What the Battery Backup Runtime Calculator does
This calculator tells you how long a battery bank, home inverter or UPS will keep a load running, from the battery's capacity in amp-hours or watt-hours, its voltage, how deeply you are willing to discharge it and the inverter's efficiency. Enter the runtime you need and it also works out the capacity that would deliver it.
For lead-acid batteries it can apply Peukert's law, which captures the part most simple calculators leave out: a lead-acid battery drained quickly gives noticeably less energy than its label promises, because the label is measured over 20 hours.
How to use it
- Choose the chemistry. It sets a typical usable depth of discharge - 50% for lead-acid, 80-90% for lithium - which you can change to match your battery's data sheet.
- Enter the capacity and the bank voltage. Two 12 V 150 Ah batteries in series are a 24 V 150 Ah bank; in parallel they are 12 V 300 Ah. Both are 3,600 Wh.
- Enter the load in watts: the total of everything the battery will run at the same time. Use the inverter size calculator if you need to add appliances up.
- Set the inverter efficiency, or 100% for a DC load connected straight to the battery.
- Leave Peukert on for lead-acid banks. Enter the rated discharge time from the data sheet (C20 means 20 hours).
- Optionally enter the runtime you need to see the capacity required, and read the table to see how runtime changes if the load changes.
Reading the results
Runtime is the time until the battery reaches the depth of discharge you set, not until it is completely flat. Stopping at 50% is what keeps a lead-acid battery alive for hundreds of cycles.
Battery current and C-rate show how hard the load pushes the bank. 0.05C is the gentle 20-hour rate; lead-acid loses real capacity above about 0.2C, lithium chemistries far less.
When Peukert is on, compare the two runtimes. The gap is the capacity a lead-acid battery cannot deliver at your load; it shrinks as the load falls towards the rated 20-hour current.
Worked example: a 150 Ah home inverter battery running 300 W
A 12 V 150 Ah flooded lead-acid battery stores 12 x 150 = 1,800 Wh. Using half of it (50% depth of discharge) through an 85% efficient inverter leaves 1,800 x 0.5 x 0.85 = 765 Wh at the socket, so a simple estimate at 300 W is 765 / 300 = 2.55 hours.
The battery current is 300 / (12 x 0.85) = 29.4 A, well above the 7.5 A that would empty it in 20 hours. With a Peukert exponent of 1.25, the full-discharge time is 20 x (150 / (29.4 x 20))^1.25 = 20 x 0.255^1.25 = 3.62 hours, and half of that is 1.81 hours.
To run the same 300 W for 3 hours to 50% with Peukert applied, the bank would need 29.4 x 20 x (3 / (0.5 x 20))^(1/1.25) = about 225 Ah.
Formulas and scoring rules
- Stored energy
Wh = Ah x V- Simple runtime
hours = Wh x DoD x inverter efficiency / load W- Battery current
I = load W / (V x inverter efficiency)- Peukert runtime
hours = H x (Ah / (I x H))^k x DoDH is the rated discharge time (20 for C20), k the Peukert exponent. At the rated current I = Ah / H it gives exactly H hours.- Capacity needed
Ah = load x hours / (V x DoD x efficiency); with Peukert, Ah = I x H x (hours / (DoD x H))^(1/k)
Limitations: what the result does not prove
- Peukert's law is an approximation fitted to constant-current tests. Real loads switch on and off, and temperature, age and the battery's state of health change capacity further; an old battery may give half its label.
- Cold reduces capacity. Lead-acid at 0 °C typically gives around 20% less than at 25 °C; the calculator assumes room temperature.
- Lithium batteries also have a battery management system that may cut off earlier or limit current. Its settings, not this formula, decide the true usable capacity.
- It does not size the charger, solar input or cable. A UPS or inverter also has its own maximum current and standby draw, which shorten runtime at very light loads.
Privacy: where your data goes
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Standards and sources
- Sandia National Laboratories - Energy storage systems handbook
- NREL - PVWatts Version 5 Manual (system losses, for sizing solar charging)
Frequently asked questions
How long will a 150 Ah battery last with a 300 W load?
About 2.5 hours to 50% depth of discharge through an 85% efficient inverter, using the simple formula. For a lead-acid battery the Peukert effect at that current brings it nearer 1.8 hours. A lithium battery of the same size, used to 90%, would run about 4.6 hours.
Why should lead-acid batteries only be discharged to 50%?
Cycle life falls steeply with depth of discharge. A typical deep-cycle lead-acid battery might manage several hundred cycles at 50% but far fewer if routinely taken to 80% or more. Using only half the capacity is the trade-off for a battery that lasts years instead of months.
What is Peukert's exponent and where do I find it?
It describes how much capacity a battery loses as the discharge current rises. 1.0 would mean no loss; flooded lead-acid is often 1.2-1.3, AGM and gel 1.1-1.15, lithium close to 1.05. Some data sheets state it; otherwise it can be worked out from two rated capacities at different hours.
Should I enter the capacity in amp-hours or watt-hours?
Either, as long as the voltage is right. Amp-hours only mean something together with a voltage, so a 100 Ah 12 V battery and a 100 Ah 48 V battery hold very different energy (1.2 kWh and 4.8 kWh). Watt-hours already include the voltage and are easier to compare across banks.
How do I work out the battery size for a runtime I need?
Enter the runtime in the optional box. The calculator divides load x hours by voltage, depth of discharge and inverter efficiency, and, if Peukert is on, raises the result for the extra loss at that current. Round up to the next battery size you can actually buy.
Does a UPS use the same calculation?
Yes for the battery side, but a UPS inverter's efficiency at light load can be well below its rating, and it draws some power itself. Manufacturers publish runtime charts for their models; use those where they exist and this calculation to check battery replacements or external packs.
What does C-rate mean?
It is the discharge current as a fraction of the amp-hour rating. A 100 Ah battery supplying 10 A is at 0.1C; supplying 50 A it is at 0.5C. Low C-rates are gentle, and lead-acid in particular gives much less usable capacity and ages faster at high C-rates.
Last reviewed by the A2Z.Tools team against the sources listed above.
