Four Charges on the Box, Two and a Half in Your Pocket

Why a 20,000 mAh power bank charges a 5,000 mAh phone about 2.56 times, how long batteries really take to charge, and which power banks may fly on a plane.

Patryk Matyjasik · 19 September 2026 · 11 min read

Four Charges on the Box, Two and a Half in Your Pocket

"Spare (uninstalled) lithium ion and lithium metal batteries, including power banks and cell phone battery charging cases, must be carried in carry-on baggage only."

That sentence comes from the FAA, and the rule behind it judges a power bank by the right number. The airline does not care about the 20,000 mAh printed in large type on the front. It cares about watt-hours. Most buyers do the opposite, and the first thing they do with the big number is divide it: 20,000 ÷ 5,000 = 4, so a 20,000 mAh bank should charge a 5,000 mAh phone four times.

It will not. Put both batteries through the power bank capacity calculator and the answer is 2.56 charges: two full ones and 56% of a third. Even with no losses at all, a perfect bank could never do more than 3.84. The missing 1.44 charges are not a defect. It is arithmetic done in the wrong unit.

Where the missing charges go

A milliamp-hour is a quantity of charge, not of energy. It only turns into energy with a voltage attached, and the three voltages involved here are all different. The cells inside a power bank sit at about 3.7 V, which is the voltage the label's mAh refer to. A recent phone battery is nearer 3.85 V. And between the two there is a USB cable at 5 V.

So the honest comparison is in watt-hours. 20 Ah × 3.7 V = 74 Wh in the bank. 5 Ah × 3.85 V = 19.25 Wh in the phone. Divide those and you get the ceiling of 3.84 charges. Wikipedia's power bank article adds the first loss on top: a 3.7 V rating read at a 5 V output is only 74% of the printed mAh, so the 20,000 mAh bank is 14,800 mAh at the port before a single milliwatt is lost to heat.

Then the heat. The bank has to step 3.7 V up to 5 V, which is the job of a boost converter, a switching circuit that stores energy in an inductor, a capacitor or both on every cycle. The phone steps it back down and runs its own charging circuit. The same Wikipedia article cites measurements in which the average power bank delivered about 2/3 of its cell energy into the devices it charged. That is the figure the calculator uses when the efficiency box is left empty: 74 Wh × 2/3 = 49.33 Wh reaches the phone, 24.67 Wh does not, and 49.33 ÷ 19.25 is the 2.56.

Power bank capacity calculator: 20,000 mAh bank at 3.7 V into a 5,000 mAh phone at 3.85 V gives 2.56 charges, ceiling 3.84, 74 Wh, carry-on under FAA rules

Is 2/3 pessimistic? For a good bank, maybe a little. The same article describes a 26,800 mAh unit rated at 19,832 mAh in theory at 5 V that measured 15,682 mAh at the port, or 78.41 Wh, which is 79% of its cell energy. Type 79% in and the calculator gives 4.07 charges of the same phone, and that is before the phone's own charging loss, which the 2/3 average already includes.

What each size really gives

The table puts eight common sizes through the calculator with the same 5,000 mAh, 3.85 V phone. The third column is the division on the box, the fourth the calculator at the measured average, the fifth the no-loss ceiling. The last column is the FAA tier, which depends only on the bank's watt-hours.

Power bankEnergyLabel ÷ labelAt about 2/3No-loss ceilingFAA
5,000 mAh18.5 Wh10.640.96Carry-on
10,000 mAh37 Wh21.281.92Carry-on
20,000 mAh74 Wh42.563.84Carry-on
25,000 mAh92.5 Wh53.24.81Carry-on
26,800 mAh99.16 Wh5.363.435.15Carry-on
30,000 mAh111 Wh63.845.77Airline approval
40,000 mAh148 Wh85.137.69Airline approval
50,000 mAh185 Wh106.419.61Over the limit

Two rows deserve a second look. A 5,000 mAh bank does not quite fill a 5,000 mAh phone even once: 0.64 of a charge. And the jump from 26,800 to 30,000 mAh is small in charges but large at the airport. 26,800 mAh at 3.7 V is 99.16 Wh, just under the 100 Wh carry-on tier; 30,000 mAh is 111 Wh and needs the airline's approval, with at most two such batteries per passenger. At 3.7 V the 100 Wh line falls at 27,027 mAh and the 160 Wh line at 43,243 mAh, so a 50,000 mAh bank, 185 Wh, is above anything the FAA lets a passenger carry as a spare. Airlines can be stricter still, especially on international routes.

The other number on the box: charging time

The same habit of dividing labels shows up with chargers. A 5,000 mAh phone at 20% on a 20 W adapter at 85% efficiency needs 14.8 Wh, and the battery charging time calculator gives 52 min to full and 39 min to 80%. The adapter supplies 17.41 Wh for the job. The charge rate is 0.92C, a current close to the battery's own amp-hour rating per hour.

Battery charging time calculator: 5,000 mAh at 3.7 V on a 20 W adapter at 85 percent from 20 percent, 52 min to full, 39 min to 80 percent, 0.92C

Why does the last fifth take a separate line? A lithium-ion charger holds a constant current, then a constant voltage, 4.2 V per cell for typical lithium cobalt oxide cells, while the current falls, and it stops at about 3% of the starting current. The straight-line time is honest up to the switch and optimistic after it.

Now type 140 W, the largest number on some laptop adapters, for the same phone. The calculator says 10 min and flags it at once: 6.05C, six times the battery's rating every hour. The phone's charge controller takes only what it negotiates over USB Power Delivery, so the adapter's label is a ceiling on supply, not a promise about the phone.

