ELECTRICAL Formulas
E = Voltage / I = Amps /W = Watts / PF = Power Factor / Eff = Efficiency / HP = Horsepower
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AC/DC Formulas
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To Find
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Direct Current
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AC / 1phase
115v or 120v |
AC / 1phase
208,230, or 240v |
AC 3 phase
All Voltages |
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Amps when
Horsepower is Known |
HP x 746
E x Eff |
HP x 746
E x Eff X PF |
HP x 746
E x Eff x PF |
HP x 746
1.73 x E x Eff x PF |
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Amps when
Kilowatts is known |
kW x 1000
E |
kW x 1000
E x PF |
kW x 1000
E x PF |
kW x 1000
1.73 x E x PF |
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Amps when
kVA is known |
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kVA x 1000
E |
kVA x 1000
E |
kVA x 1000
1.73 x E |
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Kilowatts
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I x E
1000 |
I x E x PF
1000 |
I x E x PF
1000 |
I x E x 1.73 PF
1000 |
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Kilovolt-Amps
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I x E
1000 |
I x E
1000 |
I x E x 1.73
1000 |
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Horsepower
(output) |
I x E x Eff
746 |
I x E x Eff x PF
746 |
I x E x Eff x PF
746 |
I x E x Eff x 1.73 x PF
746 |
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Three Phase Values
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For 208 volts x 1.732, use 360
For 230 volts x 1.732, use 398 For 240 volts x 1.732, use 416 For 440 volts x 1.732, use 762 For 460 volts x 1.732, use 797 For 480 Volts x 1.732, use 831 |
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AC Efficiency and
Power Factor Formulas
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To Find
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Single Phase
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Three Phase
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Efficiency
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746 x HP
E x I x PF |
746 x HP
E x I x PF x 1.732 |
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Power Factor
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Input Watts
V x A |
Input Watts
E x I x 1.732 |
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Power - DC Circuits
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Watts = E
xI
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Amps = W /
E
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Ohm's Law / Power
Formulas
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P = watts
I = amps
R = ohms
E = Volts
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Voltage Drop Formulas
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Single Phase
(2 or 3 wire) |
VD =
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2 x K x I x L
CM |
K = ohms per mil foot
(Copper = 12.9 at 75°) (Alum = 21.2 at 75°)
L = Length of conductor in
feet
I = Current in conductor (amperes) CM = Circular mil area of conductor |
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CM=
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2K x L x I
VD |
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Three Phase
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VD=
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1.73 x K x I x L
CM |
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CM=
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1.73 x K x L x I
VD |
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Calculating Motor Speed:
A
squirrel cage induction motor is a constant speed device. It cannot operate for
any length of time at speeds below those shown on the nameplate without danger
of burning out.
To Calculate the speed of a induction motor, apply this formula:
Srpm = 120 x F
P
P
Srpm = synchronous revolutions per
minute.
120 = constant
F = supply frequency (in cycles/sec)
P = number of motor winding poles
120 = constant
F = supply frequency (in cycles/sec)
P = number of motor winding poles
Example: What is
the synchronous of a motor having 4 poles connected to a 60 hz power supply?
Srpm = 120 x F
P
Srpm = 120 x 60
4
Srpm = 7200
4
Srpm = 1800 rpm
P
Srpm = 120 x 60
4
Srpm = 7200
4
Srpm = 1800 rpm
Calculating Braking Torque:
Full-load
motor torque is calculated to determine the required braking torque of a motor.
To Determine braking torque of a motor, apply this formula:
To Determine braking torque of a motor, apply this formula:
T = 5252 x HP
rpm
rpm
T
= full-load motor torque (in lb-ft)
5252 = constant (33,000 divided by 3.14 x 2 = 5252)
HP = motor horsepower
rpm = speed of motor shaft
5252 = constant (33,000 divided by 3.14 x 2 = 5252)
HP = motor horsepower
rpm = speed of motor shaft
Example: What
is the braking torque of a 60 HP, 240V motor rotating at 1725 rpm?
T = 5252 x HP
rpm
T = 5252 x 60
1725
T = 315,120
1725
T = 182.7 lb-ft
rpm
T = 5252 x 60
1725
T = 315,120
1725
T = 182.7 lb-ft
Calculating Work:
Work is
applying a force over a distance. Force is any cause that changes the position,
motion, direction, or shape of an object. Work is done when a force overcomes a
resistance. Resistance is any force that tends to hinder the movement of an
object.If an applied force does not cause motion the no work is produced.
To
calculate the amount of work produced, apply this formula:
W = F x D
W = work (in lb-ft)
F = force (in lb)
D = distance (in ft)
F = force (in lb)
D = distance (in ft)
Example: How much
work is required to carry a 25 lb bag of groceries vertically from street level
to the 4th floor of a building 30' above street level?
