Usable capacity is always less than nameplate capacity, and both depth of discharge and round-trip efficiency reduce it. Enter the daily load in watt-hours, the days of autonomy required, the system voltage, the usable depth of discharge and the round-trip efficiency to get the required capacity in amp-hours, the energy stored, the number of units needed and the daily discharge depth.
Calculator
Units:
Wh
Energy consumed per day at the load
days
Days the bank must sustain the load with no charging
V
Nominal bank voltage. Higher voltage means lower current for the same power
%
50% for lead-acid daily cycling, 80–90% for LiFePO4
%
Including inverter and charge controller. Lithium 85–90%, lead-acid nearer 80%
Ah
Nameplate capacity of one battery at the system voltage
Calculation Result
Press Calculate for the required capacity in amp-hours, the energy stored, the number of units at the size you specified, and the proportion of the installed bank one day's load consumes.
Step-by-Step Solution
Preliminary design aid. Results follow the published formulas cited
below and are intended for estimating, study and early design. Final design must be
verified by a licensed Professional Engineer against the code in force for your project.
Key Benefits
✓Applies both the depth of discharge and the round-trip efficiency correction
✓Converts to a whole number of real battery units
✓Reports the daily discharge depth, which governs cycle life
✓Warns where the depth of discharge suits lithium but not lead-acid
✓Sensitivity chart shows the step function that unit granularity creates
✓Shareable links and CSV export for design records
What Is Battery Bank Sizing?
Battery bank sizing starts from the energy the load needs over the period the bank must cover unaided — the days of autonomy. That energy cannot simply be the bank's nameplate capacity, because discharging a battery fully damages it, and because energy is lost on the way in and out. Dividing by the usable fraction and by the round-trip efficiency gives the capacity that must actually be installed.
Depth of discharge and cycle life
Every battery chemistry trades usable depth against life. Lead-acid cycled to 50% daily lasts roughly three times as long as one cycled to 80%, which is why 50% is the conventional design figure for it despite the extra capacity that implies. Lithium iron phosphate tolerates 80 to 90% routinely, and that single difference is why a lithium bank for a given duty is often little more than half the size of a lead-acid one.
Why the answer moves in steps
Capacity is bought in units, so the required amp-hours are rounded up to a whole number of them. That makes the relationship between design parameters and cost a staircase rather than a slope. In the default case, improving usable depth from 80% to 90% reduces the requirement from 289 Ah to 257 Ah — and changes nothing, because both round up to three 100 Ah units. Improving from 75% to 80%, a smaller change, removes a whole unit.
Formula
E_required = (E_daily × days) / (DoD × η)
Energy that must be installed, grossed up for usable depth and round-trip efficiency
Related Formulas
C_Ah = E_required / V_system
n = ⌈C_Ah / C_unit⌉
Daily depth = (E_daily / η) / (V × C_installed)
Variable Definitions
Symbol
Variable
Unit
Description
E_daily
Daily Load
Wh
Energy consumed per day at the load, before efficiency losses.
days
Days of Autonomy
days
How long the bank must sustain the load with no charging.
V
System Voltage
V
Nominal bank voltage. 12, 24 or 48 V for most installations.
DoD
Depth of Discharge
%
Fraction of nameplate capacity considered usable. 50% lead-acid, 80–90% lithium.
η
Round-Trip Efficiency
%
Energy out divided by energy in, including inverter and controller losses.
C
Capacity
Ah
Nameplate capacity that must be installed.
How to Use This Calculator
Measure the daily load rather than adding up nameplatesSummed appliance ratings assume everything runs continuously at full power, which overstates the real consumption substantially. A metered figure over a representative week is far more reliable, and for a new installation an itemised estimate with realistic duty cycles is the next best thing.
Choose autonomy from the charging source, not from comfortFor a solar system, autonomy covers consecutive days of poor generation. Two to three days suits most temperate sites; less where a generator backs the system up, more where access for maintenance is difficult. Each extra day adds proportionally to the cost.
Set the depth of discharge to the chemistry50% for lead-acid in daily cycling, 80% for LiFePO4, and 90% only where the manufacturer supports it. Using a lead-acid bank at 80% will work and will roughly third its life, which usually costs more than the capacity it saved.
Include inverter losses in the efficiencyBattery round-trip efficiency alone is 90 to 95% for lithium, but at the AC outlet the inverter and charge controller bring it to 85 to 90%. Lead-acid is nearer 80% at the battery and lower still at the outlet.
