Batteries
Battery autonomy (hours of supply)
- where
- hours of supply (h)
- usable battery energy (kWh)
- reserve kept back (%)
- average load (kW)
Explain this equation
Estimates how long a battery can run a given load, for example overnight or during a power cut.
E_u is the usable energy. Some batteries keep a reserve back for backup or to protect the cells, so only 1 − r/100 of it is available. Energy in kWh divided by power in kW gives hours.
Time equals energy divided by power.
Sense check: 9 kWh running an average 0.4 kW load lasts about 22 hours. Double the load and it halves.
Watch out: the load is rarely steady. A kettle or shower can exceed the battery inverter's power rating even when there is plenty of energy left.
Roughly how long a battery can run the home's load, for evening coverage or backup planning.
Enter your values to see the result.
Good to know
Use usable energy from the previous calculator. Evening loads in a typical home are a few hundred watts with peaks from cooking and kettles. Check the inverter's continuous and peak output too: a battery with plenty of energy can still trip on a large load.
Common mistake
Dividing by a single appliance's power rather than the true average over the period.
Limits
Constant average load. Real autonomy depends on load profile, inverter standby draw and battery temperature.
Sources
- IET Code of Practice for Electrical Energy Storage Systems, 2nd edition
- Module manufacturer datasheet: STC values (Voc, Vmp, Isc, Imp, Pmax), temperature coefficients of Voc, Pmax and Isc, NOCT/NMOT and dimensions
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow MCS standards, manufacturer data, BS 7671, the ENA connection rules and Building Regulations. System design and DNO applications need a competent, certified installer.