Conversion Factors
Test Measurement World Staff - April 13, 2007
Acceleration
Area
Density
Diffusivity
Energy, Heat, Power
Heat Capacity, Heat/
Unit Mass, Specific Heat
Heat Flux
Heat-Generation Rate
Heat-Transfer Coefficient
Length
Mass Flux
Acceleration
1 ft/s2 = 0.3048 m/s2
1 m/s2 = 3.2808 ft/s2
Area
1 in2 = 6.4516 cm2
1 in2 = 6.4516 x 104 m2
1 ft2 = 929 cm2
1 ft2 = 0.0929 m2
1 m2 = 10.764 ft2
Density
1 lb/in3 = 27.680 g/cm3
1 lb/in3 = 27.680 x 103 kg/m3
1 lb/ft3 = 16.019 kg/m3
1 kg/m3 = 0.06243 lb/ft3
1 slug/ft3 = 515.38 kg/m3
Mass
Pressure & Force
Specific Heat
Speed
Surface Tension
Temperature
Thermal Conductivity
Thermal Resisitance
Viscosity
Volume
Constants
Dynamic Measurements
1 lb mol/ft3 = 16.019 kg mol/m3
1 kg mol/m3 = 0.06243 lb mol/ft3
Diffusivity
1 ft2/s = 0.0920 m2/s
1 ft2/h = 0.2581 cm2/s
1 ft2/h = 0.2581 x 104 m2/h
1 m2/s = 10.7639 ft2/s
1 cm2/s = 3.8745 ft2/h
Energy, Heat, Power
1J=1W.s=1N.m
1 J = 107 erg
1 Btu = 1055.04 J
1 Btu = 252 cal
1 Btu = 778.161 ft . lbf
1 Btu/h = 0.2931 W
1 Btu/h = 3.93 x 104 hp
1 cal = 4.1868 J
1 cal = 3.968 x 103 Btu
1 hp = 550 ft . lbf/s
1 hp = 745.7 W
1 Wh = 3.413 Btu
Heat Capacity, Heat/Unit Mass, Specific Heat
1 Btu/h .oF = 0.5274 W/oC
1 W/oC = 1.8961 Btu/h . oF
1 Btu/lb = 2325.9 J/kg
1 Btu/lb .oF = 4186.69 J/kg . oC
1 Btu/lb . oF = 1 cal/g .oC
Heat Flux
1 Btu/h . ft2 = 3.1537 W/m2
1 Btu/h . ft2 = 3.1537 x kW/m2
1 W/m2 = 0.31709 Btu/h . ft2
Heat-Generation Rate
1 Btu/h . ft3 = 10.35 W/m3
1 Btu/h . ft3 = 8.9 kcal/h . m3
1 W/m3 = 0.0966 Btu/h . ft3
Heat-Transfer Coefficient
1 Btu/h . ft2 .oF = 5.677 W/m2 .oC
1 Btu/h . ft2 .oF = 5.677 x 104 W/cm2 .oC
1 W/m2 .oC = 0.1761 Btu/h . ft2 .oF
1 Btu/h . ft2 .oF = 4.882 kcal/h . m2 .oC
Length
1 Å = 10-10 m
1 in = 2.54 cm
1 in = 2.54 x 10-2 m
1 ft = 0.3048 m
1 m = 3.2808 ft
1 mile = 1609.34 m
1 mile = 5280 ft
1 light year = 9.46 x 1015 m
Mass Flux
1 lb mol/ ft2 . h = 1.3563 x 10-3 kg mol/m2 . s
1 kg mol/ m2 . s = 737.3 lb mol/ft2 . h
1 lb/ft2 . h = 1.3563 x 10-3 kg/m2 . s
1 lb/ft2 . s = 4.882 kg/ m2 . s
1 kg/m2 . s = 737.3 lb/ft2 . h
1 kg/m2 . s = 0.2048 lb/ft2 . s
Mass
1 oz = 28.35 g
1 lb = 16 oz
1 lb = 453.6 g
1 kg = 2.2046 lb
1 g = 15.432 grains
1 slug = 32.1739 lb
1 ton (metric) = 1000 kg
1 ton (metric) = 2205 lb
1 ton (short) = 2000 lb
1 ton (long) = 2240 lb
Pressure & Force
1 N = 1 kg . m/s2
1 N = 0.22481 lbf
1 N = 7.2333 poundals
1 N = 105 dyne
1 lbf = 32.174 ft . lb/s2
1 lbf = 4.4482 N
1 lbf / in2 = (1 psi) = 6.894.76 N/m2
1 lbf/ ft2 = 47.880 N/m2
1 bar = 105 N/m2
1 atm = 14.696 lbf / in2
1 atm = 2116.2 lbf / ft2
1 atm = 1.0132 bar
Specific Heat
1 Btu/lb .oF = 1 kcal/kg .oC = 1 cal/g .oC
1 Btu/lb .oF = 4186.69 J/kg .oC
1 Btu/lb .oF = 4.18669 J/g .oK
1 J/kg .oC = 0.23885 Btu/lb . oF
Speed
1 ft/s = 0.3048 m/s
1 m/s = 3.2808 ft/s
1 mile/h = 1.4667 ft/s
1 mile/h = 0.44704 m/s
Surface Tension
1 lbf/ft = 14.5937 N/m
1 N/m = 0.068529 lbf/ft
