A battery runtime calculator that goes beyond the naïve “amp-hours ÷ amps = hours” estimate by applying Peukert’s Law, charge/discharge efficiency, and depth of discharge — the three corrections that separate a textbook number from real-world runtime. Enter your pack’s rated capacity, chemistry, series/parallel layout and load, and it returns the corrected runtime, total energy in watt-hours, and a step-by-step working.
How it works
For an ideal battery, runtime is simply capacity divided by current. Real cells deliver less usable energy as you pull current faster — captured by Peukert’s exponent k:
t = (C / I)^k × (1 / I)^(k − 1) (equivalently t = C^k / I^k)
where C is the effective capacity in amp-hours (after depth-of-discharge and efficiency are applied) and I is the discharge current. For lithium chemistries k ≈ 1.05; for lead-acid k ≈ 1.2–1.3, which is why a lead-acid bank loses far more runtime under heavy load.
Three solve-for modes
| Mode | What you know | What it calculates |
|---|---|---|
| Runtime | Pack specs + load current | How long the pack lasts |
| Required capacity | Load + target hours | Minimum cell Ah rating you need |
| Maximum load | Pack specs + target hours | Maximum current you can draw |
All three modes use the same Peukert-corrected model, so the answers are mutually consistent.
Worked example: LiFePO4 off-grid system
A 12 V, 100 Ah LiFePO4 pack with a Peukert exponent of 1.05, 90% depth of discharge, and 96% efficiency under a 10 A continuous load:
- Usable capacity: 100 Ah × 0.90 × 0.96 = 86.4 Ah
- Peukert-corrected runtime: approximately 8.4 hours
- Total usable energy: approximately 1,036 Wh
Now compare the same pack under a heavier 30 A load (for example, a large inverter):
- Peukert effect reduces effective capacity at higher current
- Corrected runtime drops to roughly 2.6 hours — not the 2.88 hours a simple Ah ÷ A calculation would predict
The divergence between the naive estimate and the corrected figure grows larger as current increases and as the Peukert exponent rises (lead-acid is far more sensitive than lithium).
Chemistry presets and what they mean
| Chemistry | Peukert k | Typical DoD | Efficiency |
|---|---|---|---|
| Li-ion / LiPo | 1.03–1.08 | 80% | 93–97% |
| LiFePO4 | 1.05 | 90% | 95–98% |
| Lead-acid flooded | 1.20–1.30 | 50% | 75–85% |
| AGM lead-acid | 1.15–1.25 | 60% | 82–88% |
| NiMH | 1.10–1.20 | 80% | 80–90% |
These are typical values from manufacturer datasheets and published research. Your specific cells may differ — if your datasheet lists a Peukert exponent or a C-rate derating curve, enter those values directly.
Series vs parallel cells
Series (S): Multiplies voltage. A 4S pack of 3.7 V cells gives 14.8 V. Capacity stays the same as a single cell.
Parallel (P): Multiplies capacity. A 2P pack of 3 Ah cells gives 6 Ah. Voltage stays the same.
Combined: A 2S2P pack of 3.7 V / 3 Ah cells gives 7.4 V and 6 Ah. The calculator computes pack voltage and usable Ah from your S and P values before applying Peukert.
Common sizing mistakes
- Using rated capacity at a light discharge rate. Battery capacities are rated at a specific C-rate (typically C/10 or C/20). At higher discharge rates, available capacity is lower. Peukert’s correction accounts for this.
- Ignoring depth of discharge. Using 100% DoD on every cycle degrades most chemistries rapidly and voids many warranties. Size the pack for the DoD your chemistry recommends.
- Forgetting inverter efficiency. If you are powering AC loads through an inverter, the inverter typically adds 8–15% of losses on top of the battery’s own losses. Factor those in separately when sizing for an off-grid system.