Read the daily discharge depth as well as the capacityIt shows how hard the installed bank is worked each day, which is what governs cycle life. A bank sized for several days of autonomy is cycled shallowly and lasts much longer than one sized for a single day.
Worked Examples
Example 1
An off-grid installation using 5,000 Wh per day, requiring 2 days of autonomy on a 48 V system. LiFePO4 batteries at 80% usable depth, 90% round-trip efficiency, in 100 Ah units.
Step-by-Step Solution
Energy over the autonomy period: 5,000 × 2 = 10,000 Wh
Grossed up for usable depth and efficiency: 10,000 / (0.80 × 0.90) = 13,889 Wh
The two corrections together add 38.9% to the raw requirement
Capacity at 48 V: 13,889 / 48 = 289.4 Ah
Units required: 289.4 / 100 = 2.89, rounded up to 3 units — 300 Ah installed
Daily discharge depth: (5,000/0.90)/48 = 115.7 Ah, which is 38.6% of the installed 300 Ah
Interpretation: cycling to 38.6% daily is comfortable for LiFePO4 and will give long life. The 2-day autonomy has effectively bought shallow cycling as well as reserve.
Example 2
The same duty on lead-acid instead of lithium — 50% usable depth rather than 80% — which is the comparison that decides most off-grid budgets.
Step-by-Step Solution
Grossed up: 10,000 / (0.50 × 0.90) = 22,222 Wh, against 13,889 Wh for lithium
Capacity at 48 V: 22,222 / 48 = 463.0 Ah
Units required: 463.0 / 100 = 4.63, rounded up to 5 units — 500 Ah installed
Five units against three: the lead-acid bank is 67% larger for identical service.
That is before efficiency is corrected. Lead-acid round-trip efficiency is nearer 80% than 90%, which would push the requirement higher again.
The comparison usually favours lithium on total cost even when the price per kWh of nameplate capacity is higher, because so much less nameplate is needed — and because cycle life at the design depth is longer as well.
There is a boundary effect worth noticing here too. At 80% depth the requirement is 289 Ah and at 90% it is 257 Ah, but both round up to three units. Improving depth from 80% to 90% changes nothing. Improving from 75% to 80% — a smaller change — removes a whole unit, because 309 Ah crosses the three-unit boundary and 289 Ah does not.
Depth of Discharge Sensitivity
Required capacity falls smoothly as usable depth rises, but the battery unit count falls in steps — and between steps, an improvement in depth buys nothing at all. Switch between the two series to see where the boundaries fall. The marker shows your current setting.
Required Capacity vs Usable Depth of Discharge
Recomputed live from your inputs. The marker shows your current value.
Line chart of Required Capacity against Usable Depth of Discharge. The same
values are listed in the data table below.
Values plotted above, sampled across the usable depth of discharge range.
How to Interpret Your Results
The unit count is the practical answer. The daily discharge depth is the one that predicts how long the bank will last, and a shallow daily cycle is worth more than it appears.
Daily Discharge Depth: < 20Shallow daily cycling — long life
Each day takes your result% of the installed bank. Cycle life at this depth is several times what it would be at 50%, so a bank sized generously for autonomy also lasts considerably longer. This is usually the better economic choice over the bank's lifetime.
Each day takes your result% of the installed bank, which is a reasonable working range for most chemistries. Confirm it against the manufacturer's cycle life curve, since the relationship between depth and life is strongly non-linear.
Daily Discharge Depth: 50 – 80Deep daily cycling
Each day takes your result% of the installed bank. Lithium will tolerate this; lead-acid will lose much of its life to it. Adding a day of autonomy reduces the daily depth proportionally and may pay for itself in replacement cycles avoided.
Daily Discharge Depth: ≥ 80Very deep daily cycling
Each day takes your result% of the installed bank, leaving almost no reserve for a poor charging day. Any shortfall in generation puts the bank into deep discharge, which is where damage accumulates fastest in every chemistry.
Battery Units: ≥ 20Large bank — check the configuration
your result units is a substantial bank. Long parallel strings share current unevenly as cells age, so several shorter strings at a higher system voltage is usually better than many units in parallel at a low one.
Common Mistakes to Avoid
Sizing on nameplate capacity
Why it matters:Nameplate assumes a full discharge, which no chemistry tolerates as a daily routine. Using it directly undersizes the bank by the reciprocal of the usable depth — a factor of two for lead-acid at 50%.
✓How to avoid it:Divide by the usable depth of discharge, and again by the round-trip efficiency. Together those corrections added 38.9% in the worked example.