Temperature
1 K = 1.8 oR
T (oF) = 1.8 (K-273) + 32
T (oC) = 1/1.8 (oR-492)
D T (oC) = 1.8 D T (oF)
Thermal Conductivity
1 Btu h . ft .oF = 1.7303 W/m .oC
1 Btu h . ft .oF = 0.4132 cal/s . m2 .oC
1 W/m .oC = 0.5779 Btu/h. ft .oF
Thermal Resistance
1 h .oF Btu = 1.896 oC/W
1 oC/W = 0.528 h .oF Btu
Viscosity
1 poise = 1 g/cm . s
1 poise = 241.9 lb/f . h
1 lb/ft . s = 1.4882 kg/m . s
1 lb/ft . s = 14.882 poises
1 lb/ft . h = 0.4134 x 10-3 kg/m . s
1 lb/ft . h = 0.4134 x 10-2 poise
Volume
1 in3 = 16.387 cm3
1 cm3 = 0.06102 in3
1 liter = 1 x 10-3 m3
1 oz (U.S. fluid) = 29.573 cm3
1 ft3 = 28.3168 liters
1 ft3 = 7.4805 gal (U.S.)
1 m3 = 35.315 ft3
1 gal (U.S.) = 3.7854 liters
Constants
Gravitational Acceleration Conversion Factor
gc = 32.1739 ft . lb/ lbf. s2
= 4.1697 x 108 ft . lb/ lbf. h2
= 1 g . cm/dyn . s2
= 1 kg . m/N . s2
= 1 lb . ft/poundal . s2
= 1 slug . ft/ lbf. s2
Mechannical Equivalent of Heat
J = 778.16 ft . lbf /Btu
Gas Constant
R = 1544 ft . lbf /lb mol .oR
= 0.730 ft3 . atm/lb mol .oR
= 0.08205 m3 . atm/kg mol . K
= 8.314 J/g mol . K
= 8.314 N . m/g mol . K
= 1.987 cal/ g mol . K
Stefan-Boltzman Constant
d = 0.1714 x 10-8 Btu/h . ft2 .oR4
= 0.56697 x 10-8 W/m2 . K4
Dynamic Measurements
Sinusoids
rms vallue = 0.707 x peak value
rms value = 1.11 x average value
peak value = 1.414 x rms value
peak value = 1.57 x average value
average value = 0.637 x peak value
average value = 0.90 x rms value
peak-to-peak = 2 x peak value
crest factor = (peak value)/(rms value)
(applies to any varying quantity)
Random excitation
G = Ö (B Go)
where: G = rms level in g units
B = frequency bandwidth in Hz
Go = acceleration density in g2/Hz
crest factor = (peak magnitude)/(rms magnitude)
Displacement, Velocity, Acceleration Relationships
(for sinusoidal motion only)
d = do sin 2p ft
v = do 2p ft cos 2p ft
a = -do (2p ft ) 2 sin 2p ft
G = accleration/g
vo = 6.28 f do =3.14 f D
vo = 61.42 (G/f) in/s pk
= 1.560 (G/f) m/s pk
do = 9.780 (G/f2) inches pk
= 0.2484 (G/f2) meters pk
where:
do = peak displacement
D = pk-pk displacement
G = acceleration in g units
f = frequency in Hz
T = period in seconds
g = 9.80665 m/ s2
= 32.174 ft/ s2
= 386.09 in/ s2
G = 0.0511 f2 D (where: D = inches pk-to-pk)
G = 2.013 f2 D (where: D = meters pk-to-pk)
T = 1/f seconds
Acceleration Due to Rotational Motion
G = 0.000028 42 r n2
where: G = acceleration in g
r = radius arm in inches
n = revolutions per minute
G = 0.10225 rf2
where: r = radius of arm in inches
f = revolutions per second
G = 4.02568 rf2
where: r = radius of arm in meters
f = revolutions per second
Ohm’s Law for AC Circuits
I = E/Z = P/(E cos q )
E = IZ = P/(I cos q )
Z = E/I = P/(I2 cos q ) = (E2 cos q )/P
P = I2Z cos q = EI cos q = (E2 cos q )/Z
where:
cos q = R/Z = P/EI = power factor
q = angle of lead or lag between current & voltage
Z = ohms
Resistors or Capacitors in Series
Rt = R1 + R2 + R3 + ...
