Battery Backup Calculator
How the formula works
A battery backup system stores energy and gives it to a load through an inverter or UPS when the mains power fails. To size it, you need the load, the backup time, the battery voltage, how deeply the battery can be discharged, and the efficiency of the inverter.
1. Load in watts
Load (W) = W, or kW x 1000, or VA x power factor
2. Battery energy needed
Battery energy (Wh) = load (W) x backup time (h) / inverter efficiency
3. Required battery capacity
Capacity (Wh) = battery energy / depth of discharge x (1 + margin)
Capacity (Ah) = capacity (Wh) / battery system voltage
4. Discharge current
Current (A) = load (W) / (inverter efficiency x system voltage)
C-rate = discharge current / battery capacity (Ah)
5. Backup time of a known battery bank
Usable energy (Wh) = Ah x voltage x depth of discharge / (1 + margin)
Backup time (h) = usable energy x inverter efficiency / load (W)
6. Battery bank layout (12 V batteries)
Batteries in series = system voltage / 12
Strings in parallel = ROUNDUP(required Ah / battery Ah)
Total batteries = series x parallel
7. Solar array
Array size (kWp) = daily energy (kWh) / (peak sun hours x performance ratio)
Number of panels = ROUNDUP(array W / panel Wp)
Charge controller current (A) = array W / battery voltage x 1.25
Where
- Depth of discharge (DoD) = the share of the battery energy you are allowed to use
- Peak sun hours = hours per day of full 1000 W per square metre sunshine, a measure of the solar energy at the site
- Performance ratio = overall solar system efficiency after losses from heat, dust, wiring, charge controller and battery charging
Typical values used
- Depth of discharge: lead acid (tubular, flooded, VRLA, AGM, gel) about 50 %, lithium iron phosphate (LiFePO4) about 80 %
- Inverter or UPS efficiency: about 85 % to 95 %
- Ageing factor: about 25 % extra capacity, so the battery still meets the load near end of life
- Peak sun hours: about 3 to 6 hours, depending on the location and season
- Solar performance ratio: about 70 % to 80 %
- VA to watts: power factor about 0.8 for a typical UPS
How to use the calculator
- Select the calculation. For battery size, enter the load, the unit and the backup hours.
- Select the battery system voltage, the battery type and the inverter efficiency.
- Optionally add an ageing margin and a 12 V battery size to see how many batteries are needed.
- For solar, enter the daily energy, the peak sun hours, the performance ratio and the panel rating.
- Click Calculate, then Download PDF Result if you need a record.
Important notes
- Typical values only. The battery datasheet, the inverter datasheet and the site data are final.
- Battery capacity is rated at a slow discharge rate. At a faster rate the real capacity is lower, especially for lead acid batteries, so short backup times need extra capacity.
- Cold temperatures reduce battery capacity. Add a margin if the battery room is not air conditioned.
- Solar sizing here is a simple estimate. A full off-grid design also needs days of autonomy, string layout and charge controller checks.
Worked example
Example 1 – 1000 W load for 4 hours, VRLA batteries
Load 1000 W, backup 4 hours, 24 V system, VRLA (50 % DoD), efficiency 90 %, 150 Ah 12 V batteries.
Battery energy = 1000 x 4 / 0.90 = 4444 Wh (4.44 kWh)
Required capacity = 4444 / 0.50 = 8889 Wh = 8.89 kWh
Capacity in Ah = 8889 / 24 = 370.4 Ah at 24 V
Discharge current = 1000 / (0.90 x 24) = 46.3 A
Batteries in series = 24 / 12 = 2. Strings in parallel = ROUNDUP(370.4 / 150) = 3.
Total = 2 x 3 = 6 batteries of 12 V 150 Ah, giving 450 Ah installed.
Example 2 – UPS in VA with lithium battery and margin
1500 VA UPS, power factor 0.8, backup 2 hours, 24 V system, LiFePO4 (80 % DoD), efficiency 95 %, margin 10 %.
Load = 1500 x 0.8 = 1200 W
Battery energy = 1200 x 2 / 0.95 = 2526 Wh
Required capacity = 2526 / 0.80 x 1.10 = 3474 Wh = 3.47 kWh
Capacity in Ah = 3474 / 24 = 144.7 Ah
Example 3 – How long will my battery last?
