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 
IMA 
Variables
AMA = Actual Mechanical Advantage
FR = Resistance force
FE = Effort force
IMA = Ideal Mechanical Advantage
DR = Resistance Distance
DE = Effort Distance
FR
FE
DE
DR
LeverIMA 
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 MA 
H
L
Wedge IMA 
H
C
ScrewIMA 
Pitch
1
Pitch 
TPI
rw = Wheel radius
ra = Axle radius
L = Slope length
H = Height
L = Base length
H = Height
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 
FLO
A OE
E=
E 
σ
ε
F2  F1  LO
δ 2  δ 1  A O
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 
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
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
Project Lead The Way, Inc.
Copyright 2010
Engineering Formula Sheet - Page 2
Statics
Formulas
MF d
FX  0  X(right )
 X(left )
FY  0  Y up   Y  down
M  0  CCW  CW
2J  M  R
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 and Power
Formulas
W  FD
P
W
t
P  V I
P
Q
t
T
L
P  UAT
1
U
R
P  kA
Variables
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
U = Thermal transmittance (U-factor)
R = Resistance to heat flow (R-value)
Project Lead The Way, Inc.
Copyright 2010
Engineering Formula Sheet - Page 3