Power & Energy · Worked example

Battery Runtime: Why Amp-Hours Alone Do Not Tell You Runtime

Estimate runtime from battery voltage, amp-hours, usable depth of discharge, inverter efficiency, and load power using a 48 V battery example.

By Neutron Studios LLC8 minute readPublished 2026-08-11Reviewed 2026-08-11

Why this calculation matters

A 100 Ah battery is not a fixed number of usable watt-hours under every condition. Runtime depends on nominal voltage, allowable depth of discharge, conversion efficiency, battery chemistry, temperature, age, discharge rate, and load profile.

This worked example uses a 48 V, 100 Ah battery and a 1200 W AC load. It is intentionally a first-order energy balance; a real battery model can produce a different result.

What you will calculate

Convert voltage and amp-hours to nominal energy.
Apply a usable-depth-of-discharge limit.
Account for inverter efficiency.
Identify effects omitted by a simple watt-hour runtime estimate.

Given values

Battery nominal voltage = 48 V
Rated capacity = 100 Ah
Usable depth of discharge = 80%
AC load = 1200 W
Inverter efficiency = 92%
Constant-load first-order model

Governing equations

Nominal battery energy

Enom = Vnom × Ah

Produces watt-hours when volts and amp-hours are used.

Usable stored energy

Eusable = Enom × DoDusable

A planning limit prevents using the entire nameplate capacity.

DC power required by inverter

Pdc = Pac / ηinv

The battery supplies more power than the AC load receives.

First-order runtime

t = Eusable / Pdc

Assumes constant power and ignores voltage-dependent cutoff effects.

Worked solution

1. Convert the battery rating to energy

A 48 V, 100 Ah nameplate corresponds to 4800 Wh, or 4.8 kWh, at the nominal-voltage approximation.

Enom = 48×100 = 4800 Wh = 4.8 kWh

2. Apply the usable depth-of-discharge limit

Using 80% of nameplate energy leaves 3.84 kWh as the planned energy budget. This is a user-selected operating limit, not a universal chemistry rule.

Eusable = 4.8×0.80 = 3.84 kWh

3. Account for inverter loss

A 1200 W AC load requires about 1304 W from the DC side at 92% conversion efficiency, before standby loads or wiring losses.

Pdc = 1200/0.92 ≈ 1304 W

4. Estimate runtime

Dividing the usable energy by the DC input power gives approximately 2.94 hours. That is an energy-balance estimate, not a guarantee that the inverter will remain above its low-voltage cutoff for exactly that long.

t ≈ 3840/1304 ≈ 2.94 h

Result

Engineering interpretation

The first-order runtime is about 2.94 hours for the stated 48 V, 100 Ah battery, 80% usable depth of discharge, 1200 W AC load, and 92% inverter efficiency.

Real runtime may be shorter because of battery temperature, aging, BMS limits, cell imbalance, inverter standby consumption, cable loss, high discharge rate, or chemistry-specific capacity behavior.

Sanity checks

At fixed load, doubling usable watt-hours should approximately double runtime.
Reducing inverter efficiency must reduce runtime.
A 48 V 100 Ah battery should not be treated as only 100 Wh; amp-hours require voltage to become energy.
For lead-acid batteries, high discharge rates can reduce available capacity substantially through Peukert behavior.

Common mistakes

Dividing amp-hours directly by watts.
Using 100% of nameplate energy as routinely usable.
Applying a lithium-style simple energy model to lead-acid without considering rate-dependent capacity.
Ignoring inverter low-voltage cutoff and BMS current limits.

References and model boundaries

Battery manufacturer datasheets and BMS documentation should control usable capacity, discharge limits, and temperature behavior.
Inverter efficiency should come from the operating point on the actual product efficiency curve when available.

For safety-critical, regulated, production, or otherwise consequential work, independently verify the result using the governing standard, current manufacturer data, and qualified engineering review. See the site methodology and engineering disclaimer.