W = F x D
W = 25 x 30
W = 750 -lb
W = 25 x 30
W = 750 -lb
Calculating Torque:
Torque
is the force that produces rotation. It causes an object to rotate. Torque
consist of a force acting on distance. Torque, like work, is measured is
pound-feet (lb-ft). However, torque, unlike work, may exist even though no
movement occurs.
To calculate torque, apply this formula:
T = F x D
T = torque (in lb-ft)
F = force (in lb)
D = distance (in ft)
F = force (in lb)
D = distance (in ft)
Example: What
is the torque produced by a 60 lb force pushing on a 3' lever arm?
T = F x D
T = 60 x 3
T = 180 lb ft
T = 60 x 3
T = 180 lb ft
Calculating Full-load Torque:
Full-load
torque is the torque to produce the rated power at full speed of the motor. The
amount of torque a motor produces at rated power and full speed can be found by
using a horsepower-to-torque conversion chart. When using the conversion chart, place a straight
edge along the two known quantities and read the unknown quantity on the third
line.
To calculate motor full-load torque, apply this formula:
T = HP x 5252
rpm
rpm
T = torque (in lb-ft)
HP = horsepower
5252 = constant
rpm = revolutions per minute
HP = horsepower
5252 = constant
rpm = revolutions per minute
Example: What
is the FLT (Full-load torque) of a 30HP motor operating at 1725 rpm?
T = HP x 5252
rpm
T = 30 x 5252
1725
T = 157,560
1725
T = 91.34 lb-ft
rpm
T = 30 x 5252
1725
T = 157,560
1725
T = 91.34 lb-ft
Calculating Horsepower:
Electrical
power is rated in horsepower or watts. A horsepower is a unit of power equal to
746 watts or 33,0000 lb-ft per minute (550 lb-ft per second). A watt is a unit
of measure equal to the power produced by a current of 1 amp across the
potential difference of 1 volt. It is 1/746 of 1 horsepower. The watt is the
base unit of electrical power. Motor power is rated in horsepower and watts.
Horsepower is used to measure the energy produced by an electric motor while doing work.
Horsepower is used to measure the energy produced by an electric motor while doing work.
To calculate the horsepower of a motor when current and efficiency, and
voltage are known, apply this formula:
HP = V x I x Eff
746
746
HP
=
horsepower
V = voltage
I = curent (amps)
Eff. = efficiency
V = voltage
I = curent (amps)
Eff. = efficiency
Example:
What is the horsepower of a 230v motor pulling 4 amps and having 82%
efficiency?
HP = V x I x Eff
746
HP = 230 x 4 x .82
746
HP = 754.4
746
HP = 1 Hp
Eff = efficiency / HP = horsepower / V = volts / A = amps / PF = power factor
746
HP = 230 x 4 x .82
746
HP = 754.4
746
HP = 1 Hp
Eff = efficiency / HP = horsepower / V = volts / A = amps / PF = power factor
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Horsepower Formulas
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To Find
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Use Formula
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Example
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Given
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Find
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Solution
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HP
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HP = I X E X Eff.
746 |
240V, 20A, 85% Eff.
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HP
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HP = 240V x 20A x 85%
746 HP=5.5 |
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I
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I = HP x 746
E X Eff x PF |
10HP, 240V,
90% Eff., 88% PF |
I
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I = 10HP x 746
240V x 90% x 88% I = 39 A |
To calculate the horsepower of a motor when the speed and torque are
known, apply this formula:
HP = rpm x T(torque)
5252(constant)
5252(constant)
Example: What is the horsepower of a 1725 rpm motor with a FLT 3.1
lb-ft?
HP = rpm x T
5252
HP = 1725 x 3.1
5252
HP = 5347.5
5252
HP = 1 hp
5252
HP = 1725 x 3.1
5252
HP = 5347.5
5252
HP = 1 hp
Calculating Synchronous Speed:
AC
motors are considered constant speed motors. This is because the synchronous
speed of an induction motor is based on the supply frequency and the number of
poles in the motor winding. Motor are designed for 60 hz use have synchronous
speeds of 3600, 1800, 1200, 900, 720, 600, 514, and 450 rpm.
To calculate synchronous speed of an induction motor, apply this
formula:
rpmsyn = 120 x f
Np
Np
rpmsyn = synchronous speed
(in rpm)
f = supply frequency in (cycles/sec)
Np = number of motor poles
f = supply frequency in (cycles/sec)
Np = number of motor poles
Example: What
is the synchronous speed of a four pole motor operating at 50 hz.?
rpmsyn = 120 x f
Np
rpmsyn = 120 x 50
4
rpmsyn = 6000
4
rpmsyn = 1500 rpm
Np
rpmsyn = 120 x 50
4
rpmsyn = 6000
4
rpmsyn = 1500 rpm
