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Peukert's Law Battery Capacity

Calculate true usable battery runtime under heavy DC loads using Peukert's Law to account for electrochemical capacity collapse at high discharge rates.

Battery Bank Profiling

Chemistry & Manufacturer Baselines

⚡ ELECTROCHEMICAL WARNING: If your load is significantly higher than the standard 20-hour test rate, internal battery resistance turns your energy into heat. A 100Ah battery pulled at 30 Amps might only yield 60Ah of true usable power.

Expected Runtime

2.33 Hrs
Time until full voltage collapse.

True Usable Capacity

69.9 Ah
What you actually get (vs 100Ah rated)
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What is Peukert's Law & Battery Capacity Collapse?

A 100Ah battery does NOT deliver 100Ah under all conditions. The faster you pull current from a lead-acid battery, the less total energy you extract before voltage collapses. This is Peukert's Law — a fundamental electrochemical reality that the off-grid industry often ignores, leaving systems critically undersized. Lithium (LiFePO4) batteries are nearly immune while flooded lead-acid is severely affected.

Mathematical Foundation

Peukert's Law — Corrected Runtime
t=H⋅(CI⋅H)kt = H \cdot \left(\frac{C}{I \cdot H}\right)^k
tt= Actual runtime until full voltage collapse (hours)
HH= Manufacturer's rated discharge test time (hours). Most batteries are rated at C20 (H=20 hours).
CC= Rated capacity from the datasheet at the H-hour rate (Ah)
II= Your actual real-world load current draw (Amps)
kk= Peukert's constant (battery chemistry exponent): Lithium LiFePO4=1.05, AGM=1.15, Gel=1.20, Flooded Lead Acid=1.30, Cheap Starting Battery=1.45
True Usable Capacity
Ctrue=t×IC_{true} = t \times I
CtrueC_{true}= True amp-hours available at your discharge rate (Ah) — always ≤ rated C
tt= Runtime calculated from Peukert's equation (hours)
II= Load current (Amps)

Laws & Principles

  • The C-Rating Baseline: Manufacturer Ah ratings are measured at a specific standard discharge current. Most lead-acid batteries are C20 rated — their 100Ah capacity is measured discharging at 5A (100Ah ÷ 20hrs = 5A) over 20 hours.
  • High Discharge Penalty: Pulling 30A from that same 100Ah/C20 flooded battery (k=1.30) results in only ~60-65Ah of usable capacity — nearly 40% of your rated capacity disappears as internal resistance heat.
  • Peukert's Constant Chemistry Guide: Peukert's k is the exponent quantifying electrochemical degradation under load. Lithium (LiFePO4) cells have k≈1.05 because ion transport in lithium chemistry doesn't degrade significantly under current. Flooded lead-acid at k=1.30 is severely punished at high discharge.
  • Depth of Discharge: This calculator shows runtime to 0% remaining voltage. In practice, lead-acid batteries should never be discharged beyond 50% to preserve cycle life. Lithium can safely go to 80-90% DoD.
  • Temperature Effects Not Included: Cold temperatures significantly reduce all battery capacities further. A lead-acid battery in -10°C conditions may only deliver 60-70% of its room-temperature rated capacity, compounding the Peukert loss.

Step-by-Step Example Walkthrough

" An off-grid cabin has a 200Ah (C20 rated) flooded lead-acid battery bank running a 24V inverter. During a party, the load spikes to 50 Amps DC. How long before the bank is depleted? "

  1. 1. Identify inputs: C=200Ah, H=20 hours (C20 rating), I=50A, k=1.30 (flooded lead acid).
  2. 2. Apply Peukert's formula: t = 20 × (200 / (50 × 20))^1.30 = 20 × (200/1000)^1.30 = 20 × (0.20)^1.30.
  3. 3. Calculate (0.20)^1.30: = 0.20^1.30 ≈ 0.1316.
  4. 4. t = 20 × 0.1316 = 2.63 hours to full voltage collapse.
  5. 5. True usable capacity: 2.63 hours × 50A = 131.6 Ah — only 65.8% of the rated 200Ah.
Final Result: The 200Ah bank only yields 132Ah (66%) at 50A discharge due to Peukert's Law. The cabin will lose power in 2.6 hours, not the 4 hours (200Ah ÷ 50A) a naive calculation would predict. Upgrading to LiFePO4 (k=1.05) would yield ~190Ah — 44% more usable energy from the same rated capacity.

Quick Answer: How does Peukert's Law work?

Peukert's Law demonstrates mathematically that a battery's total usable capacity decreases exponentially as you draw current from it faster. A battery labeled "200Ah" can only provide 200 Amp-hours if drained slowly over 20 hours (at 10 Amps). If you strap a massive inverter to it and pull 80 Amps, internal resistance causes the voltage to collapse early, effectively shrinking the battery to perhaps 130Ah of usable power. The Peukert's Law Battery Capacity Calculator above recalculates exactly how much runtime you actually possess when subjecting different battery chemistries (like Lead-Acid vs. Lithium) to high-demand appliances.

