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Unit Conversion Tables
This document contains information on using units in Creo Simulate and on converting values between different systems of units. This document includes the following sections:
Topic
Introduction
Basic Equalities
System of Units
Basic Units
Examples of Values for Gravitational Acceleration and Selected Properties of Steel
Correspondence Between Mass and Force
Correspondence Between Mass and Pounds-mass
Conversion of Basic Units
Correspondence Between Degrees Celsius and Degrees Fahrenheit Throughout this document, scientific notation is written as you would type it in Creo Simulate. For example, 2.07 x 1011 is written as 2.07e11.
Introduction
This document provides an overview of the physical dimensions of many of the quantities in Creo Simulate.
The following abbreviations are used throughout this document:
L = length
M = mass
T = time
F = force
E = energy (heat)
P = power
D = temperature (such as F, C, K)
When choosing a consistent set of units, you must decide which quantities will form the basic physical dimensions and which quantities will be derived from the basic dimensions. Usually, you will choose either mass, length, and time (MLT) or force, length, and time (FLT) as the basic dimensions. The connection between these two systems is given by Newton's second law of motion:
force = mass x acceleration
the dimensions of which are:
F = ML/T2
Some quantities in Thermal are usually expressed in terms of energy and power, the dimensions of which are determined from their definitions:
energy (work, heat) = force x distance
E = FL
power = energy ÷ time
P = E/T
Basic Equalities
Following is a list of many of the quantities in Creo Simulate and the physical dimensions of each expressed in terms of common physical dimensions and also in terms of MLT and FLT.
 Quantity Common MLT FLT length L L L time T T T mass M M FT2/L force F ML/T2 F temperature D D D area L2 L2 L2 volume L3 L3 L3 velocity L/T L/T L/T acceleration L/T2 L/T2 L/T2 gravitational acceleration L/T2 L/T2 L/T2 angle, rotation R R R rotational velocity R/T R/T R/T rotational acceleration R/T2 R/T2 R/T2 density M/L3 M/L3 FT2/L4 moment, torque FL ML2/T2 FL distributed force along a curve F/L M/T2 F/L distributed moment along a curve F ML/T2 F distributed force over a surface, pressure, stress, Young's modulus F/L2 M/LT2 F/L2 distributed moment over a surface F/L M/T2 F/L translational stiffness F/L M/T2 F/L rotational stiffness FL/R ML2/T2R FL/R coefficient of thermal expansion /D /D /D moment of inertia of beam cross-sectional area L4 L4 L4 mass moment of inertia ML2 ML2 FLT2 energy, work, heat (E) FL ML2/T2 FL power, heat transfer rate (P) E/T ML2/T3 FL/T temperature gradient D/L D/L D/L heat flux P/L2 M/T3 F/TL thermal conductivity P/LD ML/T3D F/TD convection coefficient P/L2D M/T3D F/LTD specific heat (Cp) E/MD L2/T2D FL/MD
System of Units
To define a system of units, you assign a unit of measure to each of the physical dimensions. This section provides the units of the above quantities in four different systems of units, two different metric systems, MKS and mmNs, and two different English systems, FPS and IPS. The MKS system of units uses MLT as the basic dimensions. The mmNs, FPS, and IPS systems of units use FLT as the basic dimensions.
