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. In the US and Canada the same sum works for a 12 V deep-cycle or LiFePO4 battery on an inverter: enter its Ah and voltage. The socket voltage, 120 V or 230 V, makes no difference to the answer.
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
Quick answer
Backup hours = Ah × V × batteries × depth of discharge × inverter efficiency ÷ load watts, less a little for a lead-acid battery drained fast. One 150 Ah, 12 V tubular battery running two fans, four LED bulbs, a router and a TV (256 W) lasts about 4 h 1 min.
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, from batteries of a size the shop stocks, with cooler cables. The inverter must also handle the fridge's starting surge, which is several times its running power.
What battery runs 1,000 W for two hours?
A steady 1 kW through an 80 % inverter pulls 1.25 kW from the battery. On one 12 V tubular battery that is 104 A, and with the rate correction it would need 328 Ah. No single inverter battery on the shelf is that big.
Two in series at 24 V carry 52.1 A and need 164 Ah each, so a pair of 165 Ah batteries gives 2 h 1 min. Four in series at 48 V carry 26 A and need 82 Ah each; four 100 Ah batteries give 2 h 32 min. The label energy needed is the same every time, about 3,937 Wh. Each step up in voltage halves the current and the Ah each battery needs, which brings it down to sizes a shop stocks. The 48 V bank runs longer only because 82 Ah rounds up to 100.
A 100 Ah LiFePO4 battery on 100 W
An off-grid example: one 100 Ah, 12.8 V LiFePO4 battery, a sine-wave inverter at 90 % and a steady 100 W (a laptop charging, a BLDC fan and a few LED bulbs). The battery supplies 111 W, which is 8.68 A. The quick formula, 100 × 12.8 × 0.9 / 100, says 11 h 31 min. Stop at 80 % depth of discharge and the answer is 9 h 13 min. Lithium has no rate loss at this current, so that is the whole correction.
The socket voltage does not enter the sum. A 120 V inverter and a 230 V one running the same 100 W draw the same current from the battery; only the watts and the inverter's efficiency count.
The same battery four years on
Lead-acid capacity falls with age. Say a capacity test shows the 150 Ah battery from the first example now holds 80 % of its label, 120 Ah. Enter 120 Ah with the same 256 W load and the backup drops from 4 h 1 min to 3 h 4 min. This is one reason a set-up that ran through the evening when new cuts out before the power comes back a few years later.
Worked example in numbers
- Load
- 256 W
- Drawn from the battery
- 320 W
- Usable capacity
- 134 Ah
- Backup
- 4 h 1 min
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 Celsius (1.8 °F) below about 20 °C (68 °F).
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.
Tips and tricks
- Change the fans before you buy a bigger battery. With BLDC fans in place of the two ordinary ones, the same 150 Ah battery goes from 4 h 1 min to 6 h 45 min on the example load.
- Measure the load for one evening with a plug-in energy meter. Rating-label watts are maximums, and the real draw is often lower.
- Don't mix an old battery with a new one in series. The weaker one sets the limit and gets drained harder than the other.
- On a tubular battery, check the electrolyte level every month or two and top up with distilled water only. Low electrolyte loses capacity for good.
- Re-run the numbers each year. Lead-acid capacity falls with age, so the backup you timed when the battery was new won't hold in its fourth year.
- Keep a lead-acid battery in a ventilated spot, since it gives off hydrogen while it charges. The inverter's mains connection and any changeover switch are a job for a licensed electrician.
What we would do
For fans, lights, the router and a TV, we would buy one 150 Ah tubular battery and a sine-wave inverter of about 900 VA to 1 kVA, and swap to BLDC fans as they need replacing. If the fridge has to stay on through long cuts, go to 24 V with two batteries sized from the second worked example. If cuts are long and come every day, LiFePO4 is worth pricing, as long as the inverter supports it. Whatever you pick, enter the real numbers here before you pay.
Questions people ask
How long will a 150 Ah battery last on an inverter?
On a steady 200 W, one 12 V, 150 Ah tubular battery through an 80 % inverter at 80 % depth of discharge gives about 5 h 24 min. With two ordinary fans, four LED bulbs, the router and a TV (256 W) it gives about 4 h 1 min. The table on this page has 100, 150 and 200 Ah at four loads.
How do I calculate inverter backup time?
Multiply the battery Ah by its voltage and the number of batteries to get watt-hours, take the share you will really use (depth of discharge), multiply by the inverter efficiency, and divide by the load in watts. Lead-acid batteries give less than their label when drained fast, which this calculator corrects for.
Does a 24 V system give more backup than 12 V?
Two 150 Ah batteries hold the same energy whether they are wired for 12 V or 24 V. The 24 V system draws half the current from the battery terminals for the same load, so the cables and the inverter run cooler. Each battery carries the same current either way (in parallel they share it), so the backup time comes out the same. The inverter has to match the battery voltage.
Can a home inverter run a refrigerator?
Often, yes. A fridge averages about 100 W, but its compressor runs at a higher power and starts with a surge several times that. The inverter's VA rating has to cover the start, and the battery has to cover the average over the hours you want.
Is a LiFePO4 battery better than a tubular one for an inverter?
It gives more backup from the same Ah, because it has no rate loss at these currents: 4 h 48 min against 4 h 1 min on the example load. It also lasts thousands of cycles. It costs more to buy and needs an inverter or charger set up for lithium. It suits homes where long cuts come every day; for occasional short ones a tubular battery is enough.
How long will a 100 Ah battery last?
One 12 V, 100 Ah tubular battery through an 80 % inverter at 80 % depth of discharge runs a steady 100 W for about 7 h 37 min, 200 W for about 3 h 19 min and 500 W for about 1 h 6 min. A 100 Ah LiFePO4 battery on 100 W through a 90 % inverter gives about 9 h 13 min.
How long will a 200 Ah battery last?
On the same settings, one 12 V, 200 Ah tubular battery runs 100 W for about 17 h 30 min, 200 W for about 7 h 37 min and 500 W for about 2 h 32 min. Twice the Ah gives a little more than twice the time, because each amp is a smaller share of a bigger battery.
What size battery do I need to run 1,000 W for 2 hours?
On 12 V it would take one 328 Ah battery, which no shop sells as a single inverter battery. Go to 24 V with two 165 Ah batteries (2 h 1 min) or 48 V with four 100 Ah batteries (2 h 32 min), on an inverter rated for that voltage and for the load's starting surge.
Why does my inverter give less backup than the calculation?
Three things to check. The battery may have aged: at 80 % of its label, the example battery drops from 4 h 1 min to 3 h 4 min. The real load may be higher than you think, which a plug-in energy meter shows. Or the inverter is running far below its rating, where its efficiency falls well under 80 %.
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