Battery Storage & Electrical Engineering Guide
Battery Backup Runtime Formula & Calculation Guide
Learn how to estimate battery backup duration for home emergency power, off-grid systems, RVs, and UPS applications. Understand the relationship between Amp-Hours, Watt-Hours, depth-of-discharge limits, inverter conversion efficiency, and standby losses.
Live Interactive Battery Runtime Calculator
Calculate an estimated battery runtime using the transparent, deterministic energy model below across various battery chemistries (LiFePO4, AGM, Gel, Flooded Lead-Acid) and custom appliance loads.
Calculate estimated runtime
How to Calculate Battery Backup Runtime (Step-by-Step)
How to estimate battery backup runtime step-by-step using usable stored watt-hours, depth-of-discharge limits, and inverter conversion efficiency.
Calculate Effective Battery-Side Power Demand
Divide the AC appliance load wattage by inverter conversion efficiency to find the total power drawn from the battery bank.
Determine Usable Stored Energy
Multiply rated battery watt-hour capacity by the usable Depth of Discharge window (e.g., 80%–90% for LiFePO4; 50% for Lead-Acid) and State of Health (SOH).
Solve for Estimated Backup Runtime
Divide net usable battery watt-hours by the battery-side power demand to find the total operating duration.
Amp-Hours (Ah) vs. Watt-Hours (Wh): Why Voltage Changes Everything
One of the most frequent misconceptions in battery sizing is comparing batteries by Amp-hours (Ah) alone. Amp-hours measure electrical charge, but Watt-hours (Wh) measure stored energy.
Energy is the product of electrical charge and nominal voltage:
Consider three battery banks with identical 100Ah capacity ratings across different system nominal voltage standards:
| Battery Configuration | Rated Capacity | Nominal Voltage | Stored Energy (Wh) | Estimated Runtime on 200W Load |
|---|---|---|---|---|
| 12.8V LiFePO4 (4S) | 100 Ah | 12.8 V | 1,280 Wh | 5.18 Hours |
| 25.6V LiFePO4 (8S) | 100 Ah | 25.6 V | 2,560 Wh (2× Energy) | 10.37 Hours |
| 51.2V LiFePO4 (16S Server Rack) | 100 Ah | 51.2 V | 5,120 Wh (4× Energy) | 20.74 Hours |
Key Operating Factors: Depth of Discharge, Inverter Efficiency, and Rate Effects
A battery rated for 1,280Wh will not deliver 1,280Wh to an AC household appliance. Calculating realistic backup runtime requires accounting for conversion efficiencies and operating boundaries:
1. Usable Depth of Discharge (DoD)
Operating lead-acid or AGM batteries below ~50% DoD accelerates plate degradation and significantly shortens cycle life. Modern LiFePO4 packs are typically planned around an 80% to 90% usable DoD window, depending on manufacturer specifications and desired cycle life.
2. Inverter Conversion & Tare Loss
Converting DC battery voltage into 120V/240V AC power typically dissipates 7% to 15% of throughput power as heat (85%–93% efficiency). Additionally, inverters draw continuous idle tare power (often 10W to 35W) while powered on.
3. Discharge Rate & Peukert Effect
Lead-acid batteries exhibit reduced deliverable capacity at higher discharge rates (described by Peukert's empirical equation). LiFePO4 chemistries maintain stable capacity across typical residential discharge rates. Simplified planning models calculate energy-balance runtime without rate-curve integration.
| Chemistry | Typical Planned DoD | Illustrative Cycle Life (to 80% SoH) | Typical Peukert Exponent (k) | Typical DC-DC Round-Trip Efficiency |
|---|---|---|---|---|
| Lithium Iron Phosphate (LiFePO4) | 80% – 90% | 2,500 – 5,000+ cycles | ~1.02 – 1.05 (Minimal Rate Loss) | 92% – 98% |
| Absorbent Glass Mat (AGM) | 50% | 300 – 700 cycles | ~1.12 – 1.25 (Moderate Rate Loss) | 80% – 85% |
| Flooded Lead-Acid (FLA) | 50% | 250 – 500 cycles | ~1.20 – 1.35 (Significant Rate Loss) | 70% – 80% |
| Lithium NMC (Home Storage & Power Stations) | 80% – 90% | 1,000 – 2,500 cycles | ~1.03 – 1.06 | 90% – 95% |
Calculation Formulas
Battery Backup Runtime & Usable Energy Equation
Simplified energy-balance planning equation accounting for nominal capacity, chemistry depth-of-discharge window, power inverter conversion efficiency, and continuous load plus tare standby draw.
Variable Definitions
T_runtimeEstimated Backup Runtime(Hours (h))- Estimated duration until battery reaches low-voltage reserve limit
C_nom_WhNominal Battery Energy(Watt-hours (Wh))- Nominal battery capacity in Watt-hours (Ah × Nominal Pack Voltage)
DoDUsable Depth of Discharge(Decimal (0.0 – 1.0))- Planned usable fraction (e.g. 0.90 for LiFePO4, 0.50 for AGM)
η_invInverter Conversion Efficiency(Decimal (0.0 – 1.0))- DC-to-AC conversion efficiency factor (typically 0.85 to 0.93)
P_loadContinuous Appliance Load(Watts (W))- Average power drawn by connected equipment
P_tareInverter Standby Tare Draw(Watts (W))- Continuous standby power drawn by inverter circuitry (if modeled)
Calculation Notes
- For cycling loads such as refrigerators, calculate average power using the duty cycle (e.g. 150W peak × 0.35 duty = 52.5W average).