Cycling lead-acid as deeply as lithium
Why it matters:Cycle life falls steeply with depth, and it falls much faster for lead-acid. A lead-acid bank cycled to 80% daily lasts roughly a third as long as the same bank cycled to 50%, so the capacity saved is spent several times over on replacements.
✓How to avoid it:Use 50% for lead-acid daily cycling and 80% for LiFePO4. The chemistry, not the application, sets the figure.
Using battery efficiency instead of system efficiency
Why it matters:Lithium is 90 to 95% efficient at the terminals, but the inverter and charge controller bring the figure at the AC outlet to 85 to 90%. Using the battery figure alone understates the requirement.
✓How to avoid it:Use the round-trip figure measured at the load, including all conversion stages. For lead-acid the difference is larger still.
Ignoring temperature
Why it matters:Capacity falls with temperature — a lead-acid bank at 0 °C delivers roughly 80% of its 25 °C rating. Lithium should not be charged below freezing at all, and many battery management systems will refuse to.
✓How to avoid it:Size on the coldest expected battery temperature, not on ambient air temperature or on the datasheet's 25 °C rating.
Adding autonomy days without checking the charging source
Why it matters:A bank sized for five days of autonomy needs a charging source able to refill it after a five-day outage, on top of meeting the daily load. Otherwise the reserve is used once and never restored.
✓How to avoid it:Check that the array or generator can recover the bank in a reasonable time. On solar, that means looking at the worst month rather than the annual average.
Optimising a parameter that does not cross a unit boundary
Why it matters:Capacity is bought in whole units, so the requirement is a staircase. Improving usable depth from 80% to 90% in the default case reduces the calculated requirement but leaves the unit count at three — the improvement is entirely absorbed by rounding.
✓How to avoid it:Check the unit count, not just the amp-hours. It is worth testing which parameter changes actually move it before paying for any of them.
Practical Applications
▸Sizing off-grid solar battery banks
▸Specifying backup storage for critical loads
▸Comparing lead-acid and lithium options for a given duty
▸Checking whether an existing bank meets a revised load
▸Assessing the effect of additional autonomy days
▸Estimating storage for a self-consumption solar system
Industry Use Cases
Off-grid solar
Autonomy is set by the longest realistic run of poor generation at the site, commonly two to three days in temperate climates. The bank is then sized on the worst month rather than the annual average, since that is when both generation is lowest and the reserve is most likely to be needed.
Telecommunications and critical backup
Backup banks are cycled rarely but must be reliable when called upon, so they are sized shallowly and monitored continuously. Float life rather than cycle life is the governing parameter, and temperature control matters more than in a cycling application.
Residential self-consumption
Storage is sized to the evening load rather than to days of autonomy, because the grid remains available. The economics turn on the spread between import and export prices, which makes the calculation quite different from an off-grid one.
Expert Tips
💡Divide by depth of discharge and by efficiency — both increase the requirement.
💡Lead-acid at 50% needs 67% more capacity than lithium at 80% for the same duty.
💡Cycle life falls steeply with daily depth, and faster for lead-acid than lithium.
💡Capacity comes in whole units, so improvements only help when they cross a boundary.
💡Size on the coldest expected battery temperature, not on ambient.
💡More autonomy also means shallower daily cycling, which extends life twice over.
Advantages & Limitations
Advantages
✓Applies both corrections that separate usable energy from nameplate capacity
✓Converts to a whole number of real units, which is the practical answer
✓Reports the daily discharge depth, which predicts cycle life
✓Makes the staircase effect of unit granularity visible
✓Fast enough to compare chemistries and autonomy periods during design
Limitations
!Assumes a constant daily load, with no seasonal variation
!Takes no account of temperature, which reduces available capacity
!Does not model the charging source or whether it can recover the bank
!Ignores capacity fade over the bank's life, typically 20% before replacement
!Assumes all units are identical and share current evenly
!Does not distinguish float life from cycle life for backup applications
!The relationship between depth of discharge and cycle life is chemistry-specific and not modelled
How Usable Depth Changes the Bank
A 5,000 Wh daily load with 2 days of autonomy on a 48 V system at 90% efficiency, in 100 Ah units. Watch the last two columns diverge — the calculated requirement falls smoothly, the units bought do not.
5,000 Wh/day, 2 days autonomy, 48 V, 90% round-trip efficiency, 100 Ah units. The 60%, 70% and 75% rows all buy four units despite a 77 Ah spread in the calculated requirement — and 80% to 90% is a 32 Ah improvement that buys nothing. The step from 75% to 80% is the only one in that range that removes a unit.
