N 1 N = 1 kg m/s
2
5.2 Momentum newton-second Ns 1 Ns = 1 kg m/s
5.3 Pressure pascal Pa 1 Pa = 1 N/m
2
bar bar 1 bar = 10
5 Pa
1)
See also notes to columns 3 and 4 and to column 7 on page 15.
(
continued)
Units of weight as a quantity
of force are the units of force,
see DIN 1305.
see Note to columns 3 and 4
see DIN 1314
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1
Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
5.4 Mechanical newton per N/m
2, Pa 1 Pa = 1 N/m2
stress square metre,
pascal
5.5 Energy, work, joule J 1 J = 1 Nm = 1 Ws
quantity of heat = 1 kg m
2/s2
kilowatt-hour kWh 1 kWh = 3.6 MJ
electron volt eV 1 eV = 1.60219 ·10
–19J
5.6 Torque newton-metre Nm 1 Nm = 1 J = 1 Ws
5.7 Angular newton-second- Nsm 1 Nsm = 1 kg m
2/s
momentum metre
1)
See also notes to columns 3 and 4 and to column 7 on page 15.
(
continued)
In many technical fields it has
been agreed to express mechanical
stress and strength
in N/mm
2.
1 N/mm
2 = 1 MPa.
see DIN 1345
At the present state of
measuring technology the
3-fold standard deviation for
the relationship given in col. 7
is ± 2 · 10
–24 J.
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Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
5.8 Power watt W 1 W = 1 J/s
energy flow, =1 N m/s
heat flow = 1 VA
6 Viscometric quantities
6.1 Dynamic pascal-second Pas 1 Pas = 1 Ns/m
2 see DIN 1342
viscosity = 1 kg/(sm)
6.2 Kinematic square metre m
2/s see DIN 1342
viscosity per second
1)
See also notes to columns 3 and 4 and to column 7 on page 15.
(
continued)
The watt is also termed voltampere
(standard symbol
VA) when expressing electrical
apparent power, and Var
(standard symbol var) when
expressing electrical reactive
power, see DIN 40110.
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1
Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
7 Temperature and heat
7.1 Temperature kelvin K
degree Celsius ° C The degree Celsius is
(centigrade) the special name for
kelvin when expressing
Celsius temperatures.
7.2 Thermal square metre m
2/s see DIN 1341
diffusivity per second
7.3 Entropy, thermal joule J/K see DIN 1345
capacity per kelvin
7.4 Thermal watt per W/(K m) see DIN 1341
conductivity kelvin-metre
1)
See also notes to columns 3 and 4 and to column 7 on page 15. (continued)
Thermodynamic temperature;
see Note to No. 7.1 and
DIN 1345.
Kelvin is also the unit for
temperature differences and
intervals.
Expression of Celsius temperatures
and Celsius temperature
differences, see
Note to No 7.1.
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Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
7.5 Heat transfer watt per W/(Km
2) see DIN 1341
coefficient kelvin-square
metre
8 Electrical and magnetic quantities
8.1 Electric current, ampere A see DIN 1324 and
magnetic
potential DIN 1325
difference
8.2 Electric voltage, volt V 1 V =1 W/A see DIN 1323
electric potential
difference
8 3 Electric siemens S 1 S = A/V see Note to columns 3 and
conductance 4 and also DIN 1324
8.4 Electric ohm
Ω 1 Ω = 1/S see DIN 1324
resistance
1)
See also notes to columns 3 and 4 and to column 7 on page 15. (continued)
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1
Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
8.5 Quantity of coulomb C 1 C = 1 As see DIN 1324
electricity, electric ampere-hour Ah 1 Ah = 3600 As
charge
8.6 Electric farad F 1 F = 1 C/V see DIN 1357
capacitance
8.7 Electric flux coulomb per C/m
2 see DIN 1324
density square metre
8.8 Electric field volt per metre V/m see DIN 1324
strength
8.9 Magnetic flux weber, Wb, Vs 1 Wb = 1 Vs see DIN 1325
volt-second
8.10 Magnetic flux tesla T 1 T = 1 Wb/m
2 see DIN 1325
density, (induction)
8.11 Inductance henry H 1 H = 1 Wb/A see DIN 1325
(permeance)
1)
See also notes to columns 3 and 4 and to column 7 on page 15. (continued)
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Table 1-3 (continued)
List of units
1 2 3 4 5 6 7 8
Sl unit
1) Other units
No. Quantity Relationship
1) Remarks
Name Symbol Name Symbol
8.12 Magnetic field ampere A/m see DIN 1325
intensity per metre
9 Photometric quantities
9.1 Luminous candela cd
intensity
9.2 Luminance candela per cd/m
2 see DIN 5031 Part 3
square metre
9.3 Luminous flux lumen Im 1 Im = 1 cd · sr see DIN 5031 Part 3
9.4 Illumination lux Ix 1 lx = 1 Im/m
2 see DIN 5031 Part 3
1)
See also notes to columns 3 and 4 and to column 7 on page 15.
