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Battery runtime

Ah to Wh, a battery’s runtime under a load or the capacity to plan, with usable share and efficiency.

Parameters

Li-ion: 3.7 V per cell. Lead-acid: 12 V. LiFePO₄: 12.8 V.
Lead-acid: 50%. LiFePO₄: 80-90%. Li-ion: 80-100% depending on the wear you accept.
Inverter or regulator: 85-95%. 100% for a directly wired load.

Result

Runtime

8 h 30 min

Calculation
t = available E / P = 510 Wh / 60 W = 8.5 h
Nameplate energy
1200 Wh
Available energy
510 Wh
Notes (2)

The battery lasts 8 h 30 min under this load.

The Peukert effect and cold, which are not modelled, reduce the real runtime: keep a margin.

Calculation, assumptions and sources

OverviewEnergy of a battery (Ah × V, in watt-hours; 100 Ah at 12 V make 1,200 Wh), runtime under a given load, or the capacity to plan for a target runtime.

Energy of a battery (Ah × V, in watt-hours; 100 Ah at 12 V make 1,200 Wh), runtime under a given load, or the capacity to plan for a target runtime. Two discounts apply: the usable share of the capacity and the conversion efficiency.

Method & formulasE (Wh) = capacity (Ah) × voltage (V)
E (Wh) = capacity (Ah) × voltage (V)runtime (h) = E × usable × efficiency / Pcapacity (Ah) = P × t / (V × usable × efficiency)

Batteries of different voltages compare in watt-hours; in ampere-hours, only at equal voltage.

Ampere-hour (Ah)
the charge: one ampere for one hour; 1000 mAh = 1 Ah.
Watt-hour (Wh)
the energy: Ah × V.
Depth of discharge
share of capacity drawn before recharging. A lead-acid battery discharged flat lasts a few dozen cycles, half-discharged several hundred; lithium chemistries tolerate deeper discharges.
Nominal voltage
the average voltage of the chemistry: 3.7 V per li-ion cell, 12 V for six lead-acid cells, 12.8 V for four LiFePO₄. The real voltage varies during the discharge.
Validity domainThe model assumes constant capacity and constant nominal voltage.

The model assumes constant capacity and constant nominal voltage. Two effects are not modelled: the Peukert effect (a lead-acid battery discharged at high current delivers fewer ampere-hours than its nameplate capacity, measured at C/20) and cold, which reduces the delivered capacity, noticeably below 0 °C.

mAh and Wh of a power bankA power bank’s mAh are counted at 3.7 V, the voltage of the internal cells: 20,000 mAh make 74 Wh.

A power bank’s mAh are counted at 3.7 V, the voltage of the internal cells: 20,000 mAh make 74 Wh. At the 5 V of USB, only a theoretical 14,800 mAh remain, before conversion losses, that is three recharges of a 4500 mAh phone. Airlines check the value in Wh: 100 Wh in the cabin without approval.

Reading the resultThe nameplate energy is the one on the label; the available energy is what remains after the usable share and the efficiency.

The nameplate energy is the one on the label; the available energy is what remains after the usable share and the efficiency. The capacity to plan is a minimum, with no safety margin.