Calculating Battery required for solar powered motor
Your answer would be approximately correct only if your battery voltage was ~= 220V.
As that is probably not what you had in mind, your answer is probably wrong.

IF you are using a lower voltage battery then you need to use energy rather than current capacity to calculate equivalent amounts at different voltages.

A 420 Watt motor requires 420 Wh (Watt Hours) of energy per hour. That's the easy part :-).

The Wh capacity of a battery is V_battery x Ah_capacity_battery.
Battery energy capacity in Wh = V x Ah
If voltage is changed energy will be lost in the process.
Call the efficiency factor Zbm = Z_battery_motor, where Zbm &lt; 1.
eg if Zbm = 0.85 then 15% of the energy is lost during conversion.
 figure of Zbm = 0.8 is an OK starting point from say 12V or 24V to 220V.

Motor energy requirement per hour = Wm  = Vbat  x Ibat / Zbm
Ibat = Wmotor / Vbat / Zbm
For a 24 V battery Ibat = Wm/Vb/Zbm = 420/24/.8 ~= 22A.
To run the system for one hour you'd need a nominally 22Ah battery. BUT batteries are usually rated at the 10h rate or some other period of some hours, so at the 1h rate they will have much lower capacity. You would need to look at specifications for the battery you had in mind but a factor of say 1.5 is probably not overly pessimistic. So Ah required from 1h operation ~= 1.5 x 22 = 33Ah.
If you want to not go below 50% capacity (which is very wise for lead acid batteries) you need double that so say 66Ah.

So your originally stated 40 Ah battery would run a 420W motor at 220V for about 60 minutes x 40/66 ~+ 36 minutes IF it was a 24V battery. A 12V battery with the same assumptions would run the motor for about 18 minutes.

A lot depends on assumptions made.
Above I have used:


Up converter efficiency low voltage to 220V = 80%
Battery 1h Ah rate = Specification sheet rate / 1.5
Discharge depth = 50%
12V or 24V system.