Battery Storage & Electrical Engineering Guide

Battery Backup Runtime Formula & Calculation Guide

Q: What is the formula to calculate battery backup runtime?

The fundamental 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 Watt-hours first: Watt-hours = Amp-hours × Battery Voltage.

Q: How long will a 100Ah 12V battery run an appliance?

A 12V 100Ah battery contains 1,200 Watt-hours of nominal energy. On a LiFePO4 battery (90% usable DoD = 1,080Wh) powering a 100W appliance through a 90% efficient inverter, runtime is: (1,200 × 0.90 × 0.90) ÷ 100W = 9.72 Hours. On a Lead-Acid/AGM battery (50% recommended DoD = 600Wh), runtime is: (1,200 × 0.50 × 0.90) ÷ 100W = 5.40 Hours.

Q: How does inverter efficiency affect battery runtime?

DC-to-AC power inverters consume energy during the voltage conversion process, typically operating at 85% to 93% efficiency under moderate loads. In addition, inverters have an idle 'no-load tare draw' (typically 10W to 35W) that drains the battery continuously even when connected appliances are idling or cycling off.

Q: What is Peukert's Law and how does it impact high-power loads?

Peukert's Law dictates that the available capacity of lead-acid and AGM batteries decreases significantly at higher discharge rates (C-rate). A 100Ah AGM battery discharged at 50A (0.5C) may only deliver 65Ah to 70Ah before reaching cutoff voltage. Lithium Iron Phosphate (LiFePO4) has a Peukert exponent close to 1.02–1.05, meaning it retains almost 98%+ of its rated capacity regardless of discharge rate.

Q: 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, discharging to 80%–90% Depth of Discharge (DoD) yields 3,000 to 5,000+ charge cycles. Routine 100% deep discharge can accelerate cathode stress and reduce overall calendar cycle life.

Learn how to accurately calculate battery backup duration for home emergency power, off-grid cabins, RVs, and UPS systems. Understand the mathematics of Amp-Hours, Watt-Hours, depth-of-discharge limits, inverter efficiency, and Peukert capacity loss.

Live Interactive Battery Runtime Calculator

Use the deterministic calculation engine below to compute exact backup duration across various battery chemistries (LiFePO4, AGM, Gel, Flooded Lead-Acid) and custom appliance loads.

Calculate estimated runtime

⚡ 1-Click Autofill: Top 5 Battery Setups

Estimated runtime

7 h 12 min

≈ 7.2 hours

A planning estimate based on your battery energy and average device load.

Usable Energy Window80% Usable

Reserve 20%

0.80 kWh

Usable (80%)

Reserve (20%)

⏱️ Outage Survival Clock & Timeline7h 12m Backup

Usable Power (80%)

20% Reserve

100% Full

50% Half-Life

20% Low Cutoff

📈 Estimated Runtime vs. Continuous Load12V • 83.33333333333333Ah • 80% DoD

Battery capacity: 1,000 Wh
Usable battery energy: 800 Wh
Device load: 100 W average
Battery-side load: 111 W

Energy Conversion Flow

Nominal Capacity1,000 Wh

Rated pack capacity

Usable After Reserve800 Wh

80% usable DOD window

Effective Delivered Energy720 Wh

After 90% efficiency

Runtime at different loads

75 W: 9 h 36 min
100 W Your load: 7 h 12 min
125 W: 5 h 46 min

Assumptions used

Battery type: LiFePO4 / LFP
Starting charge: 100%
Reserve: 20%
Battery health: 100%
AC inverter efficiency: 90%

If your actual load is 10% higher, runtime is about 9% shorter.

Want a more accurate result?

Use your battery's actual Wh/Ah rating, your appliance's measured or nameplate watts, inverter efficiency if known, current charge, and battery health.

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 actual stored energy.

