As we know, the voltage is the difference in potential between the two-point.
A single-phase power system is one where there is only one alternating voltage source.
Single-phase consists of just two conductors, one is called phase and the other is neutral.
Voltage is measured between a phase and neutral.
While the 3 phase is the voltage between any two out of those three phases.
In 3 phase supply, there are 3 supply lines phase shifted at 120 degrees from each other.
So the net voltage difference between the two phases in accordance with the phase angle of 120 degrees is 440V.
As shown in the figure below, the 3 phase supply has three wires (RYB).
The voltage across any one phase and neutral is 220V, and the voltage across the 3 phase is 440V because we check the voltage between any two-phase RY or YB or BR.
Why 440 volts?
Consider one sine wave that has a maximum amplitude of 220 with respect to its axis. So be it in a positive cycle or in a negative it can go to a max of 220 (+220 or -220).
But when you consider the voltage between one phase to the other then it becomes 440.
Now all the 3 phases have the same max RMS value. That is if considered any of the phases and check their voltage against neutral it will come to 220 or 240 volts or so.
While in the case of three phases the voltage can be used between two phases instead of one phase and neutral. Be it three phases but you can calculate voltage between any two of them at a time.
The maximum voltage that one can get from any two phases is when one is at the top of its positive cycle (i.e +220) and the other at the lowest of its negative cycle (-220).
If we check the voltage between these two points then it is 440 volts ((+220)-(-220)=440).