MKS
Following are the basic and some of the derived units of the MKS system:
 Basic Units Some Derived Units M: kilogram (kg) F: kg-m/sec2 = Newton (N) L: meter (m) E: N-m = Joule (J) T: second (sec) P: J/sec = Watt (W) D: degree Celsius ( C)
mmNS
Following are the basic and some of the derived units of the mmNS system:
 Basic Units Some Derived Units F: Newton (N) M: (N-sec2/mm) (kg-m/N-sec2) (1000mm/m) = 1000 kg = tonne(t) L: millimeter (mm) E: (N-mm) (J/N-m) (m/1000mm) = J/1000 = mJ T: second (sec) P: (mJ/sec) (J/1000mJ) (W-sec/J) = W/1000 = mW D: degree Celsius ( C)
mmKS
Following are the basic and some of the derived units of the mmKS system:
 Basic Units Some Derived Units M: kilogram (kg) F: kg-mm/sec2= mN L: millimeter (mm) E: mN-mm = J T: second (sec) P: J/sec = W D: degree Celsius ( C)
FPS
Following are the basic and some of the derived units of the FPS system:
 Basic Units Some Derived Units F: pound-force (lbf) M: lbf-sec2/ft = slug L: foot (ft) E: ft-lbf T: second (sec) P: ft-lbf/sec D: degree Fahrenheit ( F)
IPS
Following are the basic and some of the derived units of the IPS system:
 Basic Units Some Derived Units F: pound-force (lbf) M: lbf-sec2/in L: inch (in) E: lbf-in T: second (sec) P: lbf-in/sec D: degree Fahrenheit ( F)
CGS
Following are the basic and some of the derived units of the CGS system:
 Basic Units Some Derived Units M: gram (g) F: g-cm/sec2 = 10-5 N = dyne L: centimeter (cm) E: g-cm2/sec2 = 10-7 J = erg T: second (sec) P: g-cm2/sec3 = 10-7 W D: degree Celsius ( C)
Creo Parametric Default
Following are the basic and some of the derived units of the Creo Parametric Default system:
 Basic Units Some Derived Units M: pounds-mass (lbm) F: in-lbm/sec2 L: inch (in) E: in2-lbm/sec2 T: second (sec) P: in2-lbm/sec3 D: degree Fahrenheit ( F)
Basic Units
Using the definitions from the previous section, the units of the quantities in these four systems are as follows:
Units
Metric (MKS)
Metric (mmNS)
English (FPS)
English (IPS)
length
m
mm
ft
in
time
sec
sec
sec
sec
mass
kg
tonne
slug
lbf-sec2/in
force
N
N
lbf
lbf
temperature C C F F
area
m2
mm2
ft2
in2
volume
m3
mm3
ft3 (cu-ft)
in3 (cu-in)
velocity
m/sec
mm/sec
ft/sec
in/sec
acceleration
m/sec2
mm/sec2
ft/sec2
in/sec2
angle, rotation
gravitational acceleration
m/sec2
mm/sec2
ft/sec2
in/sec2
rotational velocity
rotational acceleration
density
kg/m3
tonne/mm3
slug/ft3
lbf-sec2/in4
moment, torque
N-m
N-mm
ft-lbf
in-lbf
distributed force along a curve
N/m
N/mm
lbf/ft
lbf/in
distributed moment along a curve
N
N
lbf
lbf
distributed force over a surface, pressure, stress, Young's modulus
N/m2 (Pa)
N/mm2 (MPa)
lbf/ft2
lbf/in2 (psi)
translational stiffness
N/m
N/mm
lbf/ft
lbf/in
rotational stiffness
coefficient of thermal expansion
/ C
/ C
/ F
/ F
moment of inertia of beam cross-sectional area
m4
mm4
ft4
in4
mass moment of inertia
kg-m2
tonne-mm2
slug-ft2
lbf-in-sec2
energy, work, heat (E)
J
mJ
ft-lbf
in-lbf
power, heat transfer rate (P)
W
mW
ft-lbf/sec
in-lbf/sec C/m C/mm F/ft F/in
heat flux
W/m2
mW/mm2
lbf/ft-sec
lbf/in-sec
thermal conductivity
W/m- C
mW/mm- C
lbf/sec- F
lbf/sec- F
convection film coefficient
W/m2- C
mW/mm2- C
lbf/ft-sec- F
lbf/in-sec- F
specific heat (Cp)
J/kg- C
mJ/tonne- C
ft-lbf/slug- F
in2/sec2- F 1W = 1N-m/sec, 1mJ = 1N-mm, 1mW = 1N-mm/sec, N/m2 = Pascal (Pa)
The numerical values of conductivity are the same in the MKS and mmNS systems and in the FPS and IPS systems.
In Structure, units of modal frequency results are always cycles per unit time or Hz. The units of time are affected by the force/length/time units you used to define the model. Structure never reports modal frequency in terms of radians per unit time.
