Engineering Guide: How to Calculate Battery Run Time Under Load
Calculating battery runtime requires balancing usable electrochemical capacity against dynamic terminal voltage, inverter conversion efficiency, and discharge-rate-dependent capacity losses. Below is the complete mathematical and physical derivation governing deep-cycle energy storage systems.
1. The Physics of Battery Runtime: Usable Energy vs. Nominal Capacity
To calculate battery run time accurately, one must recognize that an Amp-hour (Ah) rating alone does not dictate operational endurance. An Amp-hour represents electric charge (3,600 Coulombs). However, appliances consume energy in Watt-hours (Wh), where energy is the product of voltage, current, and time (E = V × I × t).
Because battery terminal voltage varies dynamically throughout a discharge cycle, the fundamental battery runtime equation must balance total usable energy against continuous load dissipation and system conversion inefficiencies:
Where V_nominal is system bus voltage, C_Ah is rated capacity, DoD is usable depth of discharge, and η_inverter is inverter efficiency.
Where P_load is total continuous wattage draw. For direct DC loads, inverter efficiency is omitted (η = 1.0).
Why Rating Batteries in Amp-Hours Alone Causes System Failure
A 12V 100Ah battery stores 1,200 Watt-hours (12V × 100Ah), while a 48V 100Ah battery stores 4,800 Watt-hours (48V × 100Ah)—four times the power despite sharing the identical "100Ah" label. Overlooking Depth of Discharge limits or inverter losses causes calculated runtimes to overshoot real-world performance by 25% to 50%.
2. Battery Chemistry Discharge Physics: Flat LiFePO4 vs. Peukert's Law in Lead-Acid
The rate at which a battery discharges fundamentally alters the amount of energy it can physically release. This electrochemical relationship is governed by Peukert's Law, first formulated by German physicist Wilhelm Peukert in 1897:
Where t is actual discharge time in hours, H is rated discharge duration (standardized at 20 hours, or C/20 rate), C is nominal rated capacity, I is discharge current in Amps, and k is the dimensionless Peukert exponent.
• Lead-Acid & AGM Capacity Collapse (k = 1.15 to 1.30)
In flooded lead-acid and AGM batteries, acid diffuses through porous lead plates. Under a gentle 5A draw on a 100Ah battery (C/20), diffusion keeps pace, yielding the full 100Ah.
However, when pulling heavy loads (such as a 1,200W microwave drawing 110A from 12V), internal resistance causes acid depletion and Joule heating (I²R). A 100Ah AGM under a 50A load collapses to delivering only 55Ah to 60Ah before hitting cutoff.
• LiFePO4 Linear Discharge & Flat Plateau (k = 1.01 to 1.03)
In stark contrast, Lithium Iron Phosphate (LiFePO4) chemistry exhibits internal impedance measured in milliohms and near-instantaneous lithium-ion intercalation kinetics. The Peukert exponent for modern prismatic LiFePO4 cells is virtually unity (k ≈ 1.02).
Whether discharged at 0.05C (5A) or 1.0C (100A), LiFePO4 delivers 98% to 100% of its rated capacity while maintaining a flat voltage plateau between 13.0V and 13.2V across 80% of its curve, preventing inverter low-voltage shutdown.
3. The Parasitic Drain of Inverter Conversion & Standby Power
When sizing an off-grid electrical system or emergency battery backup, engineers distinguish sharply between direct-current (DC) native loads and alternating-current (AC) inverter loads. Direct DC loads—such as 12V compressor refrigerators, LED lighting, and USB-C chargers—draw power with 95% to 98% efficiency. Conversely, powering 120V household appliances requires an inverter, introducing two distinct energy penalties:
Quality pure sine wave inverters operate at peak electrical efficiencies between 88% and 93% under moderate load. The unharvested 7% to 12% is radiated as ambient waste heat through internal transformer coils and MOSFET switching stages. For budget modified sine wave units or inverters operating below 10% of rated capacity, efficiency frequently plummets below 75%.
An inverter left switched on continuously draws between 15 Watts and 40 Watts merely energizing its internal control circuitry, sensing transformers, and cooling fans—even when zero AC appliances are running. Over a 24-hour day, an idle 30W inverter consumes 720 Watt-hours of energy, consuming more than 60% of an entire 12V 100Ah lithium battery's usable capacity without performing any useful work.
4. Worked Engineering Case Studies: RV Camper vs. Residential Backup
To illustrate how battery chemistry, operating voltage, and load dynamics interact in field applications, examine two rigorous engineering benchmarks:
Designing a rugged overland electrical system with direct DC appliances:
Comparative AGM note: An equivalent 12V 200Ah AGM bank limited to 50% DoD delivers only 1,280 Wh, yielding just 18.3 hours under identical load.
Designing a residential emergency backup bank powering essential AC circuits:
Provides nearly a full 24-hour cycle of critical home warmth, refrigeration, and communication during severe winter grid blackouts.
5. Low-Voltage Cutoff Thresholds & BMS Voltage Sag Dynamics
A common failure mode in off-grid battery systems is premature inverter shutoff triggered by momentary voltage sag. Under Ohm's Law (V_sag = I_load × R_internal), when an inductive appliance—such as a refrigerator compressor or deep-well pump—starts up, its momentary inrush surge reaches 3 to 6 times continuous operating current.
• Inverter Low Voltage Disconnect (LVD) Thresholds
On a 12V lead-acid bank, a 100A surge can depress terminal voltage by 1.2V to 1.8V instantaneously. If inverter Low Voltage Disconnect (LVD) is set too high (e.g., 11.8V), this temporary dip trips the inverter into fault-lockout, even though the battery retains 70% charge.
Program inverter operational LVD to 11.8V–12.0V under load for LiFePO4 (roughly 10%–15% resting SoC), or 11.5V under load for AGM batteries to prevent premature tripping.
• BMS Disconnect Hazards & Inductive Voltage Spikes
For LiFePO4 battery banks, the internal Battery Management System (BMS) incorporates low-voltage cell protection (typically 2.50V per cell, or 10.0V per 12V battery). Never rely on the BMS as your daily operational cutoff switch.
When a BMS abruptly disconnects MOSFETs while an inverter pulls heavy current, the collapse produces severe inductive kickback spikes (V = L × di/dt) across DC busbars. These transients can destroy MPPT charge controllers and inverter input stages. Always set inverter LVD to gracefully shut down loads before the BMS safety cutoff engages.