Battery Runtime Calculator: How Long a Battery Lasts, and the Battery Size for a Load

Find how long a battery will run a load, or how big a battery you need.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the battery capacity and voltage, the load in watts, the depth of discharge, the efficiency of the inverter and, if you want it, the Peukert exponent.

The calculator finds the power from the battery, the current and the usable energy, and the runtime in hours. With the Peukert exponent it gives the shorter runtime when the discharge is fast.

For the size case, enter the hours you need and it gives the capacity in amp-hours and kilowatt-hours.

Formulas used

  • t = \frac{C V\times DoD}{P/\eta}
  • C = \frac{P\,t}{\eta\,V\,DoD}
  • t = H\left(\frac{C\,DoD}{I H}\right)^k

Worked example

With the default numbers in the calculator above:

  1. Power drawn from the battery (the load plus the converter loss): 222.22 W
  2. Current drawn from the battery: 18.52 A
  3. Usable energy in the battery: 960.00 Wh
  4. Runtime (no Peukert correction): 4.32 hours (259.20 minutes)

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is depth of discharge?

The share of the capacity that you use. Using less of the battery makes it last more cycles.

What is the Peukert effect?

A lead-acid battery gives less than its rated capacity when it is discharged quickly. The exponent is 1.1 to 1.3 for lead-acid.

Why include inverter efficiency?

The inverter loses 5 to 15 percent as heat, so the battery has to supply more than the load uses.

Does temperature matter?

Yes. A cold battery gives much less capacity, so allow extra for cold sites.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Battery manufacturers' data sheets; Linden and Reddy, Handbook of Batteries; AS/NZS 5139 Electrical installations: safety of battery systems.

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