- Lead-acid batteries can exhibit additional capacity loss at high discharge rates (Peukert effect). This simplified equation models constant energy delivery.
- Sub-freezing ambient temperatures (<0°C / 32°F) can reduce available battery capacity and discharge voltage.
Worked Sizing Examples: Refrigerator, High-Load Pump, & Workstation
Step-by-step calculations for three illustrative backup scenarios showing all assumed parameters:
Scenario A: 12.8V 100Ah LiFePO4 + Refrigerator
Load: 150W refrigerator at 35% duty cycle (52.5W average) + 10W inverter tare = 62.5W total.
Battery Energy: 100 Ah × 12.8 V = 1,280 Wh nominal.
Usable Delivered Energy: 1,280 Wh × 0.90 DoD × 0.90 η_inv = 1,036.8 Wh.
Total Modeled Load: 52.5W + 10W = 62.5 Watts.
Estimated Runtime: 1,036.8 Wh ÷ 62.5W = 16.59 Hours.
Scenario B: 12.0V 100Ah AGM + Heavy 800W Load (Illustrative Rate Derate)
Load: 800W continuous pump load (tare negligible relative to 800W).
Battery Energy: 100 Ah × 12.0 V = 1,200 Wh nominal.
Base Usable Energy: 1,200 Wh × 0.50 DoD × 0.88 η_inv = 528 Wh.
Illustrative Peukert Rate Derate: Rapid discharge (~0.7C) modeled with an illustrative 30% capacity reduction: 528 Wh × 0.70 = 369.6 Wh delivered.
Estimated Runtime: 369.6 Wh ÷ 800W = 0.46 Hours (~28 Minutes).
Scenario C: 1,000Wh Station + Laptop & Starlink
Load: 65W Laptop + 50W Starlink terminal = 115W continuous (100% duty).
Storage: 1,000 Wh nominal LiFePO4 power station.
Usable Storage: 1,000 Wh × 0.90 usable DoD = 900 Wh.
Delivered AC Energy: 900 Wh × 0.88 η_inv = 792 Wh.
Estimated Runtime: 792 Wh ÷ 115W = 6.89 Hours (~6.9 Hours).
Frequently Asked Questions
What is the formula to calculate battery backup runtime?
The fundamental simplified battery runtime formula is: Runtime (Hours) = (Battery Nominal Capacity in Watt-hours × Depth of Discharge × Inverter Efficiency) ÷ Total Load in Watts. If starting from Amp-hours, calculate nominal Watt-hours first: Watt-hours = Amp-hours × Battery Nominal Voltage. If continuous inverter tare standby draw is modeled, add it to the total load in the denominator.
How long will a 100Ah 12V battery run an appliance?
A 12.8V 100Ah LiFePO4 battery contains 1,280 Watt-hours of nominal energy. At 90% usable DoD (1,152Wh usable) powering a 100W appliance through a 90% efficient inverter with zero tare, estimated runtime is: (1,280 × 0.90 × 0.90) ÷ 100W = 10.37 Hours. On a 12.0V 100Ah Lead-Acid/AGM battery (1,200Wh nominal, 50% recommended DoD = 600Wh usable) with 90% inverter efficiency, estimated runtime is: (1,200 × 0.50 × 0.90) ÷ 100W = 5.40 Hours.
How does inverter efficiency affect battery runtime?
DC-to-AC power inverters consume energy during conversion, typically operating at 85% to 93% efficiency under moderate loads. In addition, inverters draw continuous idle tare power (often 10W to 35W) that drains the battery whenever the inverter is turned on, even when connected appliances cycle off or idle.
What is Peukert's Law and how does it impact high-power loads?
Peukert's Law describes how the deliverable capacity of lead-acid and AGM batteries decreases significantly at higher discharge rates (C-rate). For example, drawing high current from an AGM battery can reduce its deliverable capacity relative to its 20-hour rating. Lithium Iron Phosphate (LiFePO4) exhibits minimal rate-dependent capacity derating under typical residential discharge rates. Simplified planning models calculate energy-balance runtime without rate-curve integration.
Can I completely drain a lithium (LiFePO4) battery to 0%?
While modern LiFePO4 batteries feature an internal Battery Management System (BMS) with low-voltage cutoff protection, typical manufacturer design guidance recommends operating within an 80%–90% Depth of Discharge (DoD) window for longevity. Operating parameters, cycle life expectations, and cutoff thresholds vary by manufacturer and operating temperature.
Technical References & Model Basis
Technical references providing contextual background include IEEE Std 485 (Recommended Practice for Sizing Lead-Acid Batteries for Stationary Applications), IEC 62619 (Safety requirements for secondary lithium cells), UL 1973, and NFPA 70 / NEC Article 706 (Energy Storage Systems). These references provide technical context; this calculator is a simplified planning model and does not determine standards compliance, battery suitability, or installation requirements.