Battery Capacity Ah to Wh Converter
Convert battery capacity metrics between Amp-hours (Ah) and Watt-hours (Wh) using nominal pack voltage. Fast, transparent calculator.
Parameters
Nominal voltage of cell stack or module
Estimated Outputs
A 1.28 kWh pack can power a 100W load for approximately 11.5 hours at 90% system efficiency.
Why nominal voltage matters
Two batteries with identical 100 Ah capacities can hold very different amounts of total energy. A 100 Ah 12V pack holds 1.2 kWh, whereas a 100 Ah 48V pack holds 4.8 kWh. Total energy capacity is the correct index for comparisons.
Formulas & Worked Examples
Mathematical Formulas
The conversion between electric charge capacity (Ah) and total energy capacity (Wh) is direct, based on Ohm's law:
Example 1: Convert 200Ah at 12.8V to Wh
You have a 200Ah LiFePO4 battery at 12.8V nominal and need to find the total energy in Watt-hours.
Given Values
- Capacity: 200 Ah
- Nominal Voltage: 12.8 V
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Final Answer
2,560 Wh
A 200Ah battery at 12.8V stores 2,560 Wh (2.56 kWh) of total energy — enough to power a 256W load for 10 hours.
Example 2: Convert 5kWh to Ah at 48V
You're designing a 48V battery bank and need to determine the Amp-hour capacity required for 5 kWh of usable energy.
Given Values
- Energy: 5 kWh (5,000 Wh)
- Nominal Voltage: 48 V
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Final Answer
≈ 104.17 Ah
At 48V, a 5 kWh battery bank requires approximately 104.17 Ah of capacity. This is equivalent to about 3.3 cells in a 16S LFP 48V configuration at 105Ah each.
Example 3: Convert 500Wh to Joules and kWh
You have a portable power station rated at 500Wh and need to express its capacity in both Joules (SI unit) and kWh for comparison.
Given Values
- Energy: 500 Wh
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Final Answer
1,800,000 J (1.8 MJ) or 0.5 kWh
500 Wh equals 1.8 million Joules or 0.5 kWh. For context, 0.5 kWh can run a 50W refrigerator for 10 hours or charge a smartphone approximately 40 times.
Energy Unit Conversion Reference
| From | To | Formula | Example |
|---|---|---|---|
| Ah → Wh | Multiply by voltage | Wh = Ah × V | 100Ah × 12.8V = 1,280 Wh |
| Wh → Ah | Divide by voltage | Ah = Wh / V | 1,280 Wh / 12.8V = 100 Ah |
| Wh → kWh | Divide by 1000 | kWh = Wh / 1000 | 1,280 Wh = 1.28 kWh |
| kWh → Wh | Multiply by 1000 | Wh = kWh × 1000 | 1.28 kWh = 1,280 Wh |
| Wh → Joules | Multiply by 3600 | J = Wh × 3600 | 1,280 Wh = 4,608,000 J |
| Wh → BTU | Multiply by 3.412 | BTU = Wh × 3.412 | 1,280 Wh = 4,367 BTU |
Common energy unit conversions for battery calculations
Frequently Asked Questions
What is the difference between Ah and Wh?
Amp-hours (Ah) measure electric charge capacity (the volume of electrons moving past a point). Watt-hours (Wh) measure total electric energy capacity (the volume of electrons multiplied by the electrical force, or voltage). Wh is the actual measurement of energy potential.
What voltage value should I use for nominal voltage?
Always use the average nominal voltage of the pack rather than peak charge or low discharge cut-off voltages. For example, a single LiFePO4 cell is nominal 3.2V (peak 3.65V, cut-off 2.5V). For a 4S system, nominal is 12.8V.
Why is capacity sometimes measured in Ah instead of Wh?
Historically, lead-acid batteries were standardized around 6V or 12V outputs, making Amp-hours a convenient shortcut comparison. However, with modern multi-voltage lithium architectures (12V, 24V, 48V, 400V, 800V), Watt-hours are required for safe comparison.
How do temperature effects impact Wh capacity?
Lower temperatures reduce chemical kinetics inside cells, which increases internal resistance and drops the cell's output voltage curve during discharge. Since Wh = Ah × V, this lower voltage drop directly translates to fewer total Watt-hours delivered.
How do I compare a 12V 200Ah battery with a 48V 100Ah battery?
Convert both to Wh: 12V × 200Ah = 2,400 Wh. 48V × 100Ah = 4,800 Wh. The 48V battery stores twice the energy despite having half the Ah rating. Always compare in Wh for fair comparison.
Can I use Ah to calculate runtime?
