Battery Planning & Sizing Engine
Battery Capacity Calculator
Convert battery capacity between Amp-Hours (Ah), Milliamp-Hours (mAh), Watt-Hours (Wh), and Kilowatt-Hours (kWh) across DC voltages, and calculate net usable stored energy with customizable State of Charge (SOC) and health factors.
Convert battery capacity
Battery Chemistry Depth of Discharge (DoD) & Usable Energy Matrix
Nominal nameplate capacity does not reflect usable operational capacity. In battery power planning, Depth of Discharge (DoD) thresholds represent illustrative planning baselines to define modeled usable energy windows. The table below compares typical planning baselines across primary battery chemistries:
| Battery Chemistry | Nominal Cell Voltage | Illustrative Planning DoD | Usable Energy from 12V 100Ah (1.20 kWh Nominal) | Usable Energy from 48V 100Ah (4.80 kWh Nominal) | Typical Published Cycle Life (@ Baseline DoD, 0.2C / 25°C) | Typical Round-Trip Efficiency |
|---|---|---|---|---|---|---|
| LiFePO4 (Lithium Iron Phosphate) | 3.20 V / cell | 80% – 90% (Planning baseline) | 0.96 – 1.08 kWh (960 – 1,080 Wh) | 3.84 – 4.32 kWh (3,840 – 4,320 Wh) | 3,000 – 6,000+ cycles | 92% – 98% |
| NMC Lithium (Nickel Manganese Cobalt) | 3.65 – 3.70 V / cell | 70% – 80% (Planning baseline) | 0.84 – 0.96 kWh (840 – 960 Wh) | 3.36 – 3.84 kWh (3,360 – 3,840 Wh) | 1,500 – 2,500 cycles | 90% – 95% |
| AGM Sealed Lead-Acid (Deep Cycle) | 2.00 V / cell | 50% (Planning baseline) | 0.60 kWh (600 Wh) | 2.40 kWh (2,400 Wh) | 400 – 700 cycles | 80% – 85% |
| Gel Lead-Acid (Deep Cycle) | 2.00 V / cell | 50% (Planning baseline) | 0.60 kWh (600 Wh) | 2.40 kWh (2,400 Wh) | 500 – 900 cycles | 80% – 85% |
| Flooded Lead-Acid (FLA Deep Cycle) | 2.00 V / cell | 50% (Planning baseline) | 0.60 kWh (600 Wh) | 2.40 kWh (2,400 Wh) | 300 – 600 cycles | 75% – 82% |
*Note: Illustrative planning assumptions; actual usable capacity depends on manufacturer limits, BMS/cutoff settings, temperature, discharge rate, battery condition, and application. Published cycle life and round-trip efficiency figures represent typical manufacturer benchmark ranges under nominal laboratory test conditions (25°C ambient, C/5 rate). Actual field lifespans vary depending on operating temperature, charge/discharge C-rates, and depth of cycling.
Amp-Hour (Ah) to Kilowatt-Hour (kWh) Quick Reference Matrix
Quick reference table converting common battery bank Amp-Hour (Ah) capacities into gross nominal energy (kWh) and illustrative usable energy (kWh @ 90% DoD planning baseline) across standard DC system voltages:
| Capacity (Ah) | 12V nominal (Nom / Usable) | 24V nominal (Nom / Usable) | 48V nominal (Nom / Usable) | Illustrative Example Use Case |
|---|---|---|---|---|
| 20 Ah | 0.24 kWh / 0.22 kWh | 0.48 kWh / 0.43 kWh | 0.96 kWh / 0.86 kWh | Illustrative example: small backup circuits, lightweight portable gear |
| 50 Ah | 0.60 kWh / 0.54 kWh | 1.20 kWh / 1.08 kWh | 2.40 kWh / 2.16 kWh | Illustrative example: auxiliary portable power kits, mobile setups |
| 100 Ah | 1.20 kWh / 1.08 kWh | 2.40 kWh / 2.16 kWh | 4.80 kWh / 4.32 kWh | Illustrative example: RV auxiliary storage, campervans, marine house banks |
| 200 Ah | 2.40 kWh / 2.16 kWh | 4.80 kWh / 4.32 kWh | 9.60 kWh / 8.64 kWh | Illustrative example: off-grid cabin storage, solar workshops |
| 300 Ah | 3.60 kWh / 3.24 kWh | 7.20 kWh / 6.48 kWh | 14.40 kWh / 12.96 kWh | Illustrative example: expanded off-grid systems, dual-inverter setups |
| 400 Ah | 4.80 kWh / 4.32 kWh | 9.60 kWh / 8.64 kWh | 19.20 kWh / 17.28 kWh | Illustrative example: whole-home residential battery backup banks |
*Note: Calculations use exact nominal voltages (12V, 24V, 48V). Illustrative example use cases are for general context only; actual battery sizing requires detailed load, runtime, and inverter capacity calculations.
