Peukert's Law Battery Capacity Calculator

What is Peukert's Law and Battery Chemistry?

Peukert's Law, formulated by Wilhelm Peukert in 1897, describes the phenomenon that a battery's usable capacity decreases as the discharge rate increases. This is not a defect — it is a fundamental electrochemical property of lead-acid batteries. At high discharge rates, the sulfate ions in the electrolyte cannot diffuse to the electrode surface fast enough, meaning fewer of the active chemical sites participate in the reaction. The result is an effective capacity much lower than the label rating.

Mathematical Foundation

Peukert's Effective Capacity

C_{eff} = C \times \left( \frac{C}{I \times H} \right)^{(n-1)}

C_{eff}

= Effective (true usable) amp-hour capacity at the actual discharge rate I. This is always less than or equal to the rated capacity C.

C

= Rated capacity in amp-hours at the standard (C20) discharge rate, as printed on the battery label.

I

= Actual load current in Amps. As this increases above the rated rate (C÷H), Ceff drops exponentially.

H

= Rated discharge time in hours (typically 20 hours for deep-cycle batteries — the C20 standard).

n

= Peukert's exponent — measures the battery chemistry's sensitivity to discharge rate. Higher n = worse performance under high loads. Flooded lead-acid: ~1.2. AGM: ~1.1. LiFePO4: ~1.05.

True Runtime

t = C_{eff} / I

t

= Actual runtime in hours at the load current I, after accounting for Peukert capacity loss.

C_{eff}/I

= The ratio of effective capacity to actual load. Does NOT simplify to H except when I equals the rated discharge current.

Laws & Principles

C20 Rating Standard: Nearly all deep-cycle battery capacity ratings are specified at the 20-hour rate (C20). A 100Ah C20 battery is rated to deliver 5A for 20 hours. Comparison between battery brands is only valid if they use the same rating standard.
The Deception of Amp-Hours: Drawing 50A from a 100Ah lead-acid battery does NOT give you 2 hours of runtime. With n=1.2, Ceff = 100 × (100/(50×20))^0.2 = 100 × (0.1)^0.2 = 100 × 0.631 = 63.1Ah → only 63.1÷50 = 1.26 hours. A 37% shortfall compared to naive estimates.
Lithium vs. Lead-Acid: LiFePO4 batteries have a Peukert exponent of 1.01–1.05, making them nearly immune to this effect. A lithium battery discharged at 5× its rated rate retains 95%+ of its capacity. This is one of lithium's most significant engineering advantages.
Depth of Discharge (DoD): Peukert's law applies to the usable capacity, which for lead-acid is further reduced by DoD limits. Lead-acid batteries should not be discharged below 50% SoC (to preserve cycle life), cutting usable capacity in half again.
Temperature Effect: Battery capacity degrades significantly below freezing. At 0°F (-18°C), lead-acid capacity can drop to 50% of rated capacity — compounding with Peukert losses for an even more severe reduction in cold climates.

Step-by-Step Example Walkthrough

" An off-grid cabin runs a 2,000W inverter powered by a 24V battery bank rated at 200Ah (C20). The inverter draws approximately 83 Amps from the 24V bank (2000 ÷ 24 = 83A). Peukert's exponent for flooded lead-acid: 1.2. "

1. Rated discharge current at C20: 200Ah ÷ 20h = 10A nominal rate.
2. Apply Peukert: Ceff = 200 × (200 / (83 × 20))^(1.2-1) = 200 × (200/1660)^0.2.
3. Inner ratio: 200/1660 = 0.1205. Power: 0.1205^0.2 = 0.696.
4. Effective capacity: 200 × 0.696 = 139.2Ah.
5. Usable at 50% DoD: 139.2 × 0.5 = 69.6Ah.
6. Runtime: 69.6Ah ÷ 83A = 0.84 hours (50 minutes).
Naive estimate without Peukert or DoD: 200Ah ÷ 83A = 2.4 hours — nearly 3× overestimate.

Final Result: The cabin inverter will run for approximately 50 minutes under 2,000W load, not the 2.4 hours a naive estimate suggests. The system requires at least 500Ah of battery capacity for 2 hours of reliable runtime.

Quick Answer: How do you calculate Peukert capacity loss?

