Understanding Battery Capacity: Ah vs Wh vs kWh Explained

“100 Ah” sounds like a complete battery size, but it is only half of the energy calculation. A 12.8 V, 100 Ah battery stores about 1.28 kWh at its nominal rating. A 51.2 V, 100 Ah battery stores about 5.12 kWh—four times as much energy even though the amp-hour number is identical.

watt-hours = nominal volts × amp-hours

Neither result is the energy an AC appliance will necessarily receive. Battery operating limits, discharge current, inverter efficiency, temperature, and voltage sag sit between the nameplate and the load. That distinction matters: a battery can have enough energy for the night but still lack enough power to start a motor or supply several appliances at once.

This guide keeps those questions separate—stored energy, usable energy, and instantaneous power—before estimating runtime.

---

Why Battery Capacity Matters

Battery capacity helps determine how much energy is available for your loads.

Understanding capacity can help you estimate:

• How long a battery may power an appliance
• How many batteries a system may need
• Whether a battery bank can support overnight loads
• How much energy must be replaced by the solar array
• How much backup energy is available during an outage

However, the capacity printed on a battery is not always equal to the amount of energy you can actually use.

Battery chemistry, discharge rate, temperature, age, operating limits, inverter efficiency, and the battery management system can all affect usable energy.

---

What Is an Amp-Hour (Ah)?

An amp-hour (Ah) is a unit of electrical charge.

A simple way to understand it is:

Amp-hours = Current × Time

For example, 10 amps flowing for 10 hours represents:

10A × 10h = 100Ah

A battery rated at 100Ah therefore has a nominal charge capacity of 100 amp-hours under its specified test conditions.

You may sometimes see simplified examples suggesting that a 100Ah battery can provide:

• 100A for 1 hour
• 50A for 2 hours
• 20A for 5 hours
• 10A for 10 hours

Mathematically, each example equals 100Ah.

In a real battery, however, runtime does not necessarily scale this perfectly.

The available capacity can change with discharge rate, temperature, battery chemistry, age, and other operating conditions. This effect can be particularly noticeable with lead-acid batteries.

Most importantly:

Ah alone does not tell you how much energy a battery stores.

You also need to know its voltage.

---

Why Battery Voltage Matters

Consider two nominal batteries:

• Battery A: 12V 100Ah
• Battery B: 24V 100Ah

Both have a capacity rating of 100Ah.

But they do not represent the same amount of nominal energy.

Using the simplified nominal-energy calculation:

Energy (Wh) = Voltage (V) × Capacity (Ah)

Battery A:

12V × 100Ah = 1,200Wh

Battery B:

24V × 100Ah = 2,400Wh

So the nominal 24V battery represents approximately twice the energy of the nominal 12V battery when both have the same Ah rating.

This is why batteries should not be compared using Ah alone.

---

What Is a Watt-Hour (Wh)?

A watt-hour (Wh) is a unit of energy.

For a simplified battery calculation:

Wh ≈ Nominal Voltage × Ah

For example:

12V × 100Ah = 1,200Wh

So a nominal 12V, 100Ah battery represents approximately 1,200Wh, or 1.2kWh, of nominal energy.

The word nominal is important.

A battery's actual voltage changes during operation, so multiplying the nominal voltage by the Ah rating is a useful estimate rather than a complete description of the battery's real discharge behavior.

When available, the manufacturer's specified energy rating in Wh or kWh is generally preferable to calculating it yourself from nominal values.

---

What Is a Kilowatt-Hour (kWh)?

A kilowatt-hour (kWh) is equal to 1,000 watt-hours:

1kWh = 1,000Wh

Therefore:

1,200Wh ÷ 1,000 = 1.2kWh

Using nominal values:

Battery	Approx. Nominal Energy
12V 100Ah	1.2kWh
24V 100Ah	2.4kWh
48V 100Ah	4.8kWh

The kWh is particularly useful because household electricity consumption and larger battery-storage systems are commonly expressed in kilowatt-hours.

For example, if a home consumes 5kWh per day, it is much easier to compare that demand with a battery rated in kWh than with a battery rated only in Ah.

---

Ah vs Wh vs kWh

Here's the key distinction:

Unit	Measures	Useful For
A	Electrical current	Current flowing at a particular moment
Ah	Electrical charge	Battery charge capacity
W	Power	Rate of energy use or production
Wh	Energy	Battery energy and appliance consumption
kWh	Energy	Larger batteries and household energy use

For comparing batteries with different voltages, Wh or kWh is usually more informative than Ah alone.

