AC/DC Formulas

E = Voltage / I = Amps /W = Watts / PF = Power Factor / Eff = Efficiency / HP = Horsepower

AC/DC Formulas
To Find	Direct Current	AC / 1phase  115v or 120v	AC / 1phase 208,230, or 240v	AC 3 phase All Voltages
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
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
Amps when kVA is known		kVA x 1000 E	kVA x 1000 E	kVA x 1000 1.73 x E
Kilowatts	I x E 1000	I x E x PF 1000	I x E x PF 1000	I x E x 1.73 PF 1000
Kilovolt-Amps		I x E 1000	I x E 1000	I x E x 1.73 1000
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

Three Phase Values

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

E = Voltage / I = Amps /W = Watts / PF = Power Factor / Eff = Efficiency / HP = Horsepower

AC Efficiency and Power Factor Formulas
To Find	Single Phase	Three Phase
Efficiency	746 x HP E x I x PF	746 x HP E x I x PF x 1.732
Power Factor	Input Watts V x A	Input Watts E x I x 1.732

Power - DC Circuits

Watts = E xI

Amps = W / E

Ohm's Law / Power Formulas
	P = watts I = amps R = ohms E = Volts

Voltage Drop Formulas
Single Phase (2 or 3 wire)	VD =	2 x K x I x L CM	K = ohms per mil foot   (Copper = 12.9 at 75°) (Alum = 21.2 at 75°) Note: K value changes with temperature. See Code chapter 9, Table 8 L = Length of conductor in feet I  = Current in conductor (amperes) CM = Circular mil area of conductor
	CM=	2K x L x I VD
Three Phase	VD=	1.73 x K x I x L CM
	CM=	1.73 x K x L x I VD

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

Srpm = synchronous revolutions per minute.
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

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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:

T = 5252 x HP
    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

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

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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)

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

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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)

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

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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

T = torque (in lb-ft)
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

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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.

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

HP = horsepower
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

Horsepower Formulas
To Find	Use Formula	Example
		Given	Find	Solution
HP	HP = I X E X Eff.        746	240V, 20A, 85% Eff.	HP	HP = 240V x 20A x 85%        746 HP=5.5
I	I = HP x 746      E X Eff x PF	10HP, 240V, 90% Eff., 88% PF	I	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)

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

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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

rpmsyn = synchronous speed (in rpm)
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

Transfor formula--------------------------------

To better understand the following formulas review the rule of transposition in equations.
A multiplier may be removed from one side of an equation by making it a division on the other side, or a division may be removed from one side of an equation by making it a multiplier on the other side.

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1. Voltage and Current: Primary (p) secondary (s)
Power(p) = power (s) or Ep x Ip = Es x Is

A.	Ep =	Es x Is Ip		B.	Ip =	Es x Is Ep
C.	Is =	Ep x Ip Es		D.	Es =	Ep x Ip Is

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2. Voltage and Turns in Coil:
Voltage (p) x Turns (s) = Voltage (s) x Turns (p)
or Ep x Ts = Es x Ip

A.	Ep =	Es x Ip Ts		B.	Ts =	Es x Tp Ep
C.	Tp =	Ep x Ts Es		D.	Es =	Ep x Ts Tp

3. Amperes and Turns in Coil:
Amperes (p) x Turns (p) = Amperes (s) x Turns (s)
or Ip x Tp = Is x Ts

A.	Ip =	Is x Ts Tp		B.	Tp =	Is x Ts Ip
C.	Ts =	Ip x Tp Is		D.	Is =	Ip x Tp Ts

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Formula 1 − Electrical power equation: Power P = I × V = R × I2 = V2 ⁄ R  where power P is in watts, voltage V is in volts and current I is in amperes (DC).  If there is AC, look also at the power factor PF = cos φ and φ = power factor angle  (phase angle) between voltage and amperage.  Formula 2 − Mechanical power equation: Power P = E ⁄ t = W ⁄ t  where power P is in watts, Energy E is in joules, and time t is in seconds. 1 W = 1 J/s.  Power = force multiplied by displacement divided by time P = F × s / t or:  Power = force multiplied by speed (velocity) P = F × v.  Electrical Energy is E = P × t − measured in watt-hours, or also in kWh. 1J = 1N×m = 1W×s    Undistorted powerful sound is not found in these formulas. Please, mind your ears!  The eardrum and microphone diaphragms are really only moved by the waves of the  sound pressure. That does not do either the intensity, nor the power or the energy.  If you are in the audio recording business, it is wise not to care much about the  energy, power and intensity as the cause, care more about the effect of sound pressure  and sound pressure level on the ears and the microphones and the corresponding  audio voltage.  Sound pressure and Sound power – Effect and Cause  Very loud sounding speakers will have a lot of power, but look closer at the very  important efficiency of loudspeakers. This includes the typical question:  How many decibels (dB) are actually twice or three times as loud?  There is really no RMS power. The words "RMS power" are not correct. There is a  calculation of power which is the multiplication of a RMS voltage and a RMS current.  Watts RMS is meaningless. In fact, we use that term as an extreme shorthand for power in  watts calculated from measuring the RMS voltage. Please, read here:  Why there is no such thing as 'RMS watts' or 'watts RMS' and never has been.  Power is the amount of energy that is converted to a unit of time. Expect to pay more when  demanding higher power.

The true power factor and not the conventional 50/60 Hz displacement power factor

Electrical Measurement Definitions
QUANTITY	NAME	DEFINITION
frequency	hertz (Hz)	1/s
force	newton (N)	kg·m/s²
pressure	pascal (Pa) = N/m²	kg/m·s²
energy	work joule (J) = N·m	kg·m²/s²
power	watt (W) = J/s	kg·m²/s³
electric charge	coulomb (C) = A·s
voltage	volt (V) = W/A	kg·m²/A.s³
capacitance	farad (F) = C/V = A·s/V = s/Ω	A²·s4/kg·m²
inductance	henry (H) = Wb/A = V·s/A	kg·m²/A²·s²
resistance	ohm (Ω) = V/A	kg·m²A²·s³
conductance	siemens (S) = A/V	A²·s³/kg·m²
magnetic flux	weber (Wb) = V·s	kg·m²/A·s²
flux density	tesla (T) = Wb/m² = V·s/m²	kg/A·s²