You calculate Peukert capacity loss by applying Peukert's exponent (a metric of chemical resistance) against your battery's C-rate data sheet. As the amperage draw increases, a lead-acid battery physically cannot cycle internal ions fast enough to maintain voltage, resulting in lost capacity. Use this Peukert's Law Calculator to instantly calculate the true available Amp-Hours of your specific battery bank when subjected to heavy inverter loads.

Battery Chemistry	Typical "n" Value	High-Load Viability
Lithium / LiFePO4	1.01 – 1.05	Excellent
Sealed AGM (Lead)	1.08 – 1.15	Moderate
Gel Cell	1.10 – 1.25	Low-Moderate
Flooded Lead Acid (FLA)	1.20 – 1.35	Poor

Battery Chemistry

Typical "n" Value

High-Load Viability

Lithium / LiFePO4

1.01 – 1.05

Excellent

Sealed AGM (Lead)

1.08 – 1.15

Moderate

Gel Cell

1.10 – 1.25

Low-Moderate

Flooded Lead Acid (FLA)

1.20 – 1.35

Poor

Off-Grid Diagnostics

The Solar Blackout

An off-grid cabin uses four 100Ah Flooded Lead Acid batteries (400Ah total) at 12V. They install a 3,000W electric kettle which pulls 250 Amps when operating. The owner naturally assumes 400Ah ÷ 250A = 1.6 hours of runtime. However, because flooded batteries have a Peukert coefficient of 1.25, the 250A blast drops the effective capacity from 400Ah down to just 180Ah. If the batteries were already partially discharged, the voltage sags immediately and the inverter triggers a low-voltage catastrophic alarm within 5 minutes, completely defeating the entire solar grid.

The Lithium Upgrade

An RV owner upgrades their 200Ah Lead-Acid bank to a 200Ah Lithium (LiFePO4) bank. While the numerical Ah size didn't change, the new LiFePO4 chemistry has a Peukert coefficient of 1.05. When the RV air conditioner turns on and draws 120 Amps, the lithium bank effortlessly delivers its near full capacity, extending the heavy-draw runtime by almost 70% compared to the old lead-acid loop which choked heavily under the same air conditioning load.

Battery Bank Architecture

Do This

✓Oversize Lead-Acid specifically for high loads. If you intend to run microwaves, air conditioners, or heaters continuously on Lead-Acid chemistry, you must over-provision your amp-hour storage bank by at least 40% purely to mitigate the Peukert capacity drop.
✓Check the C-Rate testing metric. Always look at what Hour-rate the battery was tested at. A 100Ah "C20" battery is stronger than a 100Ah "C100" battery. The C100 battery only delivers 100Ah if you drain it over 100 hours extremely slowly.

Avoid This

✗Don't ignore the DoD (Depth of Discharge). Peukert tells you the maximum bounds of charge, but you cannot drain most lead-acid batteries beyond 50% without completely destroying the lead plates. Once you calculate Peukert capacity, cut that in half again to find the actual safe threshold.

Frequently Asked Questions

What decreases a battery's Peukert Exponent?

The internal chemistry determines the exponent. A lower number (closer to 1.00) is better because it implies the battery ignores heavy loads. High-end Lithium batteries score around 1.03 because they utilize dry chemical structures, while traditional liquid Flooded Lead Acid batteries score a poor 1.25 because the heavy sulfate ions struggle to travel through the liquid layer quickly under extreme power demands.

Does Peukert effect happen when charging?

Yes, the mathematical curve also applies reciprocally during charging, known as charge acceptance rate. A heavily depleted lead-acid battery cannot forcibly accept a massive amperage charge input all at once. The charger must taper the current down or the battery will boil off its water due to the internal chemical resistance defined by its exponent.

Why don't car batteries show Amp-Hours?

Car batteries are SLI (Starting, Lighting, and Ignition) design. They are intended to deliver huge 500-Amp bursts for a few seconds to kick over an engine. Because of this, they are measured in CCA (Cold Cranking Amps). Solar and boat networks use Deep Cycle batteries intended to be slowly drained over 20 hours, which is why those labels present an Amp-Hour measurement.

How do I use this Peukert Calculator?

Input your deep-cycle battery's rated AH size and the amount of amps your inverter will be pulling from it. Select the chemistry type (which sets the 'n' coefficient automatically). The system dynamically calculates how much of the battery's theoretical power will actually be usable, and how long it will run before hitting your safety Depth of Discharge cutoff.

Peukert's Law Battery Capacity Calculator

Peukert's Law Capacity

System Parameters

Adjusted Metrics