Multiply the daily load by the days of autonomy, divide by the usable depth of discharge and by the round-trip efficiency, then divide by the system voltage. A 5,000 Wh daily load with 2 days autonomy at 80% depth and 90% efficiency needs 289 Ah at 48 V.
What is depth of discharge?
The fraction of nameplate capacity considered usable. Lead-acid is conventionally limited to 50% for daily cycling, LiFePO4 to 80 or 90%, because cycle life falls steeply as the depth increases.
How many days of autonomy do I need?
Two to three days suits most temperate solar installations. Less where a generator provides backup, more where the site is hard to reach or where consecutive poor days are common.
Why is lithium cheaper overall despite costing more per kWh?
Because much less nameplate capacity is needed. At 80% usable depth against lead-acid's 50%, the bank in the example above is three units instead of five — 67% less capacity for identical service, before cycle life is even considered.
What round-trip efficiency should I use?
85 to 90% for a lithium system measured at the AC outlet, and nearer 80% for lead-acid. Battery-only figures are higher, but the inverter and charge controller losses are real and belong in the calculation.
Does temperature affect battery capacity?
Considerably. A lead-acid bank at 0 °C delivers roughly 80% of its 25 °C rating, and lithium generally should not be charged below freezing at all. Size on the coldest expected battery temperature.
Why does improving depth of discharge sometimes change nothing?
Because capacity is bought in whole units. In the example, 80% depth needs 289 Ah and 90% needs 257 Ah, but both round up to three 100 Ah units. The improvement is absorbed entirely by the rounding.
Should I use a higher system voltage?
Generally yes for anything above a few hundred watt-hours a day. Higher voltage means lower current for the same power, which allows thinner cables, reduces losses and avoids long parallel strings that share current unevenly.
How does daily discharge depth affect life?
Strongly and non-linearly. A lead-acid battery cycled to 50% daily lasts roughly three times as long as one cycled to 80%. This is why a bank sized generously for autonomy also gains life from the shallower cycling it experiences.
Should I allow for capacity fade?
Yes for a long-lived installation. Batteries are usually considered end-of-life at 80% of original capacity, so a bank sized exactly to requirement on day one will fall short before it is replaced.
Glossary
Depth of discharge
The fraction of nameplate capacity used in a cycle, which governs cycle life.
Days of autonomy
How long the bank must sustain the load with no charging input.
Round-trip efficiency
Energy delivered to the load divided by energy supplied to the bank, including conversion losses.
Nameplate capacity
The rated capacity of a battery, of which only part is usable in practice.
Cycle life
The number of charge-discharge cycles before capacity falls to a defined end-of-life threshold.
LiFePO4
Lithium iron phosphate, the chemistry most used for stationary storage.
Float life
Life of a battery held at full charge and rarely cycled, the governing figure for backup banks.
Capacity fade
The gradual loss of capacity over a battery's life, typically to 80% before replacement.
State of charge
The fraction of usable capacity currently remaining.
Battery management system
Electronics that protect cells from over-charge, over-discharge and unsafe temperatures.
Scientific & Standards References
IEEE 1013 — Recommended Practice for Sizing Lead-Acid Batteries for Stand-Alone Photovoltaic Systems — Institute of Electrical and Electronics Engineers
IEC 62620 — Secondary lithium cells and batteries for use in industrial applications — International Electrotechnical Commission
IEEE 1188 — Recommended Practice for Maintenance, Testing and Replacement of VRLA Batteries — Institute of Electrical and Electronics Engineers
Sandia National Laboratories — Stand-Alone Photovoltaic Systems: A Handbook of Recommended Design Practices — Sandia National Laboratories
IEC 61427-1 — Secondary cells and batteries for renewable energy storage — International Electrotechnical Commission
Conclusion
Sizing a battery bank is two divisions applied to the load, and both make the answer larger: one for the fraction of capacity you are prepared to use, and one for the energy lost converting it. Together they added 38.9% in the worked example. The parameter that then dominates the cost is depth of discharge, because it is chemistry-dependent rather than adjustable — lead-acid at 50% needs 67% more capacity than lithium at 80% for identical service, which is why the comparison usually favours lithium even at a higher price per kilowatt-hour. The last thing to keep in view is that real capacity comes in units, so the requirement is a staircase rather than a slope. In the table above, three different usable depths all buy four units, and the improvement from 80% to 90% buys nothing at all. Before paying for a better parameter, check whether it actually crosses a boundary.
Enter your daily load, autonomy and chemistry above to size a bank.
