AC equations page.

Thread Starter


Joined Aug 11, 2008
Hi ALL from an electrician in the U.K.,

Mentioned on the page for A.C. circuit equations under Volume V area.

Single phase power in Watts ( W ) should be

P = Vp Ip Cos\(\phi\)

Where P is power in watts, Vp is the phase voltage, Ip is the phase current and Cos\(\phi\) is the power factor.

In other words P = Vp X Ip X Cos\(\phi\)

The power factor is the cosine of the angle phi or \(\phi\) and this is the angle the phase current waveform lags or leads the voltage waveform.
Ideally the angle phi or \(\phi\) should be close to zero
so that Cos \(\phi\) = 1

I.E. Cos(0) = 1

3 phase power in Watts is

P = Square Root(3) VL IL Cos\(\phi\)

Where VL is the Line Voltage between any two phases,
IL is the Line Current and Cos\(\phi\) is the power factor.

Additionally in all 3 phase systems the Line Voltage VL can be calculated by this

VL = Square Root(3) Vp

where the square root of 3 is approx 1.7320508075688772935274463415059
and Vp is the phase voltage.

In the U.K. and other countries

Vp = 240 Volts A.C. or 240VAC and VL = 415 Volts A.C. or 415VAC

Some countries use 220 Volts A.C.

In the USA the domestic Vp or phase voltage is 110Volts A.C. , or so I've heard. So that would make VL >>

110 X 1.7320508075688772935274463415059 =


approx 191 Volts A.C.


Last edited:


Joined Nov 17, 2003
Hi DrMarten, welcome to AAC.

You are correct in your assessment. The single-phase equations are covered in that reference section, however as you note the three-phase equations are not. I assume this is because the Power Factor section of the e-book merely deals with the case of single phase (ref. even though we have a comprehensive three-phase section (ref.

The reference section may benefit from your suggested addition. Thanks.