Milliamp-Hour (mAh) to Watt-Hour (Wh) & kWh Conversion
Portable power banks, drones, and smartphone batteries are rated in milliamp-hours (mAh). Because 1 Ah = 1,000 mAh, multiplying mAh by single-cell nominal lithium voltage (3.7V nominal) yields stored internal cell Watt-hours:
| Rating in mAh | Equivalent in Ah | Stored Internal Energy (Wh @ 3.7V) | Stored Energy (kWh) | FAA Carry-On Status (49 CFR § 175.10(a)(18)) |
|---|---|---|---|---|
| 3,000 mAh | 3.0 Ah | 11.1 Wh | 0.011 kWh | Allowed in Carry-On (≤ 100 Wh) |
| 5,000 mAh | 5.0 Ah | 18.5 Wh | 0.019 kWh | Allowed in Carry-On (≤ 100 Wh) |
| 10,000 mAh | 10.0 Ah | 37.0 Wh | 0.037 kWh | Allowed in Carry-On (≤ 100 Wh) |
| 20,000 mAh | 20.0 Ah | 74.0 Wh | 0.074 kWh | Allowed in Carry-On (≤ 100 Wh) |
| 27,000 mAh | 27.0 Ah | 99.9 Wh | 0.099 kWh | Allowed in Carry-On (Max standard limit: 100 Wh) |
| 40,000 mAh | 40.0 Ah | 148.0 Wh | 0.148 kWh | Requires Airline Approval (101–160 Wh, max 2 spares) |
| 50,000 mAh | 50.0 Ah | 185.0 Wh | 0.185 kWh | Forbidden in Passenger Baggage (> 160 Wh) |
*Regulatory Citation: Federal Aviation Administration (FAA) PackSafe and U.S. DOT Hazardous Materials Regulations (49 CFR § 175.10(a)(18)). Delivered energy at the output port will be lower than internal cell Wh due to DC-DC conversion and circuit losses.
4-Step Manual Calculation Derivation: Sizing Usable kWh & Ah
Follow this 4-step engineering walkthrough to manually calculate the required battery capacity in Amp-hours and kilowatt-hours for any DC electrical load profile:
Step 1: Calculate Total Daily Load Energy Demand (Wh)
Multiply power draw in Watts by operating hours per day across all critical AC/DC circuits:
E_load (Wh) = ∑ (Power_Watts × Hours_Per_Day) | Example: 500W load × 8 hours = 4,000 Wh (4.0 kWh)
Step 2: Adjust for Inverter & Wiring Inefficiencies
DC-to-AC inverters have conversion efficiencies typically ranging from 88% to 94%:
E_required (Wh) = E_load (Wh) ÷ Inverter_Efficiency | Example: 4,000 Wh ÷ 0.90 = 4,444.4 Wh
Step 3: Define the Modeled Usable Energy Window & Battery Health
Apply modeled discharge boundaries (e.g. 90% for lithium or 50% for lead-acid planning assumptions) and battery health capacity factor:
E_nominal (Wh) = E_required (Wh) ÷ (DoD × Health_Factor) | LiFePO4: 4,444.4 Wh ÷ (0.90 × 1.0) = 4,938.3 Wh (~4.94 kWh nominal)
Step 4: Convert Required Nominal Energy to Amp-Hours (Ah)
Divide nominal Watt-hours by system voltage (or multiply nominal kWh by 1,000 before dividing by voltage):
Capacity (Ah) = (E_nominal_kWh × 1,000) ÷ System_Voltage = E_nominal_Wh ÷ System_Voltage
12V Bank: 4,938.3 Wh ÷ 12V = 411.5 Ah | 48V Bank: 4,938.3 Wh ÷ 48V = 102.9 Ah
Calculation Formulas
Converts electrical charge capacity (Ah) to stored kilowatt-hours (kWh) and calculates real usable energy based on operating state-of-charge boundaries.
Variable Definitions
AhBattery Charge Capacity(Ah)- Rated charge capacity under the manufacturer's specified test and discharge conditions.
Voltage_VNominal System Voltage(V)- Nominal terminal voltage (3.7V, 12V, 12.8V, 24V, 48V, 51.2V, etc.).
Nominal_kWhGross Rated Energy(kWh)- Theoretical maximum stored electrical energy.
DoD WindowDepth of Discharge Window(fraction)- Modeled usable SOC window (Start_SOC minus minimum reserve cutoff).
HealthBattery Health / Capacity Factor(fraction)- Available capacity derating factor relative to nominal nameplate (1.00 = 100%).
Calculation Notes
- 1,000 milliamp-hours (mAh) = 1 Amp-Hour (Ah).
- 1 Kilowatt-Hour (kWh) = 1,000 Watt-Hours (Wh).
- Usable_Wh = Nominal_Wh × (Start_SOC − Reserve_SOC) × Health is a simplified planning model and does not capture all real-world dynamic losses or temperature effects.
- Illustrative planning assumptions: actual usable capacity depends on manufacturer limits, BMS cutoff settings, discharge rate, and temperature.
Frequently Asked Questions (FAQ)
How do you convert Amp-hours (Ah) to Kilowatt-hours (kWh)?
How many kWh is a 12V 100Ah battery?
How many kWh is a 200Ah battery?
How do you convert mAh to kWh?
How do you convert Watt-hours (Wh) to Amp-hours (Ah)?
What is the difference between nominal and usable battery capacity?
Calculation Notes & Technical References
- IEEE Std 485: IEEE Recommended Practice for Sizing Lead-Acid Batteries for Stationary Applications.
- IEC 62619: Secondary cells and batteries containing alkaline or other non-acid electrolytes — Safety requirements for secondary lithium cells and batteries.
- UL 1973: Standard for Batteries for Use in Stationary and Motive Auxiliary Power Applications.
- NFPA 70 (NEC Article 706): National Electrical Code requirements for Energy Storage Systems (ESS).