Battery capacity is described in different units. Amp-hours describes charge quantity at a given voltage. Watt-hours describe energy. For sizing portable power stations, planning runtimes, or comparing batteries, watt-hours are the more useful unit because they incorporate voltage and represent actual energy available.
The core relationship is simple:
Watt-hours (Wh) = Amp-hours (Ah) × Voltage (V)
Use the nominal voltage of the battery or battery pack for quick calculations. For more accurate results, use the measured voltage under load or the battery’s average operating voltage.
- Ah is amp-hours. 1 Ah = 1 amp supplied for 1 hour.
- Wh is watt-hours. 1 Wh = 1 watt supplied for 1 hour.
- If you have milliamp-hours (mAh), convert to Ah by dividing by 1000: 2000 mAh = 2 Ah.
Why convert amp-hours to watt-hours
Basic formula
Units and conversions
- Ah is amp-hours. 1 Ah = 1 amp supplied for 1 hour.
- Wh is watt-hours. 1 Wh = 1 watt supplied for 1 hour.
- If you have milliamp-hours (mAh), convert to Ah by dividing by 1000: 2000 mAh = 2 Ah.
Worked examples
Example 1: Typical 12 volt lead-acid battery
Battery spec: 12 V, 100 Ah.
Wh = 100 Ah × 12 V = 1200 Wh.
This battery stores 1200 watt-hours of energy at the nominal voltage.
Example 2: Lithium-ion cell pack
Battery pack spec: 14.8 V nominal, 5 Ah.
Wh = 5 Ah × 14.8 V = 74 Wh.
Example 3: Converting from mAh
Phone battery: 3500 mAh, nominal 3.7 V cell.
First convert mAh to Ah: 3500 mAh ÷ 1000 = 3.5 Ah.
Wh = 3.5 Ah × 3.7 V = 12.95 Wh.
How to calculate runtime for a device
To estimate how long a battery will run a device, divide the battery Wh by the device power draw in watts. For AC devices powered through an inverter, account for inverter efficiency.
Runtime formula
Runtime (hours) = Battery Wh × Usable fraction × Inverter efficiency ÷ Load watts
Example runtime
Battery: 1200 Wh usable. Device: 60 W lamp. Inverter efficiency or DC conversion not needed if device is DC-compatible; for AC assume 90% efficiency.
- If directly DC or no conversion losses: 1200 Wh ÷ 60 W = 20 hours.
- If using an inverter at 90%: (1200 Wh × 0.9) ÷ 60 W = 18 hours.
Common mistakes to avoid
1. Forgetting voltage
People sometimes multiply Ah by a different voltage than the battery actually uses. Always use the pack or system voltage, not a single cell voltage, unless the Ah rating refers to that cell.
2. Using nominal voltage blindly
Nominal voltage is a convenient rating. Under load or near full/empty states the actual voltage can be higher or lower. For more precise energy estimates, use the average operating voltage over the discharge curve.
3. Ignoring usable capacity
Manufacturers list total capacity, but usable capacity depends on depth of discharge limits, battery management system cutoffs, and longevity strategies. For example, a 100 Ah, 12 V battery has 1200 Wh total, but if you only use 80% to protect the battery, usable energy is 960 Wh.
4. Not accounting for conversion losses
When converting DC battery energy to AC or another voltage, converters and inverters produce heat. Typical inverter efficiency ranges from 85% to 95%. Include those losses when calculating expected runtimes.
5. Confusing series and parallel wiring
When batteries are wired in series, voltages add while Ah stays the same. When wired in parallel, Ah adds while voltage stays the same. People often assume Ah always adds regardless of configuration, which leads to incorrect Wh calculations.
- Two 12 V 100 Ah batteries in series => 24 V, 100 Ah => Wh = 24 × 100 = 2400 Wh.
- Two 12 V 100 Ah batteries in parallel => 12 V, 200 Ah => Wh = 12 × 200 = 2400 Wh.
Both configurations yield the same total Wh, but the system voltage and current characteristics differ.
6. Using inconsistent units
Mixing mAh and Ah without converting, or mixing nominal and measured voltages, leads to arithmetic errors. Convert everything to the same base units before computing.
Advanced considerations that affect real-world energy
State of charge and discharge rates
Battery chemistry behaves differently at high discharge currents. Effective capacity can decrease at high discharge rates. Manufacturers sometimes specify capacity at a particular discharge rate; use that as a guide or correct for Peukert effects when necessary.
Temperature effects
Cold temperatures reduce available capacity. For critical applications, reduce estimated usable Wh at low temperatures or use battery chemistries rated for cold operation.
Battery age and cycling
Over time, batteries lose capacity. A pack that originally stored 1000 Wh may store less after many cycles. Use a conservative capacity estimate if the battery is not new.
Measurement method for accurate Wh
For the most accurate Wh measurement, use a coulomb counter or energy meter that logs voltage and current over time. Integrate power over the discharge period to get actual Wh rather than relying on nominal ratings.
Quick reference formulas
- Wh = Ah × V
- Ah = Wh ÷ V
- mAh to Ah: Ah = mAh ÷ 1000
- Estimated usable Wh = Rated Wh × Usable fraction (for example 0.7 to 0.9)
- AC available Wh = Battery Wh × Inverter efficiency
Practical checklist before you calculate
- Confirm the battery or pack nominal voltage.
- Confirm Ah or convert mAh to Ah.
- Decide on usable capacity fraction (based on chemistry and management system).
- Account for conversion and inverter efficiencies if powering devices that require different voltages or AC.
- Adjust for temperature and battery age if relevant.
Frequently asked questions
How do I calculate watt-hours from amp-hours for a battery pack?
Multiply the amp-hours by the pack voltage using Wh = Ah × V. If you have mAh, convert to Ah first by dividing by 1000, and use the system or pack voltage rather than a single cell voltage for correct results.
Is nominal voltage accurate enough when I calculate Wh?
Nominal voltage is fine for rough estimates and quick comparisons, but actual voltage varies during discharge. For precise Wh values use the average operating voltage or measure voltage under load over the discharge period.
How should I account for inverter or converter losses when estimating usable Wh?
Multiply battery Wh by the converter or inverter efficiency (for example 0.85–0.95) to get AC or converted-DC available energy. Also include additional losses such as wiring resistance or DC-DC conversion to avoid overestimating runtime.
Do series or parallel battery connections change total Wh?
In ideal conditions total Wh remains the same: series wiring increases voltage while keeping Ah the same, and parallel increases Ah while keeping voltage the same. Always use the combined system voltage and Ah when calculating Wh for the configured pack.
What is the best way to measure the actual watt-hours delivered by a battery?
Use an energy meter or coulomb counter that logs voltage and current and integrate power over time to get actual Wh. This captures real-world effects like voltage sag, conversion losses, and varying load, which nominal ratings do not reflect.
Final notes on accuracy
Converting Ah to Wh is straightforward, but real-world usable energy differs from theoretical numbers. Treat nominal Wh as a starting point and apply the adjustments described here for planning. For precise energy accounting, measure voltage and current over time with appropriate meters.
Understanding the distinction between amp-hours and watt-hours helps with proper sizing of portable power stations and batteries and reduces errors when estimating runtimes for devices.
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