Solar Battery Runtime Calculator

A solar battery runtime calculator estimates how long a battery system can supply an entered load before reaching the selected allowable discharge limit. The primary output is Estimated runtime, expressed in hours.

This calculation supports early backup-power design, load-shedding decisions, inverter selection review, and solar-plus-storage planning. It helps determine whether a battery bank can carry a critical branch circuit, selected receptacle loads, lighting, communications equipment, refrigeration, or another defined load through the required outage period.

Runtime is an energy calculation. It does not establish conductor ampacity, feeder size, raceway fill, overcurrent protection, or voltage-drop compliance. Those decisions require the actual inverter output current, DC battery current, conductor length, terminal ratings, installation conditions, and applicable AHJ requirements.

Battery Energy and Usable Capacity

Battery capacity is commonly expressed in amp-hours (Ah), but runtime depends on stored energy in watt-hours (Wh). The calculator converts the entered battery bank capacity into nominal energy using Battery system voltage.

Input or result	Electrical meaning
Battery capacity (Ah)	Nominal battery-bank capacity in amp-hours
Battery system voltage (V)	Nominal DC voltage of the complete battery system
Load (W)	Power demand expected from the battery system
Depth of discharge (%)	Portion of nominal battery energy permitted to be used
System efficiency (%)	Allowance for conversion and system losses
Nominal energy	Theoretical stored energy before depth-of-discharge and efficiency limits
Usable energy	Energy remaining after the entered discharge and efficiency factors
Estimated runtime	Usable energy divided by the entered load
Usable factor	Combined depth-of-discharge and efficiency multiplier

The calculator treats Battery capacity (Ah) and Battery system voltage (V) as nominal battery-bank values. A 48 V, 400 Ah battery system is not evaluated the same way as a 12 V, 400 Ah battery system, even though both use the same amp-hour value. The higher-voltage system contains four times the nominal watt-hour energy when the amp-hour capacity is unchanged.

Runtime Formula

The calculation begins with nominal battery energy:

\(\displaystyle \text{Nominal energy (Wh)} = \text{Battery capacity (Ah)} \times \text{Battery system voltage (V)}\)

It then applies the entered depth of discharge and system efficiency:

\(\displaystyle \text{Usable factor} = \left(\frac{\text{Depth of discharge (\%)}}{100}\right) \times \left(\frac{\text{System efficiency (\%)}}{100}\right)\)

\(\displaystyle \text{Usable energy (Wh)} = \text{Nominal energy (Wh)} \times \text{Usable factor}\)

Estimated runtime is:

\(\displaystyle \text{Estimated runtime (h)} = \frac{\text{Usable energy (Wh)}}{\text{Load (W)}}\)

The calculation basis is straightforward: runtime equals usable battery energy divided by entered load watts.

Depth of discharge limits how much nominal battery energy is counted as available. System efficiency reduces usable energy for losses in the operating system, including energy conversion and related equipment losses represented by the entered percentage.

Calculation Example

For the following battery backup arrangement:

Field	Entered value
Battery capacity (Ah)	400 Ah
Battery system voltage (V)	48 V
Load (W)	2,400 W
Depth of discharge (%)	80%
System efficiency (%)	90%

First, calculate nominal energy:

\(\displaystyle 400\ \text{Ah} \times 48\ \text{V} = 19{,}200\ \text{Wh}\)

\(\displaystyle \text{Nominal energy} = 19{,}200\ \text{Wh}\)

Next, calculate the usable factor:

\(\displaystyle 0.80 \times 0.90 = 0.72\)

\(\displaystyle \text{Usable factor} = 0.72\text{ x}\)

Then calculate usable energy:

\(\displaystyle 19{,}200\ \text{Wh} \times 0.72 = 13{,}824\ \text{Wh}\)

\(\displaystyle \text{Usable energy} = 13{,}824\ \text{Wh}\)

Finally, divide usable energy by load:

\(\displaystyle \frac{13{,}824\ \text{Wh}}{2{,}400\ \text{W}} = 5.76\ \text{h}\)

\(\displaystyle \text{Estimated runtime} = 5.76\ \text{h}\)

At a steady 2,400 W load, the entered 48 V battery system has an estimated runtime of 5.76 hours using the selected 80% depth of discharge and 90% system efficiency.

Load Review and DC Current

The entered Load (W) should represent the expected operating load during battery discharge, not merely the nameplate total of every connected device. Intermittent equipment, motor loads, cycling refrigeration compressors, electronic power supplies, and future load additions can cause actual demand to differ from a simple connected-load total.

For conductor and overcurrent-protection review, the battery-side current can be substantially higher than the AC load current because the battery system operates at a lower DC voltage. A DC current estimate may be evaluated separately as:

\(\displaystyle \text{Approximate DC current} = \frac{\text{Load (W)}}{\text{Battery system voltage (V)} \times \text{System efficiency}}\)

Using the example values:

\(\displaystyle \frac{2{,}400}{48 \times 0.90} = 55.6\ \text{A}\)

That current estimate is not a conductor-sizing result. Battery conductors, inverter DC input conductors, disconnects, overcurrent devices, lugs, and busbars must be selected from the equipment ratings and the actual installation requirements. Ampacity can be affected by conductor material, AWG or kcmil size, insulation temperature rating, terminal rating, ambient temperature, grouping, and installation method.

On the AC side, inverter output current must also be reviewed independently for the applicable branch circuit or feeder. Long runs may require a voltage-drop evaluation even when conductor ampacity is adequate.

Field Verification

The result assumes the entered values accurately represent the operating battery system and load. Verify the following separately before using runtime for equipment selection or project commitments:

• Battery chemistry and the manufacturer’s permitted operating depth of discharge.
• Actual battery discharge behavior at the expected current and discharge duration.
• Battery temperature and the available capacity at expected site conditions.
• Inverter operating efficiency under the expected load profile.
• Battery management system limits, including discharge-current and low-voltage shutdown settings.
• Starting, surge, and cycling characteristics of connected loads, especially motors and compressor equipment.
• DC and AC conductor ampacity, termination ratings, disconnecting means, overcurrent protection, and voltage drop.
• Equipment listing, installation instructions, project specifications, utility requirements where applicable, and AHJ approval.

A runtime estimate is most reliable when the entered Load (W) reflects the actual simultaneous load and the selected Depth of discharge (%) and System efficiency (%) reflect the installed battery and power-conversion system.