200 Ah bank at 24 V, lead acid tubular (50 % DoD), load 600 W, efficiency 90 %.
Usable energy = 200 x 24 x 0.50 = 2400 Wh
Backup time = 2400 x 0.90 / 600 = 3.6 hours (3 h 36 min)
Example 4 – Solar array for 10 kWh per day
Daily energy 10 kWh, peak sun hours 5, performance ratio 75 %, panels 550 Wp, 48 V battery.
Array size = 10 / (5 x 0.75) = 2.67 kWp
Panels = ROUNDUP(2667 / 550) = ROUNDUP(4.85) = 5 panels (2.75 kWp installed)
Expected energy = 2.75 x 5 x 0.75 = 10.31 kWh per day
Charge controller current = 2750 / 48 x 1.25 = 71.6 A
Common mistakes
- Using the full battery rating as usable energy. Lead acid batteries should not be discharged below about 50 %, or their life is cut short.
- Forgetting the inverter or UPS efficiency. The battery has to supply more energy than the load uses.
- Mixing VA and watts. A 1500 VA UPS at 0.8 power factor can supply only 1200 W.
- Ignoring ageing. A battery sized exactly for today’s load will not meet it in a few years, so add a margin.
- Choosing the voltage wrongly. A higher system voltage means a lower current, thinner cables and fewer losses for the same power.
- Sizing for a short backup time without checking the discharge rate. Batteries give less capacity when discharged fast, so the real backup is shorter than the calculated one.
- Connecting batteries of different age, make or capacity in the same string. The weakest battery limits the whole bank.
- Using the peak sun hours of the best month. For a year-round system, use the value for the worst month.
- Forgetting solar system losses. Heat, dust, wiring, controller and battery charging losses mean panels never give their full rating.
Frequently asked questions
How do I calculate battery capacity for an inverter?
Battery energy (Wh) = load (W) x backup hours / inverter efficiency. Then divide by the depth of discharge, and by the battery voltage to get the capacity in Ah.
How many batteries do I need for a 1000 W load for 4 hours?
With a 24 V system, VRLA batteries (50 % DoD) and 90 % efficiency, you need about 370 Ah at 24 V, which is 6 batteries of 12 V 150 Ah (2 in series, 3 in parallel).
What is depth of discharge?
It is the share of the battery energy that you use. A 50 % DoD means you use only half of the rated capacity, which protects the battery life.
What DoD should I use for lead acid and lithium batteries?
As typical values, use about 50 % for lead acid (tubular, flooded, VRLA, AGM, gel) and about 80 % for lithium iron phosphate (LiFePO4).
How do I convert VA to watts?
Watts = VA x power factor. A typical UPS has a power factor of 0.8, so 1500 VA gives about 1200 W. Check your UPS datasheet.
What system voltage should I choose?
Small inverters use 12 V or 24 V, home systems often 48 V, and larger systems 96 V or more. For the same power, a higher voltage means lower current and lower losses.
What is the C-rate of a battery?
The C-rate is the discharge current divided by the battery capacity in Ah. A 100 Ah battery giving 20 A is discharging at 0.2C. Most batteries work best at low C-rates.
How long will my battery last?
Backup time = Ah x voltage x DoD x efficiency / load (W). A 200 Ah, 24 V lead acid bank with a 600 W load gives about 3.6 hours. Use the Backup Time mode to calculate it.
How many solar panels do I need?
Array size (kWp) = daily energy / (peak sun hours x performance ratio). Divide the array watts by the panel rating and round up. For 10 kWh per day, 5 sun hours and 75 % ratio, you need about 2.67 kWp, which is 5 panels of 550 Wp.
What are peak sun hours?
They are the hours per day at which the sun gives 1000 W per square metre. Most locations get about 3 to 6 peak sun hours, depending on the place and the season.
What size charge controller do I need?
Controller current = array watts / battery voltage x 1.25. The 1.25 factor gives a safety margin. Always check the controller voltage and current limits in its datasheet.
Is this calculator a replacement for a system design?
No. It gives a quick estimate. A complete design must check the battery datasheet, discharge curves, temperature, cable sizes, protection and, for solar, the string layout.