see DIN 5031 Part 3. The
word candela is stressed on
the 2nd syllable.
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1
Notes to Table 1-3
To column 7:
A number having the last digit in bold type denotes that this number is defined by
agreement (see DIN 1333).
To No. 1.1:
The nautical mile is still used for marine navigation (1 nm = 1852 m). For
conversion from inches to millimetres see DIN 4890, DIN 4892, DIN 4893.
To No. 3.5:
When converting the so-called “flywheel inertia GD
2” into a mass moment of
inertia J, note that the numerical value of GD
2 in kp m2 is equal to four times the
numerical value of the mass moment of inertia J in kg m
2.
To No. 4.1:
Since the year is defined in different ways, the particular year in question should
be specified where appropriate.
3 h always denotes a time span (3 hours), but 3
h a moment in time (3 o’clock).
When moments in time are stated in mixed form, e.g. 2
h25m3s, the abbreviation
min may be shortened to m (see DIN 1355).
To No. 7.1:
The (thermodynamic) temperature
(T), also known as “absolute temperature”, is
the physical quantity on which the laws of thermodynamics are based. For this
reason, only this temperature should be used in physical equations. The unit
kelvin can also be used to express temperature differences.
Celsius (centigrade) temperature
(t) is the special difference between a given
thermodynamic temperature
T and a temperature of T0 = 273.15 K.
Thus,
t
= T – T0 = T – 273.15 K. (1)
When expressing Celsius temperatures, the standard symbol °C is to be used.
The difference
Δ t between two Celsius temperatures, e. g. the temperatures
t
1 = T1 – T0 and t 2 = T2 – T0, is
Δ
t = t 1 –t 2 = T1 – T2 = Δ T (2)
A temperature difference of this nature is no longer referred to the thermodynamic
temperature
T0, and hence is not a Celsius temperature according to the
definition of Eq. (1).
However, the difference between two Celsius temperatures may be expressed
either in kelvin or in degrees Celsius, in particular when stating a range of
temperatures, e. g. (20 ± 2) °C
Thermodynamic temperatures are often expressed as the sum of
T0 and a
Celsius temperature
t, i. e. following Eq. (1)
T = T
0 + t
(3)
and so the relevant Celsius temperatures can be put in the equation straight
away. In this case the kelvin unit should also be used for the Celsius temperature
(i. e. for the “special thermodynamic temperature difference”). For a Celsius
temperature of 20 °C, therefore, one should write the sum temperature as
T = T
0 + t
= 273.15 K + 20 K = 293.15 K (4)
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1.1.2 Other units still in common use; metric, British and US measures
Some of the units listed below may be used for a limited transition period and in certain exceptional cases. The statutory requirements vary
from country to country.
