Battery Life, Runtime & Peukert's Law Calculator: Calculate battery runtime, effective capacity under Peukert. Fast, free, and secure client-side execution in your browser.
The Physics of Battery Discharge & Peukert's Law
Calculating battery runtime appears deceptively simple: dividing total Amp-hours by the load current. However, in physical electrochemical cells, a battery's delivered capacity is not a static constant. As the rate of discharge increases, chemical reaction kinetics, internal ohmic resistance ($I^2 R$ heat loss), and localized ion depletion at the electrode boundaries severely reduce the actual electrical charge that can be retrieved before the cutoff voltage is reached.
This non-linear capacity degradation was mathematically formulated by German scientist Wilhelm Peukert in 1897:
$C_p = I^k times t$ or rearranged for runtime: $t = H times left(frac{C}{I times H}right)^k$
Where:
- $C$ = Rated battery capacity (in Amp-hours) at discharge rating $H$ (typically 20 hours)
- $I$ = Continuous discharge current (in Amperes)
- $k$ = Peukert's exponent (a dimensionless property of the chemistry)
- $t$ = Actual time to full discharge (in hours)
Peukert's Exponent ($k$) Across Cell Chemistries
In a hypothetical ideal battery with zero internal resistance and instantaneous ion diffusion, Peukert's exponent would equal $1.00$—meaning capacity remains completely identical regardless of whether you discharge it over 100 hours or 5 minutes.
- Flooded Lead-Acid ($k approx 1.20 - 1.30$): Flooded lead-acid batteries suffer from heavy lead sulfate crystallization and electrolyte stratification. Under high-drain loads (such as electric winches or induction cooktops), usable capacity collapses by over 40%.
- AGM Lead-Acid ($k approx 1.12 - 1.18$): Absorbed Glass Mat batteries bind electrolyte in fiberglass mats, lowering internal resistance and reducing Peukert loss compared to flooded designs.
- Lithium Iron Phosphate / LiFePO4 ($k approx 1.02 - 1.05$): Modern LiFePO4 cells feature ultra-low internal impedance and rapid lithium-ion intercalations. Because $k$ is close to 1.00, LiFePO4 delivers virtually full rated capacity across high C-rate draws without severe thermal dissipation.
Step-by-Step Worked Numerical Example
Consider an off-grid camper powering an induction burner from a 12V 100Ah battery system:
- Appliance Load: 600 Watts AC
- Inverter Efficiency: 90% ($0.90$)
- Nominal Voltage: 12.0 Volts DC
- Battery Pack: 100 Ah rated at 20-hour rate ($H = 20text{ hrs}$)
Step 1: Calculate the DC current drawn from the battery:
$P_{text{DC}} = frac{600text{ W}}{0.90} approx mathbf{666.67text{ Watts}}$
$I = frac{P_{text{DC}}}{V} = frac{666.67text{ W}}{12.0text{ V}} approx mathbf{55.56text{ Amperes}}$
Step 2: Contrast runtime between Lead-Acid ($k = 1.25$) and LiFePO4 ($k = 1.05$):
Flooded Lead-Acid ($k = 1.25$, max 50% DoD):
$t_{text{full}} = 20 times left(frac{100}{55.56 times 20}right)^{1.25} = 20 times (0.090)^{1.25} = 20 times 0.0487 approx mathbf{0.974text{ hours}}$
Applying 50% safe DoD limit: $text{Runtime} = 0.974 times 0.50 approx mathbf{0.487text{ hrs}}; (mathbf{29.2text{ minutes}})$
LiFePO4 Lithium ($k = 1.05$, safe 85% DoD):
$t_{text{full}} = 20 times left(frac{100}{55.56 times 20}right)^{1.05} = 20 times (0.090)^{1.05} = 20 times 0.0797 approx mathbf{1.594text{ hours}}$
Applying 85% safe DoD limit: $text{Runtime} = 1.594 times 0.85 approx mathbf{1.355text{ hrs}}; (mathbf{81.3text{ minutes}})$
Even though both batteries have identical "100 Ah" nameplates, the LiFePO4 battery runs for 81 minutes compared to just 29 minutes for lead-acid—nearly 3x longer under heavy loads!
C-Rate & Depth of Discharge (DoD) Cycling Life
The C-Rate measures the speed of battery charging or discharging normalized to its rated capacity:
$text{C-Rate} = frac{text{Current (Amperes)}}{text{Rated Capacity (Amp-hours)}}$
A 100 Ah battery discharged at 100 Amps is operating at 1C (discharging completely in 1 hour). Discharging at 20 Amps represents 0.2C (5 hours). Operating continuously above 0.5C increases cell operating temperature, accelerating solid-electrolyte interphase (SEI) degradation and shortening overall lifespan.