Battery Systems Explained: Ah, Wh, Joules, and Run Time

Battery specifications read like a foreign language: 100Ah, 1.2 kWh, 4,320,000 J, 80% DoD. What does any of this mean in practice, and how do you predict how long a battery will actually power your setup? This guide breaks it all down from first principles.

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The Three Capacity Units

Battery capacity describes how much energy a battery stores. The same battery can be described in three different units, each useful in different contexts.

1. Ampere-Hours (Ah) — Charge Capacity

Ampere-hours measure electric charge — how many electrons the battery holds, regardless of voltage. A 100Ah battery can theoretically supply 100A for 1 hour, 10A for 10 hours, or 1A for 100 hours.

mAh (milliampere-hours) = Ah × 1,000. Used for small batteries like phone packs and AA cells.

2. Watt-Hours (Wh) — Energy Capacity

Watt-hours are the most practically useful unit because they account for voltage:

Wh = Ah × Voltage

A 100Ah, 12V lead-acid battery stores: 100 × 12 = 1,200 Wh = 1.2 kWh

The same 100Ah battery at 48V (a common solar bank voltage) stores: 100 × 48 = 4,800 Wh = 4.8 kWh

3. Joules (J) — SI Energy Unit

Joules are the International System (SI) base unit of energy. One watt-hour equals exactly 3,600 joules:

J = Wh × 3,600

So our 12V, 100Ah battery stores: 1,200 × 3,600 = 4,320,000 J = 4.32 MJ

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Depth of Discharge (DoD)

DoD is the percentage of a battery's total capacity that can be safely used before recharging. Discharging beyond the rated DoD causes permanent cell damage and reduces lifespan.

Usable Energy = Total Wh × (DoD / 100)

A 1,200 Wh lead-acid battery at 50% DoD has only 600 Wh usable. The same sized LiFePO4 at 90% DoD gives 1,080 Wh — 80% more usable energy from the same nominal capacity.

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Calculating Battery Run Time

Run Time (hours) = Usable Wh / Load (Watts)

Example 1: Camping Setup

12V, 100Ah LiFePO4 battery at 90% DoD = 1,080 Wh usable

Powering a 50W refrigerator: 1,080 / 50 = 21.6 hours

Example 2: Off-Grid Cabin

48V, 400Ah lead-acid bank at 50% DoD = 48 × 400 × 0.50 = 9,600 Wh usable

Cabin with 800W average load: 9,600 / 800 = 12 hours before recharge needed

Example 3: UPS for a Server

12V, 9Ah sealed AGM at 80% DoD = 12 × 9 × 0.80 = 86.4 Wh usable

Server draws 200W: 86.4 / 200 = 0.43 hours = 26 minutes of backup

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Peukert's Law: Why Ah Rating is Load-Dependent

Lead-acid batteries lose capacity faster when discharged rapidly. A 100Ah battery discharged at 100A (1-hour rate) may only deliver 70Ah. Discharged slowly at 5A (20-hour rate), it may deliver the full 100Ah or more.

This is called Peukert's Effect and it's why lead-acid battery datasheets specify capacity at the C20 rate (20-hour discharge). Lithium chemistries are much less affected by discharge rate, delivering close to their rated capacity even at high currents.

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Battery Chemistry Comparison

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Energy in Joules: Why It Matters

Joules connect battery energy to physical work. Understanding this matters for:

• Motor sizing: Can this battery spin a pump to lift 100 kg of water 5 meters? (Answer: 100 × 9.81 × 5 = 4,905 J minimum)
• Thermal loads: How many joules does it take to heat a kettle from 20°C to 100°C?
• Regulatory compliance: Aviation, shipping, and hazmat regulations restrict lithium batteries by Wh capacity — which converts directly to Joules.

Use our Battery Run Time Calculator to instantly estimate run time for any capacity and load combination.

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Quick Reference: Run Time Table

12V 100Ah LiFePO4 (90% DoD = 1,080 Wh usable):