Battery Energy Calculator: Ah to Wh

What does this quantity describe?

A battery's nominal energy follows from its nominal voltage U and charge capacity Q: E = U·Q. Ah describes only the transported electric charge, while Wh states the actually usable energy — two different physical quantities linked only through voltage.

Two batteries with the same Ah rating can store very different amounts of energy if their voltage differs — comparable to two equally sized water tanks (same 'amount'), one standing on a taller tower and therefore delivering more potential energy. Only charge (Ah) and voltage (V) together give energy (Wh).

Formula and variables

E = U · Q

• E = U · Q
• U = E / Q
• Q = E / U

Choose the inputs correctly

Enter two of the three quantities. Nominal energy requires voltage and charge capacity, voltage requires energy and capacity, capacity requires energy and voltage. Use the manufacturer's nominal voltage for U, not the full-charge or the lower discharge cut-off voltage.

How to use the calculator

Select the target quantity and enter the two known values with units. For multi-cell battery packs, check whether the stated voltage refers to the whole pack or a single cell.

Worked example

Given U = 48 V and Q = 50 Ah, substitution gives E = 48 V · 50 Ah = 2,400 Wh = 2.4 kWh.

Understand the result and units

A nominal energy of 2.4 kWh is the theoretical amount available on a full discharge from 100% down to the cut-off voltage. The actually usable amount is typically lower, since manufacturers rarely allow a full discharge down to the technical limit for the sake of battery lifespan.

Charge is given in amp-hours (Ah), where 1 Ah equals 3,600 coulombs, the SI base unit of charge. Energy is given in watt-hours (Wh) or kilowatt-hours (kWh); 1,000 Wh = 1 kWh.

Why does terminal voltage differ from nominal voltage?

Nominal voltage is a manufacturer-stated reference value, roughly equal to the average voltage across the entire discharge curve. Actual terminal voltage under load additionally depends on state of charge, discharge current and the cell's internal resistance: it sits above nominal voltage at full charge and falls noticeably below it towards the end of discharge. For an energy estimate via E = U·Q, nominal voltage is therefore a good approximation, but it is only loosely suited to indicating state of charge on its own.

Typical applications

Converting between Ah and Wh is used when comparing battery specifications across different voltage classes, sizing battery storage, in electromobility, and estimating runtimes of electrical loads.

Assumptions, limits and common mistakes

The formula assumes constant voltage across the whole discharge. Real batteries instead follow a discharge curve: voltage falls from an upper value at the start of discharge down to the cut-off voltage at the end, so the actually extractable energy can differ from the nominal voltage used here.

Common mistake: Do not equate amp-hours with watt-hours: two batteries with identical Ah ratings but different voltages store different amounts of energy. Also, do not confuse nominal voltage with the momentary terminal voltage under load, which is lower depending on state of charge and discharge current.