Electrical

Amp Hour Calculator

Convert Ah, mAh, Wh, and kWh, or size battery capacity from watts, runtime, voltage, depth of discharge, and efficiency.

Formula Ah = Wh / VReviewed Sep 8, 2026

Amp-hours tell you how much charge a battery can deliver, but they only become useful for power loads when voltage is included. A 100 Ah battery at 12 V stores about 1,200 Wh, while 100 Ah at 48 V stores about 4,800 Wh. This Amp Hour Calculator converts between Ah and Wh, sizes required Ah for a load and runtime, and estimates usable runtime after depth-of-discharge and efficiency losses.

Calculation Bench

Mode

01Load Power

P · Average load power. Use measured watts or the rated steady load, not only startup surge.

02Runtime

t · Target or estimated operating time.

03Battery Voltage

V · Battery pack nominal voltage, not the peak charging voltage.

04Depth of Discharge (%)

DoD · Usable fraction of the battery capacity. Enter 80 for 80%. Lithium often uses 80-90%; lead-acid often uses about 50%.

05Efficiency (%)

eta · Fraction of stored energy that reaches the load after inverter, wiring, and conversion losses. Enter 90 for 90%.

For battery shopping, compare Wh or kWh across voltages. Ah only compares batteries at the same nominal voltage.

Solution

Enter battery voltage and the known battery/load values to calculate Ah, Wh, or runtime.

Ah = P t / (V x DoD x eta)

Formula Sheet

C_{Ah}=\dfrac{E_{Wh}}{V}

E_{Wh}=C_{Ah}V

C_{Ah}=\dfrac{Pt}{V\,DoD\,\eta}

t=\dfrac{C_{Ah}V\,DoD\,\eta}{P}

C_AhAmp-Hour Capacity
EBattery Energy
VNominal Voltage
PLoad Power
tRuntime
DoDDepth of Discharge
etaSystem Efficiency

Common Battery Voltage Presets

Preset	Nominal voltage	Common use
Single Li-ion cell	3.7 V	USB packs, cells, small electronics
12 V lead-acid	12 V	Automotive, marine, RV, small inverter systems
12.8 V LiFePO4	12.8 V	Drop-in lithium batteries
24 V system	24 V	Trucks, boats, solar, small industrial systems
48 V system	48 V	Solar storage, telecom, larger inverter systems

Variables & Units

Symbol	Variable	Description	Common Units
C_Ah	Amp-Hour Capacity	Battery charge capacity. Use the Ah or mAh rating on the battery label.	mAh, Ah
E	Battery Energy	Energy capacity in watt-hours. This is the best number for comparing packs at different voltages.	Wh, kWh
V	Nominal Voltage	Battery pack nominal voltage, not the peak charging voltage.	V
P	Load Power	Average load power. Use measured watts or the rated steady load, not only startup surge.	W, kW
t	Runtime	Target or estimated operating time.	min, h, days
DoD	Depth of Discharge	Usable fraction of the battery capacity. Enter 80 for 80%. Lithium often uses 80-90%; lead-acid often uses about 50%.
eta	System Efficiency	Fraction of stored energy that reaches the load after inverter, wiring, and conversion losses. Enter 90 for 90%.

How to Use This Calculator

01Choose Ah from Wh when a battery or power station is labeled in watt-hours and you need amp-hours at a voltage.
02Choose Wh from Ah when a battery is labeled in Ah and you need comparable energy capacity.
03Choose Required Ah when you know the load watts, target runtime, battery voltage, usable depth of discharge, and inverter/system efficiency.
04Choose Runtime from Ah when you already have a battery capacity and want estimated usable runtime for a watt load.
05Use the voltage presets as a starting point, then adjust to the actual nominal voltage printed on the battery pack.
06For loads that cycle on and off, use average watts over time instead of nameplate startup watts; for inverters, include inverter idle draw if it runs continuously.

How the Formula Works

Amp-hours are charge capacity. Watt-hours are energy capacity. The bridge is voltage: Wh = Ah x V and Ah = Wh / V.

For real runtime, not all rated energy is usable. Lead-acid systems are often limited to about 50% depth of discharge, while many lithium systems use about 80-90%. Inverter and wiring losses are represented as efficiency.

When sizing required Ah from a load, the calculator first finds energy demand in Wh, divides by usable fraction and efficiency, then divides by battery voltage.

