Project Lead The Way, Inc. Copyright 2010

Engineering Formula Sheet - Page 1

Engineering Formula Sheet

Circular Shapes

Formulas Variables

C = Circumference

C d π = 3.14

d = Diameter 2A r A = Area

r = Radius

Electrical Systems

Formulas Variables

V = Voltage

V = IR I = Current R = Resistance

Right Triangle Ratios

Formulas Variables opposite

Sinhypotenuse

adjacentCos

hypotenuse θ = Angle

oppositeTan

adjacent

Simple Machines

Formulas Variables

R

E

FAMA

F

AMA = Actual Mechanical Advantage FR = Resistance force FE = Effort force

E

R

DIMA

D

IMA = Ideal Mechanical Advantage DR = Resistance Distance DE = Effort Distance

LE

LeverIMALR

LE = Length from fulcrum to effort LR = Length from fulcrum to resistance

Wheel and Axle W

A

rIMA

r rw = Wheel radius

ra = Axle radius

Pulley IMA = Total number of strands supporting the load

Inclined Plane L

MAH

L = Slope length H = Height

Wedge L

IMAH

L = Base length H = Height

C

ScrewIMAPitch

C = Circumference

1Pitch

TPI Pitch = Screw pitch

TPI = Threads per inch

Project Lead The Way, Inc. Copyright 2010

Engineering Formula Sheet - Page 2

Properties of Materials

Formulas Variables

σO

F

A σ = Stress

F = Axial force

εOL

Ao = Cross-sectional area

ε = Strain

δ O

O

FL

A E δ = Deformation

Lo = Original length

σE=

ε

E = Modulus of Elasticity

E

δ δ2 1 O

2 1 O

F F L

A

Fluids

Formulas Variables

FPA

P = Pressure F = Force

1 2

1 2

V V

T T A = Area

V = Volume

1 1 2 2P V P V

Gear Ratios

Formulas Variables

in

out

GR

GR = Gear ratio ωin = Driver gear, rpm ωout = Driven gear, rpm

out

in

NGR

N

Nin = Number of teeth on driver Nout = Number of teeth on driven din = Diameter of driver

out out outin

in in out in

N d

N d

dout = Diameter of driven τin = Torque of driver, ft-lbs τout = Torque of driven, ft-lbs

Kinematics

Formulas Variables

-g

2

iV *Sin 2

X

X = Range Vi = Initial velocity

g

ixVSin 2

g = Acceleration due to gravity θ = Initial trajectory angle from the horizontal

ix iV V cos Vix = Initial horizontal velocity

iy iV V sin Viy = Initial vertical velocity

Project Lead The Way, Inc. Copyright 2010

Engineering Formula Sheet - Page 3

Statics

Formulas Variables

M F d M = Moment about a point F = Force d = Perpendicular distance

XF 0 X(right) X(left)

∑ = Sum of X = Force in x-direction Y = Force in y-direction

YF 0 Y up Y down CCW = Counter-clockwise moment

M 0 CCW CW CW = Clockwise moment

RMJ 2 J = Number of joints M = Number of members R = Number of reaction forces

Rectangular Sections

XXI3bh

12

IXX = Moment of inertia about x-x axis b = Base dimension

h = Height

Work and Power

Formulas Variables

W F D

W = Work F = Force D = Distance

WP

t

P = Power W = Work t = Time

P V I

V = Volts I = Current

QP

t

P = Rate of heat transfer Q = Energy transfer Δt = Difference in time

TP kA

L

k = Thermal conductivity A = Area of thermal conductivity L = Thickness ΔT = Difference in temperature

P UA T U = Thermal transmittance (U-factor)

1UR

R = Resistance to heat flow (R-value)