---

Battery Capacity Conversion Formulas

Convert Ah to Wh

For a simplified nominal calculation:

Wh ≈ V × Ah

Example:

A 24V, 200Ah battery:

24V × 200Ah = 4,800Wh

So its approximate nominal energy is:

4,800Wh

---

Convert Wh to kWh

kWh = Wh ÷ 1,000

Example:

4,800Wh ÷ 1,000 = 4.8kWh

---

Convert kWh to Wh

Wh = kWh × 1,000

Example:

5kWh × 1,000 = 5,000Wh

---

Convert Wh to Ah

If voltage is known:

Ah ≈ Wh ÷ V

For example, a battery storing approximately 2,400Wh at a nominal 24V:

2,400Wh ÷ 24V = 100Ah

Again, these calculations use nominal values and should be treated as practical estimates.

---

Real-World Runtime Example

Suppose you have a nominal:

12V 100Ah battery

Its approximate nominal energy is:

12V × 100Ah = 1,200Wh

Now suppose you want to power a 100W television.

A simplified ideal calculation would be:

Runtime = Battery Energy ÷ Load Power

1,200Wh ÷ 100W = 12 hours

So does that mean the television will always run for exactly 12 hours?

No.

That calculation assumes all 1,200Wh can be used and ignores system losses.

A more realistic estimate should consider usable battery capacity and system efficiency.

---

A Better Runtime Calculation

Suppose the same 1,200Wh battery is operated with:

• 80% usable depth of discharge
• 90% inverter efficiency

Approximate energy delivered to the AC load would be:

1,200Wh × 0.80 × 0.90 = 864Wh

For a 100W television:

864Wh ÷ 100W = 8.64 hours

So under these assumptions, the estimated runtime would be approximately:

8.6 hours

This is still only an estimate.

Actual runtime can vary because of:

• Battery chemistry
• Battery age
• Temperature
• Discharge rate
• Inverter efficiency at the actual load
• Battery-management limits
• Wiring losses
• Appliance power variation

This is why a simple Wh ÷ W calculation is useful for planning but should not be treated as a guarantee.

---

Nominal Capacity vs Usable Capacity

A battery's nominal energy capacity and usable energy capacity are not necessarily the same.

A simple estimate is:

Usable Energy ≈ Nominal Energy × Allowed Depth of Discharge

For example, suppose a 5kWh battery is operated with an 80% usable depth of discharge:

5kWh × 0.80 = 4kWh

Its approximate usable battery energy would therefore be 4kWh before considering downstream conversion losses.

---

Lead-Acid Battery Capacity

You've probably heard the common advice:

"Never discharge a lead-acid battery below 50%."

The 50% figure is better understood as a common design guideline, not a universal physical limit.

Lead-acid battery life is strongly affected by depth of discharge. Deeper cycling generally results in fewer cycles, while shallower cycling can improve cycle life.

The appropriate discharge limit depends on the particular battery, its intended application, and the manufacturer's specifications.

For system design, always consult the battery manufacturer's cycle-life and depth-of-discharge data rather than assuming every lead-acid battery has exactly 50% usable capacity.

---

LiFePO₄ Battery Capacity

Lithium iron phosphate (LiFePO₄) batteries generally support a greater usable fraction of their nominal capacity than traditional lead-acid batteries.

However, saying that every LiFePO₄ battery has exactly 80%, 90%, or 100% usable capacity would also be an oversimplification.

Usable capacity depends on:

• Manufacturer specifications
• Battery Management System (BMS) limits
• Required cycle life
• Temperature
• Charge and discharge conditions

For example, a manufacturer might specify a 5.12kWh battery with a recommended operating window that provides less than the full nominal energy.

Use the manufacturer's specified usable energy whenever it is available.

---

Power and Energy Are Not the Same Thing

Another common mistake is confusing watts (W) with watt-hours (Wh).

A watt measures power — the rate at which energy is being used or produced.

A watt-hour measures energy — power used over time.

For example, a 500W appliance running for 2 hours consumes:

500W × 2h = 1,000Wh

or:

1kWh

This distinction is important when sizing both batteries and inverters.

A battery might contain enough energy to run an appliance for several hours while the inverter may still be unable to provide the appliance's required power.

---

Battery Energy Does Not Determine Maximum Power

Suppose you have a 5kWh battery.

That tells you how much nominal or usable energy is stored, depending on how the manufacturer specifies the rating.

