ABB

MOHAMMAD.MO.....
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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2

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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3

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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4

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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6

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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8

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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10

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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11

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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12

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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14

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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15

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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16

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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17

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