Amp-Hour Calculator

What an amp-hour measures

An amp-hour is a unit of charge, and it answers one narrow question: how much electric charge can a battery push out before it runs flat. One amp flowing for one hour is one amp-hour. Multiply a current in amps by a time in hours and the product is the charge that passed through the circuit during that time.

The ampere is an SI base unit, and since the 2019 revision it is fixed by the elementary charge. The NIST introduction to the ampere puts it plainly: a coulomb passing a point in one second is one ampere, and one coulomb is about 6.24 x 10^18 electrons. That makes an amp-hour a tidy package of charge, since 1 Ah is 3,600 coulombs.

What an amp-hour is not is energy. The same 100 Ah holds 1,200 Wh in a 12 V pack and 2,400 Wh in a 24 V pack. A label that mentions only amp-hours leaves out half the story, which is why the calculator on this page reports watt-hours as soon as you give it a pack voltage.

The formulas and the unit conversions

Three relations cover nearly every battery question. Capacity in amp-hours is current in amps multiplied by time in hours: Ah = A x h. Energy in watt-hours is that capacity multiplied by the pack voltage: Wh = Ah x V. Charge in coulombs is the capacity multiplied by 3,600: C = Ah x 3,600.

Small batteries use milliamp-hours, written mAh, and one milliamp-hour is one thousandth of an amp-hour. A phone cell rated 3,000 mAh holds 3 Ah, and a 10,000 mAh power bank holds 10 Ah. Watt-hours are the better unit when the voltage moves during a discharge, because the voltage of a cell falls as it empties and a fixed amp-hour rating hides that movement.

The Department of Energy fact sheet Battery Power for Your Residential Solar Electric System makes the same point in system terms: a 12 V, 100 Ah battery stores 1,200 watt-hours, the same as a 600 Ah bank at 2 V, and a 24 V bank needs 42 amp-hours of useful storage for every 1,000 Wh of daily consumption.

Worked example: a trolling motor on a 12 V bank

Take a small fishing boat with a 12 V trolling motor that pulls 20 A and runs for 4.5 hours on a charge. Multiply the draw by the time: 20 x 4.5 gives 90 Ah. At 12 V that is 1,080 Wh of stored energy, and in coulombs it is 90 x 3,600, or 324,000 C.

Now the part that matters on the water. A flooded lead-acid battery should be kept about half charged, so only 45 Ah of that 90 is fair game in the way the label is written, which is 540 Wh. A 20 A motor on 45 Ah runs for 2.25 hours before it reaches the 50 percent line.

The same arithmetic works in reverse when you shop for a bank. If you want four hours of trolling from a 20 A motor at 50 percent depth of discharge, you need 20 x 4 x 2, which is 160 Ah, and two 80 Ah batteries in series will do it.

Worked example: a phone battery and a power bank

Handheld gear uses milliamp-hours, and the same two formulas carry over once you convert. A phone cell rated 3,000 mAh at a nominal 3.7 V holds 3 Ah, and 3 x 3.7 gives 11.1 Wh of energy.

A power bank labelled 10,000 mAh also holds 10 Ah, and at 3.7 V that is 37 Wh on the label. Converting that stored energy to a 5 V USB output always loses something, and a figure of 85 percent is a fair guess for a good power bank. So the usable energy is 37 x 0.85, which is 31.45 Wh, and the number of full phone charges is 31.45 divided by 11.1, or about 2.8.

The gap between 10 charges on the sticker and 2.8 charges in the hand is not a fault in the power bank. It is the difference between a charge rating in milliamp-hours and the energy that arrives at the phone, and it is exactly the gap the calculator makes visible when you add a voltage to the inputs.

Why the label number is an upper limit

A rated capacity is measured at a specific discharge rate, and a lead-acid battery will hand over less than its label if you pull the current harder. The Peukert effect describes this with the relation t = H x (C / (I x H))^k, where C is the rated capacity in amp-hours, H is the rated discharge time in hours, I is the actual current, and k is an exponent that sits near 1.25 for lead-acid.

Take a 100 Ah battery rated over 20 hours, which is the 5 A rate. At 10 A the relation gives 8.41 hours, and at 20 A it gives 3.54 hours. Multiplying those by the current shows what the battery gave you: 84.1 Ah at the gentler draw and 70.7 Ah at the hard one.

Cold weather and age push the same number down further, since a battery stored near freezing gives up less charge and every cycle of use wears it a little. The Department of Energy notes that car and marine batteries are built for a burst of starting current rather than for deep discharge, so they fail early in a solar bank even though the amp-hour label looks generous.

Depth of discharge: how much of the label you can use

Depth of discharge is the share of the rated capacity that a battery can give up before it should be recharged, and it differs by chemistry. Lead-acid is the cautious one and is usually held at 50 percent, lithium-ion tolerates 80 to 90 percent, and lithium iron phosphate can be cycled across almost the whole label at the cost of a shorter service life.

A worked number: a 100 Ah lithium pack held at 80 percent depth of discharge gives 80 Ah, and a 10 A load on that pack runs for 8 hours. On the same pack with the full 100 Ah you would plan 10 hours, and the difference is the 20 percent you kept back so the battery still has a charge in it when the sun goes down.

Sizing a bank from a daily load

A solar or backup bank is sized backwards from the load. Start with the energy the house uses in a day, add the losses in the inverter, convert to amp-hours at the bank voltage, multiply by the number of days of autonomy you want, and then divide by the depth of discharge you are willing to promise.

Suppose a cabin draws 2,400 Wh a day and runs on a 24 V bank through an inverter that is 90 percent efficient. The bank has to supply 2,400 divided by 0.90, which is 2,667 Wh, and at 24 V that is 111 Ah a day. Two days of autonomy need 222 Ah, and with a lead-acid bank held at 50 percent depth of discharge the nameplate has to be 444 Ah.

The Department of Energy overview of solar and storage separates the two ideas a bank has to balance, energy capacity in kilowatt-hours and power capacity in kilowatts, and notes that no storage system is free of conversion losses. The calculator handles the arithmetic once you have picked the daily figure and the bank voltage.

What the calculator returns

The default case is a 5 A load running for 4 hours on a 12 V pack, which is the shape of most small projects. The second mode works the other way and turns a known capacity and current into a run time.

Three habits keep the answers honest. Give the pack voltage, because amp-hours without a voltage cannot be turned into energy. Keep the units straight, since a 12 V pack and a 24 V pack hold different energy behind the same amp-hour number. And treat the capacity as a ceiling rather than a promise, because depth of discharge, discharge rate, temperature and age all shave the real figure below the label.