2 Corrected diagram - cos, not acos edited Dec 6 '13 at 2:04 Li-aung Yip 7,7861919 silver badges4848 bronze badges 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: Applying some basic trig: 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: 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: Applying some basic trig: 1 answered Dec 6 '13 at 1:54 Li-aung Yip 7,7861919 silver badges4848 bronze badges 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: 