Examples of Values for Gravitational Acceleration and Selected Properties of Steel
The following table shows examples of approximate values for acceleration, density, Young's modulus, thermal coefficient of expansion, and thermal conductivity:
 Units Metric (MKS) Metric (mmNS) English (FPS) English (IPS) g (gravitational acceleration) 9.81 m/sec2 9810 mm/sec2 32.2 ft/sec2 386 in/sec2 density (steel) 7830.0 kg/m3 7.83e-9 tonne/mm3 15.2 slug/ft3 7.33e-4 lb-sec2/in4 Young's modulus (steel) 2.07e11 N/m2 2.07e5 N/mm2 4.32e9 lb/ft2 3.0e7 lb/in2 coefficient of thermal expansion (steel) 12e-6/ C 12e-6/ C 6.5e-6/ F 6.5e-6/ F thermal conductivity (steel) 43.37 W/m- C 43.37 mW/mm- C 5.4 lbf/sec- F(25 Btu/hr-ft- F) 5.41bf/sec- F(2.083 Btu/hr-in- F)
Correspondence Between Mass and Force
The following list describes the correspondence between mass and force at sea level for four common unit systems:
1 kg weighs 9.81 Newtons
1 tonne weighs 9810 Newtons
1 slug weighs 32.2 lbs
1 (lb-sec2/in) weighs 386 lbs
Correspondence Between Mass and Pounds-mass
In some English systems of units, mass is sometimes given in pounds-mass (lbm). The relationship between pounds-mass and mass in the FPS and IPS systems of units is determined by the fact that one pound-mass weighs one pound-force in the gravitational field of the earth at sea level:
lbf = lbm x g
where g = 32.2 ft/sec2 = 386 in/sec2
Therefore:
lbm = 1/386 lbf-sec2/in
lbm = 1/32.2 lbf-sec2/ft = 1/32.2 slug
Conversion of Basic Units
The following tables show conversion factors for various quantities:
 Length Conversion Factors m mm ft in 1 m = 1 1000 3.281 39.37 1 mm = 1.0e-3 1 3.281e-3 3.937e-2 1 ft = 0.3048 304.8 1 12 1 in = 2.54e-2 25.4 8.333e-2 1
 Mass Conversion Factors kg tonne (N-sec2/mm) slug (lb-sec2/ft) lb-sec2/in 1 kg = 1 1.0e-3 6.852e-2 5.71e-3 1 tonne = 1000 1 68.52 5.71 1 slug = 14.59 14.59e-3 1 8.333e-2 1 lb-sec2/in = 175.1 0.1751 12 1
 Moments of Inertia kg m2 tonne mm2 slug ft2 lbf-sec2-in 1 kg m2= 1 1000 .738 8.85 1 tonne mm2= 1e-3 1 7.375e-4 8.85e-3 1 slug ft 2= 1.356 1.356e3 1 12 1 lbf-sec2-in = 0.113 113 1/12 1
 Force Conversion Factors N Kg-force lb 1 N = 1 0.101972 0.2248 1 lb = 4.448 0.453594 1
 Moment Conversion Factors N-m N-mm lb-ft lb-in 1 N-m = 1 1000 0.7376 8.851 1 N-mm = 1.0e-3 1 7.376e-4 8.851e-3 1 lb-ft = 1.356 1356 1 12 1 lb-in = 0.113 113 8.33e-2 1
 Density Conversion Factors kg/m3 tonne/mm3 slug/ft3 lb-sec2/in4 1 kg/m3 = 1 1e-12 1.94e-3 9.36e-8 1 tonne/mm3 = 1e12 1 1.94e9 9.36e4 1 slug/ft3 = 515 5.15e-10 1 4.82e-5 1 lb-sec2/in4 = 1.07e7 1.07e-5 20700 1
 Stress Conversion Factors N/m2 N/mm2 lb/ft2 lb/in2 1 N/m2 = 1 1e-6 2.09e-2 1.45e-4 1 N/mm2 = 1e6 1 20900 145 1 lb/ft2 = 47.9 47.9e-5 1 6.94e-3 1 lb/in2 = 6890 6.89e-3 144 1
 Translational Stiffness Conversion Factors N/m N/mm lb/ft lb/in 1 N/m = 1 1.0e-3 6.8525e-2 5.7104e-3 1 N/mm = 1000 1 68.525 5.710 1 lb/ft = 14.593 1.4593e-2 1 8.33e-2 1 lb/in = 175.118 1.7512e-5 12 1
 Thermal Conductivity Conversion Factors W/m- C mW/mm- C Btu/hr-ft- F Btu/hr-in- F lbf/sec- F 1 W/m- C = 1 1 0.5777 4.817e-2 0.1249 1 mW/mm- C = 1 1 0.5777 4.817e-2 0.1249 1 Btu/hr-ft- F = 1.731 1.731 1 8.333e-2 0.2162 1 Btu/hr-in- F = 20.76 20.76 12 1 2.594 1 lbf/sec- F = 8.007 8.007 4.626 0.3854 1 C = ( F 32)/1.8 F = 1.8 C + 32
Thus, a temperature difference of 1 C is equal to a difference of 1.8 F.