2 Corrected diagram - cos, not acos
source | link

No need for a complicated formula.

If you have balanced three-phase power, where all three phase voltages are equal in magnitude and 120° apart in phase, then:

$$ V_{L-L} = \sqrt{3} \times V_{L_N} $$$$ V_{L-L} = \sqrt{3} \times V_{L-N} $$

To see why, consider the phasor diagram:

enter image description here

Applying some basic trig:

enter image description here

No need for a complicated formula.

If you have balanced three-phase power, where all three phase voltages are equal in magnitude and 120° apart in phase, then:

$$ V_{L-L} = \sqrt{3} \times V_{L_N} $$

To see why, consider the phasor diagram:

enter image description here

No need for a complicated formula.

If you have balanced three-phase power, where all three phase voltages are equal in magnitude and 120° apart in phase, then:

$$ V_{L-L} = \sqrt{3} \times V_{L-N} $$

To see why, consider the phasor diagram:

enter image description here

Applying some basic trig:

enter image description here

1
source | link

No need for a complicated formula.

If you have balanced three-phase power, where all three phase voltages are equal in magnitude and 120° apart in phase, then:

$$ V_{L-L} = \sqrt{3} \times V_{L_N} $$

To see why, consider the phasor diagram:

enter image description here