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Batteries & solar

Battery Runtime Calculator with Peukert

Estimate how long a battery bank will run a load. Build the bank from series and parallel units, set the usable depth of discharge and inverter efficiency, and optionally apply Peukert's law to account for capacity falling at higher discharge currents.

For estimation and education. Not a substitute for a licensed engineer, the applicable codes (IEC 60364, NEC/NFPA 70, BS 7671, local regulations) or manufacturer data. Read the disclaimer.

Bank builder

V
Ah

Series adds voltage

Parallel adds Ah

Fraction, e.g. 0.5 = 50 %

Load

Load type
W

Typical 0.85–0.95

Result

Battery runtime — Engineerly. Estimate for education only; verify against applicable codes and manufacturer data.

Runtime
2.16h
Runtime
130min
Bank
12 V, 200 Ah
Bank energy (nominal)
2.4kWh
Usable energy at DoD
1.2kWh
Battery current
46.3A
C-rate
0.231C

Working, with your numbers

  1. 1. Bank voltage (series adds volts)
    V = V_unit × N_s
    V = 12 V × 1
    = 12 V
  2. 2. Bank capacity (parallel adds Ah)
    C = Ah_unit × N_p
    C = 200 Ah × 1
    = 200 Ah
  3. 3. Battery current
    I = P_load / (V × η)
    I = 500 W / (12 V × 0.9)
    = 46.296 A
  4. 4. Runtime (ideal capacity)
    t = C × V × DoD × η / P
    t = 200 Ah × 12 V × 0.5 × 0.9 / 500 W
    = 2.16 h

Assumptions

  • Constant power load for the whole discharge; battery voltage taken as the nominal bank voltage.
  • Usable depth of discharge 50 % of rated capacity.
  • Inverter efficiency 90 %, constant over the load range.
  • All units in the bank are identical, healthy and balanced.
Chemistry: lead-acid
Unit: 12 V, 200 Ah
Bank: 1S 1P
DoD: 0.5
Load: 500 W (AC)
Inverter efficiency: 0.9

Check before you rely on this

  • Lead-acid capacity falls at high discharge rates. Turn on the Peukert option for a more realistic figure.
  • Capacity also falls at low temperature and with ageing; many designers add an ageing factor (for example 1.25 in IEEE 485 for lead-acid).
  • Estimation and education only. Not a substitute for a licensed engineer, the applicable code (IEC 60364, NEC/NFPA 70, BS 7671 or local regulations) or manufacturer data.

How to use this calculator

  1. Pick a chemistry to load typical defaults (lead-acid 50 % DoD, LiFePO4 80 %), then adjust them to your battery's data.
  2. Enter the voltage and Ah of one battery or cell, how many are in series per string, and how many strings run in parallel.
  3. Enter the load in watts. Choose AC via inverter (and its efficiency) or a DC load.
  4. Turn on Peukert if you know the exponent k and the hour rate at which the capacity is specified (C20 = 20 h).

How it works: the formula

Bank: V = V_unit × N_series, C = Ah_unit × N_parallel Simple: t = C × V × DoD × η / P_load Current: I = P_load / (V × η) Peukert: t_100 = H × (C / (I × H))^k t ≈ t_100 × DoD

The simple method treats capacity as fixed energy. Peukert's law, an empirical relation published in 1897, describes lead-acid batteries delivering less of their rated Ah when discharged faster than the rated hour rate. With k = 1 the two methods agree.

Variables and units

SymbolMeaningUnit
CBank capacity at the rated hour rateAh
VNominal bank voltageV
DoDUsable depth of discharge (fraction)—
ηInverter efficiency (1 for DC loads)—
IBattery discharge currentA
HHour rate of the capacity ratingh
kPeukert exponent—

Worked example

Simple case: one 12 V, 200 Ah battery, DoD 0.8, inverter 90 %, 500 W load:

t = 200 × 12 × 0.8 × 0.9 / 500 = 1728 / 500 = 3.46 h

Peukert case: 12 V, 100 Ah rated at C20, k = 1.2, 120 W DC load (I = 10 A), discharged to 50 %:

t_100 = 20 × (100 / (10 × 20))^1.2 = 20 × 0.5^1.2 = 20 × 0.4353 = 8.71 h t = 8.71 × 0.5 = 4.35 h (simple method: 5.0 h)

Discharging at twice the C20 current costs about 13 % of runtime with k = 1.2.

Assumptions

  • Constant power load.
  • Nominal bank voltage throughout the discharge.
  • Identical, balanced, healthy batteries at about 25 °C.

Limitations

  • Peukert's law is an approximation. It is least reliable at very high currents and at currents below the rated-hour current. Lithium batteries follow it only weakly.
  • Capacity falls at low temperature and as batteries age. Design practice for standby batteries (for example IEEE 485 for lead-acid) adds ageing and temperature factors.
  • Inverter efficiency varies with load and is poor at very light load. The inverter's own standby draw is not included.
  • Battery management systems may cut off before the DoD you set.

References

Standards and texts that cover this topic. Use the edition adopted in your jurisdiction.

  • IEEE Std 485, Recommended Practice for Sizing Lead-Acid Batteries for Stationary Applications.
  • IEEE Std 1013, Recommended Practice for Sizing Lead-Acid Batteries for Stand-Alone Photovoltaic (PV) Systems.
  • IEC 61427-1, Secondary cells and batteries for renewable energy storage — Part 1: Photovoltaic off-grid application.
  • W. Peukert (1897), on the dependence of lead-acid battery capacity on discharge current; summarised in Linden's Handbook of Batteries.

Frequently asked questions

What depth of discharge should I use?

For lead-acid, 50 % is a common design figure that balances runtime against cycle life. For LiFePO4, 80–90 % is typical. Battery datasheets give cycle life against DoD, so use them to choose.

What Peukert exponent applies to my battery?

It should come from the manufacturer or be derived from two published capacity ratings at different hour rates. Typical values are about 1.1–1.3 for lead-acid and close to 1.0–1.05 for LiFePO4.

Why is the runtime shorter than Ah × V ÷ W?

Three effects: you should not use the full capacity (DoD), the inverter wastes some energy (η), and for lead-acid, faster discharge delivers fewer amp-hours (Peukert).

Series or parallel, what is the difference?

Series connection adds voltages while Ah stays the same. Parallel connection adds Ah at the same voltage. Energy in Wh is the same for the same number of identical batteries. Higher bank voltage means lower current for the same load.

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How these formulas were checked: methodology and testing.