Energy is the product of electrical charge and voltage:

Energy (Watt-hours) = Capacity (Amp-hours) × Nominal Voltage (Volts)

Consider three batteries with identical Amp-hour ratings or identical energy ratings:

Table 1: Comparison of Stored Energy Across Voltage Standards
Battery Configuration	Rated Capacity	Nominal Voltage	Stored Energy (Wh)	Runtime on 200W Load (90% Eff)
12V 100Ah Battery	100 Ah	12.8 V	1,280 Wh	5.18 Hours (@ 90% DoD)
24V 100Ah Battery	100 Ah	25.6 V	2,560 Wh (2× Energy)	10.36 Hours (@ 90% DoD)
48V 100Ah Server Rack	100 Ah	51.2 V	5,120 Wh (4× Energy)	20.73 Hours (@ 90% DoD)

The 3 Inevitable Losses: DoD, Inverter Inefficiency, and Peukert's Law

A battery rated for 1,200Wh will never deliver 1,200Wh to an AC household appliance. Calculating real-world runtime requires accounting for three physical loss mechanisms:

1. Depth of Discharge (DoD)

Discharging lead-acid or AGM batteries below 50% DoD causes irreversible plate sulfation and cuts cycle life from 800 cycles to under 200. LiFePO4 can safely utilize 80% to 95% DoD for 3,500+ cycles.

2. Inverter Conversion & Tare Loss

Converting 12V/24V/48V DC into 120V/240V AC dissipates 7% to 15% of incoming power as heat. In addition, the inverter's internal electronics consume 10W to 35W of constant standby power.

3. Peukert's High-Current Penalty

In lead-acid chemistries, fast discharge rates impede chemical ion diffusion. Drawing 60A from a 100Ah AGM battery drops its effective capacity by up to 35%. LiFePO4 has a near-perfect Peukert exponent (1.02).

Table 2: Battery Chemistry Performance, Usable DoD & Peukert Exponent
Chemistry	Recommended DoD	Cycle Life (to 80% SoH)	Peukert Exponent (k)	Round-Trip Efficiency
Lithium Iron Phosphate (LiFePO4)	85% – 95%	3,500 – 6,000 cycles	1.02 – 1.05 (Minimal Loss)	95% – 98%
Absorbent Glass Mat (AGM)	50%	400 – 700 cycles	1.12 – 1.20 (Moderate Loss)	80% – 85%
Flooded Lead-Acid (FLA)	50%	300 – 500 cycles	1.20 – 1.35 (Severe Loss)	70% – 80%
Lithium NMC (Powerwall / Portable Stations)	90% – 95%	1,500 – 2,500 cycles	1.03 – 1.06	92% – 95%

Deterministic Mathematical Sizing Formulas

Battery Backup Runtime & Usable Energy Equation

Comprehensive equation accounting for nominal capacity, chemistry-specific depth of discharge, power inverter conversion efficiency, tare idle draw, and Peukert high-rate discharge derating.

📐 calculation-model.ts

01

T_runtime = (C_nom_Wh × DoD × η_inv) ÷ (P_load + P_tare) | C_peukert = C_rated × (I_rated ÷ I_actual)^(k - 1)

Variable Definitions

T_runtimeEstimated Backup Runtime(Hours (h)): Duration until battery reaches manufacturer low-voltage cutoff
C_nom_WhNominal Battery Energy(Watt-hours (Wh)): Rated battery capacity in Watt-hours (Ah × Nominal Voltage)
DoDUsable Depth of Discharge(Decimal (0.0 – 1.0)): Maximum recommended discharge percentage (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 0.88 to 0.93)
P_loadContinuous Appliance Load(Watts (W)): Total average power drawn by connected equipment
P_tareInverter Idle Tare Draw(Watts (W)): Continuous background power drawn by inverter standby circuitry
kPeukert Exponent(Dimensionless): Empirical rate-capacity coefficient (1.02 for LiFePO4, 1.25 for Lead-Acid)

Engineering Notes & Standards

For cycling loads like refrigerators or sump pumps, multiply nameplate power by the compressor duty cycle (e.g., 150W × 0.35 = 52.5W average).
In sub-freezing ambient temperatures (<0°C / 32°F), apply an additional 15% to 25% temperature capacity derate.