It does not automatically mean the battery can supply a 5kW load.

Maximum output depends on factors such as:

• Maximum battery discharge current
• BMS limits
• Battery voltage
• Inverter rating
• Cable and protection-device ratings
• Manufacturer specifications

For example, a battery may store 5kWh of energy but be limited to 2.5kW of continuous output.

This is why PV system design requires checking both:

Energy capacity (kWh) and power capability (kW).

---

How Battery Capacity Affects PV System Design

Battery sizing should start with the loads you actually need to support.

Suppose a household needs the following overnight:

Load	Power	Runtime	Energy
Refrigerator*	100W average	10h	1,000Wh
Lights	60W	5h	300Wh
Television	100W	3h	300Wh
Fans	120W	8h	960Wh
Total			2,560Wh

*Actual refrigerator consumption varies because the compressor cycles on and off. Using measured daily energy consumption is preferable when available.

The estimated overnight load is:

2,560Wh = 2.56kWh

You would then account for battery operating limits, conversion losses, reserve capacity, and other design requirements when determining the appropriate battery size.

This is much more reliable than simply deciding that a "200Ah battery sounds big enough."

---

How Much Solar Is Needed to Recharge a Battery?

Battery capacity also affects PV array sizing, but battery capacity alone is not enough to determine the required number of panels.

Suppose you need to replace 4kWh of energy each day.

If the site receives an equivalent of 5 peak-sun-hours and you initially assume an overall energy factor of 80% for a simplified estimate:

Required PV power ≈ 4kWh ÷ (5h × 0.80)

Required PV power ≈ 1kW

This is only a simplified example.

Real PV design should also consider:

• Location and solar resource
• Array orientation and tilt
• Temperature
• Shading
• System losses
• Battery charging efficiency
• Seasonal conditions
• Daily household loads
• Desired recharge time
• Equipment limitations

Battery capacity is therefore only one part of PV system sizing.

---

Common Battery-Capacity Mistakes

When comparing or sizing batteries, avoid these common mistakes:

• Comparing batteries using Ah without considering voltage
• Treating nominal energy as guaranteed usable energy
• Assuming every battery can use the same depth of discharge
• Confusing watts with watt-hours
• Ignoring inverter losses
• Ignoring battery discharge-current limits
• Assuming theoretical runtime equals real runtime
• Comparing different battery chemistries using Ah alone
• Ignoring manufacturer specifications
• Sizing a battery without first estimating load energy

---

Quick Reference

Unit	Full Name	Measures	Example
A	Ampere	Current	10A
Ah	Amp-hour	Electrical charge	100Ah
W	Watt	Power	500W
Wh	Watt-hour	Energy	1,200Wh
kW	Kilowatt	Power	5kW
kWh	Kilowatt-hour	Energy	4.8kWh

Remember:

kW tells you how fast energy is being used or delivered.

kWh tells you how much energy is used or stored over time.

---

Compare Batteries by Usable Energy and Limits

Understanding battery capacity becomes much easier once you separate charge, power, and energy.

• Ah (amp-hours) measures electrical charge.
• Wh (watt-hours) measures energy.
• kWh (kilowatt-hours) is 1,000Wh and is convenient for larger energy quantities.
• W and kW describe power, not stored energy.

For a simplified nominal battery-energy estimate:

Wh ≈ V × Ah

But that is only the beginning of real battery sizing.

You should also consider usable depth of discharge, battery chemistry, discharge rate, inverter efficiency, BMS limits, temperature, battery age, maximum output power, and manufacturer specifications.

When comparing batteries for a PV system, Wh or kWh usually gives you a more meaningful energy comparison than Ah alone, especially when the batteries operate at different voltages.

And when estimating runtime, don't ask only:

"How many Ah is the battery?"

Ask:

"How much usable energy does the battery provide, and how much energy does my load actually require?"

That question leads to a much more realistic PV system design.

Reproduce the unit conversion in PVAlign

Compare a 12.8 V, 100 Ah battery with a 51.2 V, 100 Ah battery. Both have 100 Ah, but their nominal energy is approximately 1.28 kWh and 5.12 kWh respectively before usable-depth and conversion losses. Apply the same AC load to both supported systems and compare current: the higher-voltage bank supplies the same ideal power at lower current.

Sources and methodology

• U.S. Department of Energy — Solar Energy and Storage Basics
• U.S. Department of Energy — Batteries
• PVAlign editorial policy and simulation methodology