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Engineering Formula Sheet
Circular Shapes
Formulas
Variables
C   d
A    r2
C = Circumference
π = 3.14
d = Diameter
Electrical Systems
Formulas
V = IR
I = Current
R = Resistance
A = Area
r = Radius
Right Triangle Ratios
Formulas
Variables
opposite
Sin 
hypotenuse
adjacent
Cos 
hypotenuse
opposite
Tan 
adjacent
θ = Angle
Simple Machines
Formulas
AMA 
FR
FE
IMA 
DE
DR
LeverIMA 
Variables
AMA = Actual Mechanical Advantage
FR = Resistance force
FE = Effort force
IMA = Ideal Mechanical Advantage
DR = Resistance Distance
DE = Effort Distance
LE
LR
Wheel and Axle IMA 
Variables
V = Voltage
LE = Length from fulcrum to effort
LR = Length from fulcrum to resistance
rW
rA
Pulley IMA = Total number of strands
supporting the load
L
Inclined Plane or Wedge MA 
H
L
Wedge IMA 
T
C
ScrewIMA 
Pitch
1
Pitch 
TPI
rw = Wheel radius
ra = Axle radius
L = Slope length
H = Height
L = Slope length
T = Thickness
C = Circumference
Pitch = Screw pitch
TPI = Threads per inch
Project Lead The Way, Inc.
Copyright 2010
Engineering Formula Sheet - Page 1
Properties of Materials
Formulas
F
σ 
AO

ε
LO
δ 
FL O
A OE
σ
ε
F  F  L
E  2 1 O
δ 2  δ 1  A O
E=
Variables
σ = Stress
F = Axial force
Ao = Cross-sectional area
ε = Strain
δ = Deformation
Lo = Original length
E = Modulus of Elasticity
Fluids
Formulas
F
P
A
V1 V2

T1 T2
Variables
P = Pressure
F = Force
A = Area
V = Volume
P1  V1   P2  V2 
p1 p 2

T1 T2
T + 460°F
P + 14.7 lb/in.2
Q = VA
1 gal = 231 in.3
Absolute Temperature
Absolute Pressure
Q = Flow Rate gpm gallons per minute
V = Flow Velocity ft/s (feet per second)
Gear Ratios
Formulas

GR  in
out
GR 
Nout
Nin
Nout dout



 in  out
Nin
din
out
in
Variables
GR = Gear ratio
ωin = Driver gear, rpm
ωout = Driven gear, rpm
Nin = Number of teeth on driver
Nout = Number of teeth on driven
din = Diameter of driver
dout = Diameter of driven
τin = Torque of driver, ft-lbs
τout = Torque of driven, ft-lbs
Project Lead The Way, Inc.
Copyright 2010
Engineering Formula Sheet - Page 2
Kinematics
Formulas
V 2 * Sin  2 
X i
Vi  gx
Variables
-g
X = Range
Vi = Initial velocity
Sin  2 
g = Acceleration due to gravity
θ = Initial trajectory angle from the horizontal
Vix  Vi cos 
Vix = Initial horizontal velocity
Viy  Vi sin 
Viy = Initial vertical velocity
Statistics
Px 
  q 
n! p x
n x
x!  n  x  !
Px 
Fx
Fa
P = Probability
x = Number of times an outcome occurs
within n trials
n = Number of trials
p = Probability of success on a single trial
q = Probability of failure on a single trial
! means multiply all of the numbers 1 to x
Ex. 5! = 5 x 4 x 3 x 2 x 1
Project Lead The Way, Inc.
Copyright 2010
Engineering Formula Sheet - Page 3
Statics
Formulas
MF d
FX  0  X(right ) X
(left
 )
FY  0  Y  up   Y  down 
M  0  CCW  CW
2J  M  R
Fx = F cosΘ
Fy = F sinΘ
Rectangular
Sections
bh3
I XX 
12
Variables
M = Moment about a point
F = Force
 d = Perpendicular distance
∑ = Sum of
X = Force in x-direction
Y = Force in y-direction
CCW = Counter-clockwise moment
CW = Clockwise moment
J = Number of joints
M = Number of members
R = Number of reaction forces
IXX = Moment of inertia about x-x axis
b = Base dimension
h = Height
Work, Power, and Thermodynamics
Formulas
W  F D
P
W
t
P  V I
Q = m ∙ Cp ∙ ∆T
P
Q
t
P  kA
T
L
Pnet = σAe(T4-T4)
U-value = Q / A∆T
1
U
R
Variables
Cp = Specific heat capacity (a constant)
m = mass
W = Work
F = Force
D = Distance
P = Power
W = Work
t = Time
V = Volts
I = Current
P = Rate of heat transfer
Q = Energy transfer
Δt = Difference in time
k = Thermal conductivity
A = Area of thermal conductivity
L = Thickness
ΔT = Difference in temperature
σ = 5.6696 x 10-8 W/m2 k4 (Stefan’s constant)
Kelvin = C + 273.15
e = emissivity (a constant)
U = Thermal transmittance (U-factor)
R = Resistance to heat flow (R-value)
Project Lead The Way, Inc.
Copyright 2010
Engineering Formula Sheet - Page 4