Power Formulas in DC and AC SinglePhase & ThreePhase Circuits
Electric Power Formulas & Equations in DC and AC 1Φ & 3Φ Circuits
Back to basic, below are the simple Electric Power formulas for Single Phase AC Circuit, Three Phase AC Circuits and DC Circuits. You can easily find electric power in watts by using the following electric power formulas in electric circuits.
Table of Contents
Basic Electric Power Formula in AC & DC Circuits
Power Formulas in DC Circuits
 P = V x I
 P = I^{2} x R
 P = V^{2} / R
Power Formulas in Single Phase AC Circuits
 P = V x I x Cos Ф
 P = I^{2} x R x Cos Ф
 P = V^{2} / R (Cos Ф)
Power Formulas in Three Phase AC Circuits
 P = √3 x V_{L }x I_{L} x Cos Ф
 P = 3 x V_{Ph }x I_{Ph} x Cos Ф
 P = 3 x I^{2} x R x Cos Ф
 P = 3 (V^{2} / R) x Cos Ф
Where:
 P = Power in Watts
 V = Voltage in Volts
 I = Current in Amperes
 R = Resistance in Ohms (Ω)
 Cos Ф = Power Factor
AC Power Formulas in Complex Circuits:
Complex Power & Apparent Power:
When there is an inductor or capacitor in a circuit, the power becomes complex power “S”, meaning it has two parts i.e. real & imaginary part. The magnitude of Complex power is called Apparent power S.
 P is the real power
 Q is the reactive power
Active or Real Power & Reactive Power:
The real part is Complex power “S” is known as active or real power “P” & the imaginary part is known as reactive power “Q”.
 S = P + jQ
 P = V I cosθ
 Q = V I sinθ
Where
θ is the phase angle between voltage & current.
Power Factor:
Power factor “PF” is the ratio of real power “P” to apparent power “S”. Mathematically, Power factor is the cosine of angle θ between real power and apparent power.
S = √(P^{2}+Q^{2})
Other formulas used for Power Factor are as follow:
Cosθ = R/Z
Where:
 Cosθ = Power Factor
 R = Resistance
 Z = Impedance (Resistance in AC circuits i.e. X_{L}, X_{C} and R known as Inductive reactance, capacitive reactance and resistance respectively).
Cosθ = kW / kVA
Where
 Cosθ = Power Factor
 kW = Real Power in Watts
 kVA = Apparent Power in VoltAmperes or Watts
Additional formulas used for power factor.
 Cosθ = P / V I
 Cosθ = kW / kVA
 Cosθ = True Power/ Apparent Power
Real Power Of Single Phase & 3Phase Current
Where
 V_{rms } & I_{rms} is the root mean square value of voltage & current respectively.
 V_{LN }& I_{LN } is the linetoneutral voltage & current respectively.
 _{ }V_{LL} & I_{LL }is the linetoline voltage & current respectively.
 Cosθ is the power factor PF.
Reactive Power Of Single & 3Phase Current:
Where
θ = is the phase angle i.e. phase difference between voltage and current.
The following table shows the different electrical power formulas in both AC and DC circuits.
Quantity  DC  AC (1Phase)  AC (3Phase) 
Power (W) 



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When there is no retreat, the potential power will be exerted.
Dear i want to know about, why we rated primmover in MW (MegaWatt) while our Generator rated in KVA………please tell me.
The out put of the Generator will change depending on the load power factor ,0.8, 0.9 or unity power factor which is only in lighting load also if capacitance load is their the KW OR MEGA WATT WILL BE MORE.
This Answer KVA*.8=KW And KW/1000= Mega Watt
Hi Arsalan,
Check it here.
Why Generator / Alternator rated in kVA?
Why Motor Rated in kW?
In 45 kw ac drive, output motor consumes 30kw, then another how much dc current use in dc bus.
Means what is the formula od dc current.
Sir i want to know about single phase circuit. pls help me.
If you are talking about single phase formulas and MCQS, check it here.
Dear sir,
i want to know about contactor relays its types rating wiring could you please help me in this matter
Can you tell me about load calculation and size of wire depending on load
Hi Mohammad,
Check the Wire size and Load calculation tutorials with examples here.
Check the Wire size calculator here.
Sir i want to know in detail about KVA
Hi Naeem,
Check the kVA power triangle here.
Formula P=(I^2)*(R)*Cos(A) is P=(I^2)*R.
P=3*(I^2)*(R)*Cos(A) is P=3*(I^2)*R.