Worked Sizing Examples: Refrigerator, CPAP, & Sump Pump

Here is how to calculate runtime step-by-step for three common emergency backup scenarios:

Scenario A: 12V 100Ah LiFePO4 + Refrigerator

Load: 150W refrigerator running at 35% duty cycle (52.5W avg) + 10W inverter tare.
Battery Energy: 100Ah × 12.8V = 1,280 Wh.
Usable Energy: 1,280Wh × 0.90 DoD × 0.90 η_inv = 1,036.8 Wh.
Total Load: 52.5W + 10W = 62.5 Watts.
Runtime: 1,036.8 Wh ÷ 62.5W = 16.59 Hours.

Run Battery Runtime Calculator →

Scenario B: 12V 100Ah AGM + Heavy 800W Load

Load: 800W continuous pump load (~75A DC draw).
Battery Energy: 100Ah × 12V = 1,200 Wh.
Usable Energy: 1,200Wh × 0.50 DoD × 0.88 η_inv = 528 Wh.
Peukert Derate: Drawing 0.75C reduces effective capacity by 30% (369.6 Wh usable).
Runtime: 369.6 Wh ÷ 800W = 0.46 Hours (28 Minutes).

Size Inverter for 800W Load →

Scenario C: 1,000Wh Station + Laptop & Starlink

Load: 65W Laptop + 50W Starlink terminal = 115W continuous.
Storage: 1,000Wh LiFePO4 power station.
Internal DC-to-AC Loss: 88% overall efficiency.
Usable Energy: 1,000Wh × 0.90 usable = 900 Wh.
Runtime: (900Wh × 0.88) ÷ 115W = 6.88 Hours.

Size Portable Power Station →

Connected Battery Planning & Electrical Tools

Explore the full suite of deterministic battery, solar, and home energy sizing calculators:

Battery Runtime Calculator Battery Size Calculator Battery Capacity Calculator UPS Runtime Calculator DC Voltage Drop Calculator Home Battery Size Calculator

Frequently Asked Questions

What is the formula to calculate battery backup runtime?

The fundamental 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 Watt-hours first: Watt-hours = Amp-hours × Battery Voltage.

How long will a 100Ah 12V battery run an appliance?

A 12V 100Ah battery contains 1,200 Watt-hours of nominal energy. On a LiFePO4 battery (90% usable DoD = 1,080Wh) powering a 100W appliance through a 90% efficient inverter, runtime is: (1,200 × 0.90 × 0.90) ÷ 100W = 9.72 Hours. On a Lead-Acid/AGM battery (50% recommended DoD = 600Wh), 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 the voltage conversion process, typically operating at 85% to 93% efficiency under moderate loads. In addition, inverters have an idle 'no-load tare draw' (typically 10W to 35W) that drains the battery continuously even when connected appliances are idling or cycling off.

What is Peukert's Law and how does it impact high-power loads?

Peukert's Law dictates that the available capacity of lead-acid and AGM batteries decreases significantly at higher discharge rates (C-rate). A 100Ah AGM battery discharged at 50A (0.5C) may only deliver 65Ah to 70Ah before reaching cutoff voltage. Lithium Iron Phosphate (LiFePO4) has a Peukert exponent close to 1.02–1.05, meaning it retains almost 98%+ of its rated capacity regardless of discharge rate.

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, discharging to 80%–90% Depth of Discharge (DoD) yields 3,000 to 5,000+ charge cycles. Routine 100% deep discharge can accelerate cathode stress and reduce overall calendar cycle life.

Methodology & Standards Citations

Calculations adhere to 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).

Full PowerLab Calculation Methodology →Technical Standards & Data Sources →