What is Peukert's Law and why does it matter?

Peukert's Law (1897) captures the fact that batteries deliver less total energy when discharged faster. The formula is t = C^k / I^k, where C is effective capacity (Ah), I is discharge current (A), and k is the Peukert exponent. For an ideal battery k = 1 and the formula reduces to t = C / I. For a lead-acid battery k is typically 1.2–1.3, meaning pulling twice the current gives you noticeably less than half the runtime. Li-ion cells have k ≈ 1.03–1.08, making them far less sensitive to discharge rate — one reason they dominate portable electronics.

What is depth of discharge (DoD) and should I use 100%?

Depth of discharge is the fraction of nominal capacity you actually use before recharging. Using 100% DoD on every cycle degrades most chemistries rapidly. Practical limits are: Li-ion 80%, LiFePO4 90%, lead-acid 50–60%, NiMH 80%. The calculator applies your DoD percentage to the rated capacity before computing anything else, so the result already reflects realistic operating range. If you are sizing a battery for a product, use the chemistry's recommended DoD — oversizing by the corresponding factor extends cycle life dramatically.

How do series and parallel cells affect runtime?

Connecting cells in series multiplies voltage (V_pack = V_cell × S) but does not increase Ah capacity. Connecting cells in parallel multiplies capacity (C_pack = C_cell × P) but keeps voltage the same. A 2S2P pack of 3.7 V / 3 Ah cells gives 7.4 V and 6 Ah. The calculator automatically computes pack voltage and usable Ah from S and P before applying Peukert and efficiency corrections.

What efficiency value should I use?

Efficiency (η) accounts for heat losses from internal resistance, voltage sag under load, and self-discharge. Typical values by chemistry: Li-ion/LiPo 93–97%, LiFePO4 95–98%, lead-acid flooded 75–85%, AGM 82–88%, NiMH 80–90%. The chemistry presets fill sensible defaults. If your application involves high ambient temperature or aged cells, subtract another 5–10 percentage points.

What is the difference between this and a simple Ah ÷ A = hours calculation?

The simple formula ignores three real-world losses: (1) Peukert effect — capacity shrinks at higher discharge rates; (2) efficiency — internal resistance converts some stored energy to heat; (3) depth of discharge — cycling to 0% destroys most cells. This calculator applies all three corrections, so for a lead-acid bank the simple formula might predict 10 hours but the corrected answer might be 6–7 hours — a 30–40% error that matters for off-grid sizing.

How do I use the 'required capacity' mode to size a battery pack?

Select 'Required capacity', enter your average load in amps and your target runtime in hours, then set your Peukert exponent, efficiency, DoD, and number of parallel cells. The calculator tells you the minimum rated cell capacity in Ah (per cell) you need. Multiply by your pack price per Ah to compare options, or round up to the nearest standard cell size (e.g. 18650 = 3 Ah, 26650 = 5 Ah, 100 Ah lifepo4 prismatic).

Battery Runtime Calculator

A battery runtime calculator that goes beyond the naïve “amp-hours ÷ amps = hours” estimate by applying Peukert’s Law, charge/discharge efficiency, and depth of discharge — the three corrections that separate a textbook number from real-world runtime. Enter your pack’s rated capacity, chemistry, series/parallel layout and load, and it returns the corrected runtime, total energy in watt-hours, and a step-by-step working.

How it works

For an ideal battery, runtime is simply capacity divided by current. Real cells deliver less usable energy as you pull current faster — captured by Peukert’s exponent k:

t = (C / I)^k × (1 / I)^(k − 1) (equivalently t = C^k / I^k)

where C is the effective capacity in amp-hours (after depth-of-discharge and efficiency are applied) and I is the discharge current. For lithium chemistries k ≈ 1.05; for lead-acid k ≈ 1.2–1.3, which is why a lead-acid bank loses far more runtime under heavy load.

Worked example

A 12 V, 100 Ah LiFePO4 pack (k = 1.05, 90% DoD, 96% efficiency) under a 10 A load delivers roughly 100 × 0.90 × 0.96 = 86.4 Ah usable, and with the Peukert correction about 8.4 hours of runtime and 1,036 Wh of usable energy.

Modes

Solve for runtime (how long it lasts), required capacity (what size pack you need for a target runtime), or maximum load (how much you can draw for a given runtime). All three share the same corrected model, so the answers stay consistent.