1/Ct = 1/C1 + 1/C2 + 1/C3 + ...
Resistors or Capacitors in Parallel
1/Rt = 1/R1 + 1/R2 + 1/R3 + ...
Ct = C1 + C2 + C3 + ...
Two Resistors in Parallel
Rt = (R1 R2 )/(R1 + R2)
R1 = (Rt R2)/(R2 - Rt)
Impedance
Series Circuit:
Z = / [R2 + (XL+ XC)] 2
Parallel Circuit:
Z = (RX)/ Ö (R2 + X2)
Reactance
XC = - [1/(2p fC)]
XL = 2p fL
Resonance Frequency of First Bending Mode
(Unloaded beams)
fn = C Ö [(EIg)/(L4W)]
where: C = constant, function of method of support
E = elastic modulus
I = moment of inertia of cross section
g = acceleration of gravity
L = length
W = Weight per unit length
Support Method
Cantilever 0.56
Point support each end 1.57
Both ends fixed 3.56
Totally unsupported 3.56
Angular Motion (sinusoidal)
Measurand
Magnitude
Angular displacement
q = q o sin 2p ft
Angular velocity
Angular acceleration
W = 2p f q o cos 2p ft
W o = 2p f q o
a = 4p 2 f2qo sin 2p ft
a o = 4p 2 f2 q o = 2p f W o
where
q o = peak angular
displacement
Wo
= peak angular velocity
a o = peak angular
acceleration
q = radians
r = radius of rotation
Arc distance
s = rq
Tangential velocity
v t = rW
W = radians/s
Tangential acceleration
A t = ra
G t = (ra )/(386.1) g units
a = radians/s2
(r = inches)
G t = (ra )/(9.806) g units
(r = meters)
Driving Long Lines
Eo = Im / Ö [(1/RL2) + ([2p fpl] 2)/1012]
Eo = maximum output voltage of signal conditioner in volts without exceeding current rating.
Im = maximum output current in milliamperes.
RL = resistive termination at end of cable in kilo-ohms.
f = maximum frequency in kHz.
p = capacitance in pF per unit length of cable.
l = cable length in selected units.
Forced Vibration
X = (Fo/k) / Ö ((1-mw 2/k)2 +cw /k)2)
tan f = (cw /k) / (1-mw 2/k)
These terms may be further reduced in terms of the following quantities:
w n = Ö (k/m) = natural frequency of undamped oscillation in radians per second.
z = c/c c = damping factor.
c c = 2mw n = critical damping coefficient.
X o = F o /k = zero frequency deflection for the spring-mass system under the action of a steady force
F o (not to be confused with statical deflection D = W/k).
The nondimensional form of X and f then becomes:
X/ X o = 1 / Ö [1-(w /w n) 2]2 + (2z w /w n) 2
tan f = (2z w /w n ) / (1-(w /w n) 2)
The term X/ X o, called the magnification factor, represents the factor by which the zero frequency
deflection must be multiplied to determing the amplitude X. These equations indicate that X/ X o and
f are functions only of the frequency ratio w /w n and the damping factor z .
Conversion Charge to Voltage Sensitivity
Es = 1000 Qs
Cp + Ct
where:
Es = voltage sensitivity, mV/g
Qs = charge sensitivity, pC/g
Cp = transducer capacitance, pF
Ct = total external capacitance, pF