Watts to Amp Hours: Formula and Battery Calculator

This calculator converts power in watts and operating time into amp-hours, using the battery voltage you enter. Enter watts, hours, and volts to get the amp-hour estimate, along with the equivalent energy in watt-hours.

Formula

Amp-hours = watts × hours ÷ volts. In symbols, Ah = (W × h) ÷ V. Energy in watt-hours = watts × hours, or Wh = W × h.

• W is power in watts (W).
• h is operating time in hours (h).
• V is the voltage used for the calculation, in volts (V).
• Ah is charge capacity in amp-hours; Wh is energy in watt-hours.

Watts measure the rate of energy use, while amp-hours describe electric charge over time. Voltage connects the two: at a fixed power, a lower voltage means more current and therefore more amp-hours over the same duration. The conversion assumes the listed power and voltage remain constant.

Worked Example

Using the calculator’s defaults—100 W for 2 hours at 12 V:

1. Calculate energy: 100 W × 2 h = 200 Wh.
2. Divide energy by voltage: 200 Wh ÷ 12 V = 16.666… Ah.
3. Rounded to two decimal places, the result is 16.67 Ah.

The energy output is 200.00 Wh. These are the calculator’s mathematical results; an actual battery may need more rated capacity because of losses and limits on usable discharge.

When to Use the Conversion

Use watts to amp-hours when estimating how much battery charge a device may use during a known period, or when comparing a device’s energy demand with a battery rating. For example, a 60 W load running for 3 hours uses 180 Wh. At 12 V, that corresponds to 15 Ah under the ideal calculation: 60 × 3 ÷ 12.

The calculation is useful for planning, but it does not by itself guarantee a particular runtime. Actual use can differ if the device changes its power draw, the battery voltage varies, or a power converter consumes energy. For a device rated in watts, first estimate its energy use over the expected time, then divide by the battery-system voltage to express the result as amp-hours.

Battery Voltage, Wh, and Ah

Amp-hours alone do not tell you how much energy a battery stores unless you also know its voltage. A 10 Ah battery at 12 V represents about 120 Wh; a 10 Ah battery at 24 V represents about 240 Wh. The charge rating is the same, but the energy is not.

Watt-hours are often the clearest unit for comparing energy needs across different voltages. Amp-hours are useful when matching equipment within a particular battery voltage system. Keep the voltage basis consistent: do not compare Ah ratings from different-voltage batteries as if they represented equal energy.

In US customary measurements, power is still commonly stated in watts and battery voltage in volts; the same formula applies. If a load is specified in horsepower, convert it to watts before using this calculator (one mechanical horsepower is approximately 746 W). Hours must also be in hours: convert minutes to hours by dividing by 60.

Why Real Battery Capacity Can Differ

The formula gives an ideal estimate based on constant power and voltage. A real battery’s usable output can be lower than its nominal rating. The amount available depends on battery chemistry, temperature, age, discharge rate, battery condition, and any limits set by the battery or its management system. A device’s power demand may also rise or fall while it runs.

For an AC appliance powered from a battery through an inverter, account for inverter losses. If the inverter efficiency is known as a decimal, estimate battery-side energy by dividing the appliance’s watt-hours by that efficiency, then divide by battery voltage to estimate amp-hours. For example, do not use an efficiency percentage as though it were a voltage or a direct multiplier without converting it to a decimal.

For a practical runtime estimate, start with the battery’s watt-hour rating or convert its Ah rating using its nominal voltage. Then allow for the portion of capacity you can actually use and for conversion losses. Those figures depend on the specific battery and equipment, so check their specifications rather than assuming the full rated capacity is available.

Common Conversion Mistakes

• Leaving out voltage: watts and hours produce watt-hours, not amp-hours. Divide by volts to obtain Ah.
• Mixing units: use watts, volts, and hours together. Convert minutes to hours and kilowatts to watts before calculating.
• Comparing Ah without voltage: include voltage or compare watt-hours when assessing energy capacity.
• Assuming the result is guaranteed runtime: the calculation estimates demand; it does not account automatically for battery limits, losses, or changing load.
• Rounding too early: keep intermediate values precise and round the final result to a sensible number of decimal places.

Frequently Asked Questions

How many amp-hours is 100 watts?
It depends on voltage and time. At 12 V for one hour, 100 W uses 100 ÷ 12 = 8.33 Ah. At 24 V for one hour, it uses about 4.17 Ah.

Can I convert watts to amp-hours without knowing voltage?
No. Watts and time give watt-hours; voltage is needed to convert that energy to amp-hours. Find the relevant system or battery voltage first.

How many amp-hours does a 100-watt device use in 5 hours at 12 V?
Calculate 100 × 5 ÷ 12, which gives about 41.67 Ah in the ideal estimate. Real battery demand may be higher because of losses or changing conditions.

Are amp-hours the same as watt-hours?
No. Amp-hours measure charge, while watt-hours measure energy. To relate them, multiply or divide by voltage: Wh = Ah × V, and Ah = Wh ÷ V.

Does a battery’s Ah rating tell me how long a device will run?
Not on its own. You also need the battery voltage, the device’s power demand, usable battery capacity, and any losses from equipment such as an inverter.

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in w | Power | W | 100 | 0
in t | Operating time | h | 2 | 0
in v | Voltage | V | 12 | 0
out ah | Amp-hours | Ah | w * t / v | 2
out wh | Energy | Wh | w * t | 2