Calculators
Inverter battery backup calculator
By Bulan Sarkar
Tick off what you run during a power cut, enter your battery and inverter, and get the backup time in hours and minutes. It allows for how deep the battery may be drained, the inverter's losses and the fact that a lead-acid battery gives less than its label when it is drained fast. Flip it round to find the battery a target backup time needs. The defaults follow the usual Indian home set-up: a 150 Ah, 12 V tubular battery, or two of them in series for 24 V.
What runs during a power cut
- Ceiling fan, ordinarytypical 75 W2
- Ceiling fan, BLDCtypical 30 W0
- LED bulbtypical 9 W4
- LED tube lighttypical 20 W0
- LED TV, 32 to 43 inchtypical 60 W1
- Wi-Fi routertypical 10 W1
- Refrigerator (average)typical 100 W0
- Laptop, chargingtypical 50 W0
- Phone chargertypical 10 W0
Watts from the label, or from a plug-in meter.
Total load
256 W
The watts are typical figures, not any particular model. A BLDC fan's rating is on its box; a fridge's 100 W is the average of a compressor that runs about half the time.
The battery and inverter
Deep-cycle, so 80 % is allowed. Stopping nearer 50 % on each outage gives a longer life.
Square and modified-sine home inverters: 75 to 85 %. Good sine-wave units: 90 % or so.
- Backup time
- 4 h 1 min
- 4.01 hours at a steady 256 W
- The quick formula says
- 5 h 38 min
- Ah × V × efficiency ÷ load, with no depth-of-discharge limit
- Drawn from the battery
- 320 W
- 26.7 A at 12 V
- Capacity at this current
- 134 Ah
- against 150 Ah at C10; the battery runs at about C6
- Energy used
- 1.28 kWh
- of 1.8 kWh on the labels
- Inverter size
- 350 VA or more
- load ÷ 0.8 power factor, plus room for motor starts
The formula
hours = Ah × V × batteries × DoD × efficiency / load W
Ah × V is the energy on the label, in watt-hours: a 150 Ah, 12 V battery holds 1,800 Wh. The inverter loses some of it as heat, so a 200 W load at 80 % efficiency pulls 250 W from the battery. And no battery is run all the way to empty: the depth of discharge (DoD) is the share you actually use. That formula, with DoD, is most of the answer.
The rest is the discharge rate. A lead-acid battery's Ah figure is measured over 10 hours (C10) or 20 hours (C20). An inverter running a few fans and lights often drains it in four or five, and at that pace it delivers less. The calculator corrects for this with Peukert's law, t = H × (C / (I × H))k, using k = 1.2 for tubular, 1.25 for flat-plate and 1.1 for sealed batteries. Those sit at the low end of the ranges usually quoted (1.2 to 1.6 for flooded, 1.05 to 1.15 for sealed AGM), so the correction is on the gentle side. LiFePO4 is treated as having no rate loss at these currents. Turn the correction off to see the simpler figure.
Worked examples
One 150 Ah battery, two fans, four bulbs, the router and the TV
The load: two ordinary ceiling fans at 75 W, four 9 W LED bulbs, a 10 W router and a 60 W TV, 256 W in all. Through an 80 % inverter the battery supplies 320 W, which is 26.7 A from 12 V.
The quick formula, 150 × 12 × 0.8 / 256, says 5 h 38 min. Allow 80 % depth of discharge and it drops to 4 h 30 min. The battery is rated at C10, 15 A, but it is being drained at 26.7 A, and at that rate it gives about 134 Ah rather than 150. The calculator's answer is 4 h 1 min. A 150 Ah LiFePO4 battery (12.8 V) on the same load and the same 80 % gives 4 h 48 min, mostly because it has no rate loss.
Six hours with the fridge on, on a 24 V system
Add a refrigerator to the same house and the load becomes 356 W. For six hours on two 12 V tubular batteries in series (24 V), at 80 % DoD and 80 % inverter efficiency, each string carries 18.5 A. Solving the Peukert equation for capacity gives 145.9 Ah per battery, so a pair of 150 Ah batteries does it, with 6 h 12 min of backup.
A single 12 V battery would have to deliver twice the current, 37.1 A, and would need 291.8 Ah, more than any single inverter battery on the shelf. That is why bigger home systems go to 24 V: the same energy at half the current, which the rate correction rewards. The inverter must also handle the fridge's starting surge, which is several times its running power.
Backup at a glance
One 12 V tubular battery rated at C10, 80 % depth of discharge, 80 % inverter. Loads are steady watts at the socket.
| Battery | 100 W | 200 W | 300 W | 500 W |
|---|---|---|---|---|
| 100 Ah | 7 h 37 min | 3 h 19 min | 2 h 2 min | 1 h 6 min |
| 150 Ah | 12 h 23 min | 5 h 24 min | 3 h 19 min | 1 h 48 min |
| 200 Ah | 17 h 30 min | 7 h 37 min | 4 h 41 min | 2 h 32 min |
Depth of discharge by battery type
| Type | Default DoD | Rate exponent |
|---|---|---|
| Lead-acid, tubular (flooded) | 80 % | 1.2 |
| Lead-acid, flat plate (flooded) | 50 % | 1.25 |
| Lead-acid, sealed (SMF / VRLA) | 50 % | 1.1 |
| Lithium (LiFePO4) | 80 % | none |
PVEducation's notes on lead-acid batteries put a deep-cycle battery's depth of discharge above 50 % and as high as 80 %, with more than 1,000 cycles even beyond 50 %. Tubular inverter batteries are the deep-cycle kind, so the calculator starts them at 80 %. Flat-plate and sealed batteries start at 50 %. Lithium iron phosphate (LiFePO4) cells last thousands of cycles, and makers commonly rate that life at 80 % DoD, so 80 % is the starting point there too. Every default can be changed.
Change the DoD to 50 % for a tubular battery and the backup falls, but the battery lasts more years. That is the trade the setting controls. Cold matters as well: lead-acid capacity falls by roughly 1 % for every degree below about 20 °C.
Where the appliance watts come from
The list uses typical running figures, not measurements of any particular model. An ordinary induction-motor ceiling fan draws about 70 to 80 W at full speed, and a BLDC fan about 30 W, so changing the fans stretches the backup a long way. The refrigerator's 100 W is an average: Prayas (Energy Group) logged 86 refrigerators in Maharashtra minute by minute and found an average draw of about 100 W, with the compressor running about half the time. The compressor's running power is higher than the average, and its start-up surge higher again, which is what the inverter's VA rating has to cover.
For anything else, the watts on the rating label are a maximum; a plug-in energy meter gives the real figure. Inverter efficiency depends on the design and the load: good sine-wave inverters reach 90 to 95 %, cheaper modified-sine units 75 to 85 %, and all of them do much worse below about 10 to 15 % of their rating. A 1,500 VA inverter running a single 60 W TV is in that poor region.
The lessons on batteries in series and parallel and battery types cover why series doubles the voltage but not the Ah, and why runtime is never simply capacity divided by current.