Commonly Used Equations
Common Mathematical Formulas for Area
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Area
Area
Area
Area
Area
Area
Area
of
of
of
of
of
of
of
a rectangle = length times width A = lw
a circle = pi times the radius squared or A = πr2 or A = ¼d2
a triangle = one half the altitude times the base or A = ½ab
the surface of a sphere = four times pi times the radius squared or A = 4πr2 or A = πd2
a square = length times width or one side squared or A = s2
a cube= square of the length of one side times or A = 6s2
an ellipse = long diameter times short diameter times 0.7854 = .7854l1l2
Common Mathematical Formulas for Volume
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Volume of a sphere = 4/3 times pi times the cube of the radius = V = 4/3πr3
Volume of a pyramid = 1/3 times the area of the base times height = V = 1/3bh
Volume of a cylinder = area of base time the height = V = Ah
Volume of a circular cylinder (with circular base) = pi times the square of the radius of the base times
the height = V = πr2h
Volume of a cube = the length of one side cubed = V = S3
Volume of a cone = 1/3 times pi times the square of the radius of the base times the height = V =
1/3πr2h
Volume of a rectangular solid = length times width times height = V = lwh
Power and Energy Equations
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BTU per hour x 0.293 = watts
Kilowatts x 1.341 = Horsepower
Kilowatt-hour x 3412.14 = BTU
Horsepower x 476 = watts
Horsepower x 550 = foot pounds per second
Horsepower x 33,000 = foot-pounds per minute
Horsepower x 42.4072 = BTU per minute
Watts x 0.00134 = Horsepower
Watts x 44.2537 = Foot pounds per second
Watts x 0.0568 = BTU per minute
Watts x 3.412 = BTU per hour
Watts second x 1 = Joule
Metric System Basics and Conversion
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One
One
One
One
One
One
One
One
One
One
inch = 2.54 centimeters (cm) {multiply # inches x 2.54 = cm}
cm = 0.3937 inches
inch = 25.4 millimeters (mm) {multiply # inches x 25.4 = mm}
mm = 0.03937 inches
foot = 0.3048 meters (m) {multiply # feet x .3048 = meter}
meter = 3.281 fee
yard = 0.9144 m {multiply # yards x 0.91 = m}
meter = 1.094 yards
mile = 1.609 kilometers (km) {multiply # miles x 1.6 = km}
kilometer = 0.6214 miles
micro
milli
centi
deci
deka
hecto
kilo
mega
0.000001
0.001
0.01
0.1
10
100
1,000
1,000,000
Ohm's Law Ω
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Ohm - the resistance between two points when a potential difference of one volt between them
produces a current of one ampere
Ohm's Law states that the current flowing in a metallic conductor maintained at a constant
temperature is directly proportional to the potential difference (or voltage) between its ends.
[Discovered in 1827 by German physicist Georg Ohm] Not all conductors obey Ohm's law, but those
that do are called ohmic conductors.
Fahrenheit to Celsius Conversion
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To convert Fahrenheit (F) to Celsius (C) use the following formula:
 (5/9)*(Temperature F-32) = o Celsius
To convert Celsius (C) to Fahrenheit (F) use the following formula:
 [(9/5)*Temperature C] + 32 =o Fahrenheit