هngstrِm إ length 1 إ = 0.1 nm = 10
–10m
atmosphere physical atm pressure 1 atm = 101 325 Pa
atmosphere technical at, ata pressure 1 at = 98 066.5 Pa
British thermal unit Btu quantity of heat 1 Btu
≈ 1055.056 J
calorie cal quantity of heat 1 cal = 4.1868 J
centigon c plane angle 1 c = 1 cgon = 5
π · 10–5 rad
degree deg, grd temperature difference 1 deg = 1 K
degree fahrenheit °F temperature T
K = 273.15 + (5/9) · (tF – 32)
dyn dyn force 1 dyn = 10
–5 N
erg erg energy 1 erg = 10
–7 J
foot ft length 1 ft = 0.3048 m
gallon (UK) gal (UK) volume 1 gal (UK)
≈ 4.54609 · 10–3 m3
gallon (US) gal (US) liquid volume 1 gal (US)
≈ 3.78541 · 10–3 m3
gauss G.Gs magnetic flux density 1 G = 10
–4T
gilbert Gb magnetic potential difference 1 Gb = (10/4
π) A
gon g plane angle 1 g = 1 gon = 5
π · 10–3 rad
horsepower hp power 1 hp
≈ 745.700 W
hundredweight (long) cwt mass 1 cwt
≈ 50.8023 kg
inch (inches) in,
" length 1 in = 25.4 mm = 254 · 10–4 m
international ampere A
int electric current 1 Aint ≈ 0.99985 A
international farad F
int electrical capacitance 1 Fint = (1/1.00049) F
international henry H
int inductance 1 Hint = 1.00049 H
international ohm
Ωint electrical resistance 1 Ωint = 1.00049 Ω
international volt V
int electrical potential 1 Vint = 1.00034 V
international watt W
int power 1 Wint ≈ 1.00019 W
kilogramme-force, kilopond kp, kgf force 1 kp = 9.80665 N
≈ 10 N
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1
Unit of mass ME mass 1 ME = 9.80665 kg
maxwell M, Mx magnetic flux 1 M = 10 nWb = 10
–8 Wb
metre water column mWS pressure 1 mWS = 9806.65 PA
≈ 0,1 bar
micron μ length 1 μ = 1 μm = 10
–6 m
millimetres of mercury mm Hg pressure 1 mm Hg
≈ 133.322 Pa
milligon cc plane angle 1 cc = 0.1 mgon = 5
π · 10–7 rad
oersted Oe magnetic field strength 10e = (250/
π) A/m
Pferdestنrke, cheval-vapeur PS, CV power 1 PS = 735.49875 W
Pfund Pfd mass 1 Pfd = 0.5 kg
pieze pz pressure 1 pz = 1 mPa = 10
–3 Pa
poise P dynamic viscosity 1 P = 0.1 Pa · s
pond, gram
-force p, gf force 1 p = 9.80665 · 10
–3 N ≈ 10 mN
pound
1) Ib mass 1 Ib ≈ 0.453592 kg
poundal pdl force 1 pdl
≈ 0.138255 N
poundforce Ibf force 1 Ibf
≈ 4.44822 N
sea mile, international n mile length (marine) 1 n mile = 1852 m
short hundredweight sh cwt mass 1 sh cwt
≈ 45.3592 kg
stokes St kinematic viscosity 1 St = 1 cm
2/s = 10–4 m2/s
torr Torr pressure 1 Torr
≈ 133.322 Pa
typographical point p length (printing) 1 p = (1.00333/2660) m
≈ 0.4 mm
yard yd length 1 yd = 0.9144 m
Zentner z mass 1 z = 50 kg
1)
UK and US pounds avoirdupois differ only after the sixth decimal place.
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18
Table 1-4
Metric, British and US linear measure
Metric units of length British and US units of length
Kilometre Metre Decimetre Centimetre Millimetre Mile Yard Foot Inch Mil
km m dm cm mm mile yd ft in or " mil
1 1 000 10 000 100 000 1 000 000 0.6213 1 093.7 3 281 39 370 3 937 · 10
4
0.001 1 10 100 1 000 0.6213 · 10
–3 1.0937 3.281 39.370 39 370
0.0001 0.1 1 10 100 0.6213 · 10
–4 0.1094 0.3281 3.937 3 937.0
0.00001 0.01 0.1 1 10 0.6213 · 10
–5 0.01094 0.03281 0.3937 393.70
0.000001 0.001 0.01 0.1 1 0.6213 · 10
–6 0.001094 0.003281 0.03937 39.37
1.60953 1 609.53 16 095.3 160 953 1 609 528 1 1 760 5 280 63 360 6 336 · 10
4
0.000914 0.9143 9.1432 91.432 914.32 0.5682 · 10
–3 1 3 36 36 000
0.305 · 10
–3 0.30479 3.0479 30.479 304.79 0.1894 · 10–3 0.3333 1 12 12 000
0.254 · 10
–4 0.02539 0.25399 2.53997 25.3997 0.158 · 10–4 0.02777 0.0833 1 1 000
0.254 · 10
–7 0.254 · 10–4 0.254 · 10–3 0.00254 0.02539 0.158 · 10–7 0.0277· 10–3 0.0833 · 10–3 0.001
