Peukert's Law Battery Runtime Calculator
How long a battery really lasts at a given current, allowing for the capacity it loses when discharged faster than its rated time.
Results
Runtime with Peukert's law
8.706
h
Runtime if capacity were fixed
10.000
h
Capacity actually delivered
87.06
Ah
Lost to the high current
12.9
%
The dashed line marks the value you entered.
What this tool does
Battery capacity is quoted at a gentle discharge — lead-acid batteries usually over 20 hours — and drawing current faster gets less out of it. Peukert's law captures this with one exponent: about 1.1 to 1.3 for lead-acid, close to 1.05 for lithium, where the effect is small. At ten times the rated current a lead-acid battery can lose a third of its capacity. The law is an empirical fit, less accurate at very low currents and with temperature changes, but much closer to reality than dividing amp-hours by amps.
Formula
t = H × (C ÷ (I × H))^k
Variables
| Symbol | Meaning | Unit |
|---|---|---|
c | Battery capacity | Ah |
hr | Hours the rated capacity refers to (e.g. 20 h) | h |
i | Discharge current | A |
k | Peukert exponent | — |
T | Runtime with Peukert's law | h |
TN | Runtime if capacity were fixed | h |
EC | Capacity actually delivered | Ah |
CL | Lost to the high current | % |
Worked example
- Battery capacity100 Ah
- Hours the rated capacity refers to (e.g. 20 h)20 h
- Discharge current10 A
- Peukert exponent1.2
- Runtime with Peukert's law8.706 h
- Runtime if capacity were fixed10.000 h
- Capacity actually delivered87.06 Ah
- Lost to the high current12.9 %
Limitations
- A battery does not give its full rated capacity at a heavy load: the higher the current, the less energy you actually get out. This calculation is linear, so treat it as an upper bound and use the efficiency field to allow for the difference.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.