Only if the load is specified in amps. If the load is in watts (the more common case), convert to Wh first, then divide by load watts. Formula: Runtime (hours) = (Ah × V × DoD) / (Load W / Efficiency).
What is the relationship between Ah, Wh, and kWh?
Ah × Voltage = Wh. Wh / 1000 = kWh. For example, a 200Ah battery at 51.2V = 10,240 Wh = 10.24 kWh. kWh is simply Wh expressed in thousands for large systems.
Why do some batteries list only Ah and others only Wh?
Ah is traditional for lead-acid and some lithium manufacturers. Wh is increasingly preferred because it directly represents energy content. Always check if the stated Ah is at the pack's nominal voltage before comparing.
Does Ah capacity change with discharge rate?
Yes. Higher discharge rates reduce usable Ah due to internal resistance losses. This is especially pronounced in lead-acid (Peukert effect). A 100Ah lead-acid battery may deliver only 60Ah at 1C rate. LFP is less affected but still shows some capacity reduction at high C-rates.
How does DoD affect the Ah vs Wh comparison?
DoD limits reduce usable capacity in both Ah and Wh equally. A 100Ah battery at 80% DoD provides 80Ah usable, or (80Ah × V) Wh usable. The conversion between Ah and Wh remains valid regardless of DoD — DoD simply scales both proportionally.
Is Wh the best metric for comparing all batteries?
Wh is the best metric for comparing total energy content. However, for applications requiring high current, also consider max continuous discharge (A) and C-rate. Two batteries with the same Wh may have very different current delivery capabilities.
What Is Battery Capacity Ah to Wh Converter?
Why This Calculation Matters
→ Comparing batteries by Ah alone is misleading — a 100Ah 12V battery holds 3× less energy than a 100Ah 48V battery.
→ Load calculations require Wh, not Ah — a 500W load runs for 2.4 hours on 1,200 Wh but you need the correct unit.
→ Batteries at different voltages cannot be compared by Ah — only Wh provides a fair energy comparison.
→ Solar and backup systems are designed in Wh/kWh — converting Ah to Wh is the first step in any sizing calculation.
→ Charger specifications often mix Ah and Wh ratings — confusion leads to undersized or oversized charging systems.
Practical Applications
Battery Comparison Shopping
Compare batteries of different voltages and chemistries on equal footing by converting to Wh.
System Sizing
Convert Ah ratings to Wh for load-based energy storage sizing calculations.
Solar Design
Convert battery Ah ratings to Wh to match against daily solar production and consumption.
Runtime Estimation
Convert Ah to Wh to calculate how long a battery can sustain a given wattage load.
EV Range Calculation
Convert pack capacity from Ah to Wh for range estimation and energy consumption analysis.
Common Mistakes to Avoid
✗ Comparing batteries by Ah alone without considering voltage — a 100Ah 48V battery stores 4× more energy than a 100Ah 12V battery. Always convert to Wh for fair comparison.
✗ Using peak charge voltage instead of nominal voltage — Wh calculations must use nominal voltage (e.g., 3.2V for LFP, 3.7V for NMC), not the peak charge voltage (3.65V or 4.2V).
✗ Ignoring DoD when converting — a 100Ah battery at 80% DoD only provides 80Ah usable. Convert the usable Ah, not the total rated Ah, for runtime calculations.
✗ Confusing Wh and Ah for load calculations — loads are specified in watts, not amps. Always convert battery capacity to Wh before dividing by load power for runtime.
✗ Forgetting system efficiency — a 100Ah 12.8V battery stores 1,280 Wh, but after inverter losses (90% efficiency), only 1,152 Wh reaches the load.
✗ Assuming Ah is independent of discharge rate — higher C-rates reduce usable Ah due to internal resistance losses, especially in lead-acid batteries (Peukert effect).
✗ Using kWh for small battery comparisons — kWh is appropriate for large systems, but Wh provides more intuitive resolution for small batteries under 5 kWh.
✗ Mixing units in calculations — never mix Ah and Wh in the same formula without converting. Ah × Voltage = Wh; Wh / Voltage = Ah.
✗ Ignoring temperature derating — cold temperatures reduce both Ah and Wh capacity. A battery rated at 100Ah at 25°C may only deliver 85Ah at 0°C.
✗ Not verifying nominal voltage — always check the manufacturer's nominal voltage specification. Using 12V instead of 12.8V for LFP introduces a 6.25% error.
Why Trust These Calculations?
The conversion formulas (Wh = Ah × V, Ah = Wh / V) are fundamental electrical relationships. All calculations are transparent and use standard SI units.
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