When you need to know exactly how long your off-grid power system will run before the lights go out, a battery length calculator is your most critical design tool. The direct answer to sizing your bank comes down to this core formula: Battery Capacity (Ah) = (Daily Watt-Hours / Inverter Efficiency) / (DoD * System Voltage). However, plugging raw numbers into this equation without accounting for Peukert's effect, depth of discharge (DoD) limits, and C-rate constraints will leave you with a bank that dies prematurely or trips its battery management system (BMS) under load.
This guide walks through the exact physics, system block architecture, and sizing math required to calculate true battery runtime for 12V, 24V, and 48V systems, ensuring your inverter and charge controllers are perfectly matched to the cells.
The Source-to-Load System Block
Before calculating capacity, you must define the system block from source to load. A standalone off-grid system follows a strict power flow: Generation (Solar/Grid/Gen) → Charge Controller/Inverter-Charger → Battery Bank → Inverter → AC/DC Loads.
The inverter and charger sizing dictate the physical limits of your battery length. If your continuous AC load is 2,000W, you cannot simply buy a 2,000W inverter. You must size the inverter for surge loads (like compressor startups on refrigerators or well pumps), typically requiring a 3,000W to 3,500W unit, such as the Victron MultiPlus 3000VA or a Growatt 3000W off-grid inverter.
On the charging side, your AC charger or MPPT solar charge controller must be sized to replenish the bank within your available sunlight or generator window. The industry standard rule of thumb is a charge current between 10% and 20% of the battery bank's total Amp-hour (Ah) capacity. For a 400Ah 48V bank, you need a minimum of 40A (preferably 60A to 80A) of bulk charge current. If your charge controller is undersized, the battery spends too much time in the absorption phase, leading to sulfation in lead-acid or cell imbalance in lithium.
The Core Math: Sizing with Peukert and Efficiency
A naive battery length calculator assumes a 100Ah battery can deliver 10A for 10 hours, or 50A for 2 hours. In reality, electrochemical batteries suffer from internal resistance and polarization. This is where Peukert's Law and inverter efficiency factor into the math.
Peukert's Law is expressed as t = H * (C / I)^k, where t is actual time, H is the rated hour base (usually 20), C is rated capacity, I is actual discharge current, and k is the Peukert exponent. For flooded lead-acid (FLA), k is typically 1.3. For AGM, it is around 1.15. For LiFePO4 (lithium iron phosphate), k is roughly 1.02 to 1.05, meaning lithium is virtually immune to Peukert losses at high discharge rates.
Let's run a concrete sizing example for a 48V system powering a 1,500W continuous load for 4 hours (6,000Wh total AC energy):
- Inverter Losses: Assuming 90% inverter efficiency, the DC energy required is 6,000Wh / 0.90 = 6,666Wh.
- Base Ah Requirement: At a 48V nominal system voltage, 6,666Wh / 48V = 138.8Ah required at 100% DoD.
- Apply DoD Limits: If using LiFePO4 (80% usable DoD), you need 138.8 / 0.80 = 173.5Ah. If using FLA (50% usable DoD), you need 138.8 / 0.50 = 277.6Ah.
- Apply Peukert (Lead-Acid Only): Discharging 277Ah of FLA at roughly 28A (10% rate) is fine, but if the load spikes to 60A, the effective capacity of the FLA bank drops by nearly 20%. You must oversize the FLA bank to 350Ah to maintain the 4-hour runtime under variable loads.
| Chemistry | Required Nameplate Ah | Usable DoD | Peukert Exponent (k) | Max Continuous C-Rate | Estimated 2026 Pricing |
|---|---|---|---|---|---|
| Flooded Lead-Acid (FLA) | 350Ah | 50% | 1.30 | 0.2C (70A) | $450 - $600 |
| AGM / Gel | 300Ah | 50% | 1.15 | 0.3C (90A) | $700 - $900 |
| LiFePO4 (Prismatic) | 175Ah (Use 200Ah) | 80% - 90% | 1.05 | 1.0C (200A) | $500 - $750 |
Series vs. Parallel: Voltage, Amp-Hours, and C-Rate Limits
How you physically wire the cells drastically alters the output of your battery length calculator. The fundamental rules are strict: wiring in series adds voltage while Amp-hours remain constant; wiring in parallel adds Amp-hours while voltage remains constant.
| Goal | Wiring Method | Example (4x 12V 100Ah Batteries) | Best Application |
|---|---|---|---|
| Increase System Voltage | Series | 48V @ 100Ah (4.8kWh) | High-power inverters (>3000W) to reduce DC current and wire gauge. |
| Increase Runtime (Ah) | Parallel | 12V @ 400Ah (4.8kWh) | Small RV/Marine 12V systems, low continuous draw. |
| Increase Both (Series-Parallel) | Combined | 24V @ 200Ah (4.8kWh) | Mid-size cabins, balancing wire thickness and inverter limits. |
Charge and discharge limits (C-rates) are where many DIY builders make critical errors. A 1C discharge rate on a 100Ah battery means drawing 100A continuously. While a high-quality LiFePO4 cell (like EVE LF105 or Lishen 272Ah) can handle 1C, most budget drop-in 12V lithium batteries with internal BMS limits are capped at 0.5C or 100A max. If your inverter pulls 150A from a single 12V 100Ah battery, the BMS will open the contactor and kill your power instantly. Always calculate your peak DC amperage: Peak DC Amps = (Peak AC Watts / Inverter Efficiency) / Lowest Battery Voltage.
For deeper architectural guidance on balancing parallel strings and busbar sizing, the Wiring Unlimited guide by Victron Energy remains the definitive reference for preventing uneven current distribution across parallel battery nodes.
Battery Length Calculator FAQ
How does a battery length calculator account for inverter and wiring losses?
A robust calculator applies a derating factor to the AC load before converting to DC Amp-hours. Standard high-frequency inverters operate at 85% to 90% efficiency under typical loads, while low-frequency transformer-based inverters might drop to 80% at light loads. Additionally, you must factor in a 2% to 3% voltage drop across the DC cables and busbars. Therefore, a 1,000W AC load actually requires the battery to output roughly 1,150W of DC power. Always divide your total AC Watt-hours by 0.85 or 0.90 to find the true DC demand.
Can I use a battery length calculator for a mixed lead-acid and lithium bank?
No. You should never mix lead-acid and lithium chemistries in the same parallel bank. They have fundamentally different charge profiles and resting voltages. A lead-acid battery requires an absorption voltage of around 14.4V to 14.8V and a float stage, while LiFePO4 requires a strict absorption of 14.2V to 14.6V and absolutely no float stage. If wired together, the charge controller will either chronically undercharge the lead-acid (causing rapid sulfation) or overcharge the lithium (tripping the BMS high-voltage protection or degrading the cells). Calculate and build separate banks with separate charge controllers if you must use both.
What is the maximum parallel string limit when calculating battery length?
For lead-acid (FLA or AGM), the industry maximum is typically three to four parallel strings. Beyond four strings, the resistance differences in the interconnecting cables cause uneven charging and discharging, meaning the string closest to the inverter does all the work and degrades prematurely. For LiFePO4, if you are using raw cells with a single external BMS, you can parallel up to 4 strings safely. If using drop-in 12V batteries with internal BMS units, limit parallel connections to 3 or 4 unless the manufacturer explicitly supports BMS-to-BMS communication (like the Victron Smart Battery network) to actively balance the load across the strings.