Worked Example 01

Convert a 1,280 Wh lithium battery to Ah

Known

Battery energy: 1,280 Wh
Nominal voltage: 12.8 V

Formula

Ah = Wh / V

Substitution

Ah = 1,280 / 12.8

Result

Ah = 100 Ah

A 12.8 V lithium battery rated at 1,280 Wh is equivalent to 100 Ah at that same nominal voltage.

Worked Example 02

Size a 12 V battery for a 150 W load for 8 hours

Known

Load power: 150 W
Runtime: 8 h
Voltage: 12 V
Depth of discharge: 80%
Efficiency: 90%

Formula

Ah = P t / (V x DoD x eta)

Substitution

Ah = 150 x 8 / (12 x 0.80 x 0.90)

Result

Ah = 138.9 Ah, so choose a larger standard battery capacity

The load needs 1,200 usable Wh. After 80% DoD and 90% efficiency, the battery should be rated about 1,667 Wh, or 139 Ah at 12 V.

Worked Example 03

Runtime from a 100 Ah 12.8 V battery

Known

Capacity: 100 Ah
Voltage: 12.8 V
Load: 300 W
Depth of discharge: 80%
Efficiency: 92%

Formula

t = Ah x V x DoD x eta / P

Substitution

t = 100 x 12.8 x 0.80 x 0.92 / 300

Result

t = 3.14 h

The battery stores 1,280 Wh, but about 942 Wh is usable after the selected derating factors. At 300 W, that is roughly 3.1 hours.

Applications

01Converting a power-station Wh rating to Ah at 12 V, 24 V, or 48 V
02Comparing 12 V and 48 V battery packs using watt-hours
03Sizing RV, marine, backup, solar, and inverter battery capacity from load watts and runtime
04Estimating usable runtime for a known Ah battery after DoD and efficiency derating

Assumptions

01Battery voltage is nominal and constant enough for first-pass energy sizing.
02Load power is average continuous power; startup surge is not included.
03Depth of discharge and efficiency are entered as percent values and multiplied as derating factors.
04Battery Ah rating is manufacturer-rated capacity at the relevant discharge rate and temperature.

Where This Model Stops

01Does not model Peukert effect, battery aging, temperature derating, voltage cutoff curves, or BMS current limits.
02Does not confirm safe continuous discharge current, fuse size, conductor size, charger size, or inverter surge rating.
03Does not size wires, fuses, circuit breakers, chargers, inverter surge capacity, or solar recharge time.
04Does not replace manufacturer datasheets for lithium, lead-acid, marine, RV, UPS, or code-regulated systems.
05Ah is not comparable across voltages without converting to Wh first.

References

[1]
Deep Cycle Battery Amp Hour Calculator
BatteryStuff
Reference for sizing battery Ah from load current, runtime, voltage, and practical battery derating.
[2]
Battery Capacity Calculator
Omni Calculator
Reference for Ah, Wh, voltage, current, and runtime relationships.
[3]
Battery Capacity
All About Circuits
Reference explanation of amp-hour ratings, energy capacity, and discharge-rate caveats.

Frequently Asked Questions

What is the formula for amp-hours?

For energy conversion, Ah = Wh / V. For load sizing, required Ah = watts x hours / (volts x usable depth of discharge x efficiency).

Why can't I compare Ah ratings across different voltages?

Amp-hours measure charge, not total energy. A 100 Ah 12 V battery stores about 1.2 kWh, while a 100 Ah 48 V battery stores about 4.8 kWh. Convert both to Wh or kWh before comparing.

How is this different from the Battery Life Calculator?

The Battery Life Calculator uses the simple t = C / I relationship for current draw in amps or milliamps. This Amp Hour Calculator is for battery energy and system sizing: it includes voltage, watt loads, depth of discharge, efficiency, Wh, kWh, and usable runtime.

What depth of discharge should I enter?

Use the battery manufacturer's limit when available. As rough planning values, lithium systems often use 80-90%, while lead-acid systems are commonly limited near 50% to improve life.

Why does my real runtime differ from the calculator?

Real runtime changes with temperature, battery age, discharge rate, cutoff voltage, inverter idle draw, and whether the load cycles. The calculator is a planning estimate from average power and usable capacity.

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