Battery Capacity Collapse Scenarios

The Microwave Disappointment

An RV owner installs two 100Ah flooded lead-acid batteries (200Ah total, k=1.30). They want to run a 1,500W microwave via an inverter, generating a 140A DC draw. A naive calculation (200Ah ÷ 140A) implies 1.4 hours of runtime. But Peukert's Law dictates the bank only yields 77Ah under such a devastating load—barely 30 minutes of total runtime before the voltage crashes below 10.5V and the inverter shuts down. The owner realizes they need to triple their battery bank just to handle the amperage safely without deep-cycling.

The Lithium Upgrade

An off-grid telecom shack replaces a 400Ah AGM bank (k=1.15) with a 200Ah LiFePO4 bank (k=1.05). At their baseline 5A load, both banks perform adequately. But during a severe weather event, backup transmitters spike the load to 60 Amps. Under Peukert's Law, the 400Ah AGM bank collapses to ~250Ah of true usable energy. The 200Ah Lithium bank, almost entirely immune to Peukert effects at 60A, steadily delivers 185Ah. The telecom owner discovers the much smaller lithium bank performs nearly identically to the massive lead bank under high-stress conditions.

Peukert's Constants (k) by Battery Chemistry

Battery Chemistry Typical Peukert's Constant (k) Susceptibility to High Draw
Lithium Iron Phosphate (LiFePO4)1.03 – 1.05Extremely Low. Nearly linear capacity to 1C draw.
Lithium-Ion (NMC)1.02 – 1.04Extremely Low. Ideal for massive instantaneous surge.
AGM (Absorbent Glass Mat) Lead-Acid1.10 – 1.15Moderate. Better than flooded, bad for whole-house loads.
Gel Lead-Acid1.15 – 1.25High. Gel struggles with internal heat on heavy discharge.
Flooded Lead-Acid (Deep Cycle)1.25 – 1.35Very High. Capacity severely collapses above C/5 load.
Cheap Automotive Starting Battery1.40 – 1.60Catastrophic. Not meant for continuous deep discharge.

Note: "C" rating indicates the time division of the battery capacity. For a 100Ah battery, a C/20 draw is 5 Amps; a 1C draw is 100 Amps.

Pro Tips for Battery Bank Design

Do This

  • ✓Calculate to a strict 50% Depth of Discharge (DoD). Peukert's Law shows you how fast the battery reaches 0% (voltage collapse). From a lifespan perspective, you rarely want to drain a lead-acid battery past 50%. Take your Peukert-corrected runtime and cut it in half to find your safe operational limit.
  • ✓Determine your "H" rating first. Check the manufacturer specification sheet. Most deep cycle batteries are rated at C/20 (H=20). A massive fork-lift battery might be rated at C/6 (H=6). You must input this standard benchmark correctly, otherwise the exponential formula completely miscalculates your runtime.

Avoid This

  • ✗Never trust generic AH math. If an installer says "200Ah battery ÷ 50A load = 4 hours," fire them. Lead-acid chemistry drops massive amounts of energy as waste heat during high amperage loads. Depending on the Peukert constant, it might be 2.2 hours, not 4.
  • ✗Don't ignore Temperature Coefficients. Peukert's Law assumes a standard 25°C (77°F) environmental temperature. If your battery shed sits at -10°C (14°F), your bank is bleeding another 30% of its base capacity before you even apply Peukert's Law scaling.

Frequently Asked Questions

Why do lead-acid batteries lose capacity under heavy load?

It is a matter of chemical reaction speed and internal resistance. When a lead-acid battery discharges, sulfate ions must physically diffuse through the electrolyte. During a heavy load, you consume electrons faster than the chemical ions can migrate into the lead plates. The internal resistance spikes, turning your stored energy into heat rather than electricity, resulting in premature voltage collapse.

Does Peukert's Law apply to Lithium batteries?

Yes, but the effect is so minimal it's often ignored. Lithium chemistries (like LiFePO4) have a Peukert's constant (k) around 1.05. Because lithium ion pathways operate with extremely low internal resistance, pulling a 1C load (e.g., 100 Amps from a 100Ah battery) might only result in a 3-5% capacity loss. Lead-acid under the same stress could lose 50%.

How do I find my battery's Peukert's constant?

You have two options: (1) Find the constant 'k' strictly published in the manufacturer's technical data sheet (very rare outside of premium brands like Trojan or Rolls). (2) Most commonly, calculate it yourself by taking two different published discharge ratings from the spec sheet (e.g., the 20-hour capacity vs. the 5-hour capacity) and reverse-engineering the logarithm curve. Or, simply use the chemistry averages listed in our reference table.

Does capacity lost to Peukert's Law "recover"?

Partially. It's called the "recovery effect." If you pull a severe load and drop the battery voltage so low that an inverter shuts off, letting the battery sit idle for an hour allows the chemical sulfate ions to slowly diffuse back into equilibrium. The voltage will creep back up, allowing you to pull a little bit more low-amperage power out of it—but the energy lost as outright heat during the high draw is permanently destroyed for that cycle.

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