Battery Peukert Capacity Calculator
Enter rated capacity, rating period, Peukert exponent and load to see the real runtime and the capacity you actually get.
Step-by-step
- Enter valid values to begin.
Peukert’s law t = H (C / I H)k is an empirical model. It has no temperature or age term and is best between about 0.05C and 1C. The chemistry k ranges are typical values, not ratings; the exponent you enter is used. Power mode converts I = P / V at the nominal bank voltage, so a real constant-power load draws more current as the voltage sags. Usable Ah = DoD × effective capacity. Confirm with the manufacturer discharge tables (IEEE 485 / IEC 60896).
Peukert’s Law: Why a Battery Gives Less Than Its Label at High Current
Core Engineering Principles
A lead-acid label says 100 Ah, and the small print says at the 20-hour rate. That means the cell was drained over 20 hours, about 5 A, to its end voltage. Pull 40 A and the plates cannot keep up: acid at the plate surface is used faster than diffusion replaces it, and you hit cut-off with charge still in the cell. Wilhelm Peukert described it in 1897 with an empirical power law, t = H × (C / (I × H))k. We read k as how hard the battery punishes high current. Flooded lead-acid sits around 1.2–1.4, AGM near 1.05–1.15, gel 1.1–1.25 and LiFePO4 only 1.01–1.05, so lithium behaves almost like an ideal tank.
Effective capacity, I × t, is what you really get at a given load. You can measure k yourself: discharge the battery at two currents, record both runtimes to the same end voltage, and apply k = (log t2 − log t1) / (log I1 − log I2). Do not trust the law blindly. It ignores temperature, so a cold battery loses more than predicted. It ignores age, since k creeps up as plates sulfate. It fails at very low currents, where self-discharge dominates, and at very high ones, where sag and heating take over. Treat it as an estimate between about 0.05C and 1C and check critical jobs against manufacturer tables.
Imax = (C / H) × (H / ttarget)1/k
k = (log t2 − log t1) / (log I1 − log I2)
NEC & Standard References
IEC 60896-11 and IEC 60896-21/-22 define the general requirements and test methods for stationary lead-acid batteries,. IEEE 485 is the recommended practice for sizing stationary lead-acid batteries, using manufacturer discharge data. IEEE 1188 covers maintenance, testing and replacement of VRLA batteries including capacity tests. Verify the editions that apply.1. C / (I × H) = 100 / 800 = 0.125, and 0.1251.25 = 0.0743.
2. t = 20 × 0.0743 = 1.487 h, which is 1 h 29 min.
3. Effective capacity = 40 × 1.486 = 59.5 Ah, or 59.5% of rated. The C-rate is 40 / 100 = 0.40C.
4. To a 50% limit: 0.5 × 59.46 = 29.7 Ah, giving 0.743 h, or 45 min.
5. An ideal battery (k = 1) would run 100 / 40 = 2.5 h.
6. For a 5 h target: I = (100 / 20) × (20 / 5)1/1.25 = 15.2 A.
- Check the rating period. Marketing Ah are often quoted at the 100 h rate; compare batteries at the same H.
- Inverter draw rises as voltage falls. A constant-power load pulls more amps near the end, so enter a low average voltage.
- Never compare Ah across chemistries. A 100 Ah lithium battery delivers far more at 40 A than a 100 Ah flooded battery.
- Peukert has no temperature term. Derate separately for cold and age.
- Above 1C, stop. Use the manufacturer’s tables.