Charging a 12 V, 100 Ah battery

With a current instead of watts, the floor is plain division: amp-hours over amps. A 100 Ah battery on a 10 A charger can never take less than 10 h from empty. With the efficiency box left empty the calculator also gives the range for 90% and 80%, 11 h 7 min to 12 h 30 min. The table shows the seven charger sizes people ask about most.

ChargerNo-loss floorAt 90%At 80%
5 A charger20 h22 h 13 min25 h
6 A charger16 h 40 min18 h 31 min20 h 50 min
10 A charger10 h11 h 7 min12 h 30 min
15 A charger6 h 40 min7 h 24 min8 h 20 min
20 A charger5 h5 h 33 min6 h 15 min
30 A charger3 h 20 min3 h 42 min4 h 10 min
40 A charger2 h 30 min2 h 47 min3 h 8 min

A lead-acid battery is rarely charged from empty, though. From 50%, the usual floor for lead-acid, the 10 A charger needs 5 h 33 min to 6 h 15 min, with 5 h as the no-loss minimum. Half the energy, half the wait, and a number that matches what an overnight charge actually looks like.

Three more places where the first number is too high

An 18650 cell on a 1 A charger

A 3,000 mAh cell at 3.6 V holds 10.8 Wh. On 1 A the floor is exactly 3 h, and with the efficiency left empty the calculator gives 3 h 20 min to 3 h 45 min. A gentle 0.33C.

Earbuds from a small bank

An earbud case of 500 mAh at 3.7 V holds 1.85 Wh. A 5,000 mAh bank refills it 6.67 times at the measured average and 10 times at the ceiling. Here dividing the labels happens to give the ceiling, because both batteries sit at the same 3.7 V, and it still promises half as many charges again as the measured average.

The coil inside the converter

Even the inductor in a switching converter has a label-style trap. The textbook formula for a solenoid, L = µ0N²A ÷ l, assumes a coil far longer than it is wide. For 100 turns on a 20 mm form, 50 mm long, it promises 78.96 µH. The inductance calculator uses Wheeler's formula from Wikipedia's table of inductance formulas and gets 67.57 µH, a ratio of 0.856. The ideal formula overstates by about 17%. Squash the same 10 turns into 5 mm and the gap grows: 7.896 µH promised, 2.817 µH real, 2.8 times too high.

Inductance calculator: air-core coil, 100 turns, 20 mm diameter, 50 mm long, 67.57 microhenries by Wheeler's formula against 78.96 for the ideal long solenoid

Cores are worse. Multiply a coil on an open ferrite rod by the ferrite's full permeability and the answer can be off by orders of magnitude, because the field lines have to return through air. The calculator applies permeability only to a closed toroid and asks for the maker's AL value for everything else.

Mistakes that make a battery look bigger than it is

Dividing mAh by mAh. The two ratings are at different voltages and nothing is converted. Convert both to watt-hours first; for the 20,000 and 5,000 mAh pair the box says 4 and the physics says at most 3.84.

Forgetting the losses. Even the ceiling assumes a perfect converter, cable and phone. The measured average is about 2/3, and a good bank tested at the port reached 79%.

Typing the adapter's maximum. A 140 W adapter does not charge a phone in 10 minutes. Enter the device's own maximum charging wattage.

Charging from zero on paper and from 35% in real life. A phone plugged in at 35% needs only 65% of a charge. Leave the starting level empty and the estimate is 1.54 times too long.

Reading the flight rule in mAh. The FAA counts watt-hours. 27,027 mAh at 3.7 V is the 100 Wh line, and a bank that prints only mAh leaves the conversion to you.

Five rules for reading a battery label

  1. Multiply before you divide. mAh × V ÷ 1,000 gives Wh; compare batteries only in Wh.
  2. Use the cell voltage, not the port voltage. 3.7 V for the bank's rating, about 3.85 V for a phone, never 5 V.
  3. Budget two thirds. Without a measurement, expect about 2/3 of a power bank's cell energy to reach the phone.
  4. Read the time to 80% on its own. The constant-voltage finish of a lithium charge is slower than any straight-line estimate.
  5. Check the watt-hours before the airport. Up to 100 Wh in carry-on, 100 to 160 Wh with approval, never in checked bags.

Tools discussed in this article

Ready-made calculations

How long a 12 V, 100 Ah battery takes to charge: 5 amp charger, at least 20 h, 6 amp charger, at least 16 h 40 min, 10 amp charger, at least 10 h, 15 amp charger, at least 6 h 40 min, 20 amp charger, at least 5 h, 30 amp charger, at least 3 h 20 min, 40 amp charger, at least 2 h 30 min.

How many times a power bank charges a 5,000 mAh phone: 5,000 mAh, 0.64, 10,000 mAh, 1.28, 20,000 mAh, 2.56, 30,000 mAh, 3.84, 50,000 mAh, 6.41.

Whether a power bank can fly in US carry-on: 10,000 mAh, 37 Wh, carry-on, 20,000 mAh, 74 Wh, carry-on, 25,000 mAh, 92.5 Wh, carry-on, 26,800 mAh, 99.16 Wh, carry-on, 30,000 mAh, 111 Wh, airline approval, 40,000 mAh, 148 Wh, airline approval, 50,000 mAh, 185 Wh, over the limit.

More physics tools

The rest of the physics shelf, in the order it was built: