Energies and powers are for lithium batteries, which have a voltage of 3.7 Volts. The "ID #" is often used instead of cell size.
Cell Energy Power Current Mass Diameter Length Charge Price ID # size kJoule Watt Ampere gram mm mm AmpHour $ D 107 220 60 138 32 67 8.0 13 32650 C 67 220 60 92 26 50 5.0 8 26650, 25500 B 58 160 45 72 22 60 4.5 5 21700, 20700 A 47 110 30 49 18 50 3.5 3 18650 AA 9 22 6 15 14 53 .70 1 14500 AAA 4.7 11 3 7.6 10 44 .35 .5 10440 AAAA 2.3 6 1.5 3.8 8 42 .17 .25 75400 CR2032 3. Most common button cell CR1216 .33 Smallest button cell Apple Watch 4 4.0 .29 iPhoneXR 6" 41 2.94 Machine = .194 kg iPhoneXSM 6" 44 3.17 Machine = .208 kg iPhoneXS 6" 36 2.66 Machine = .177 kg iPhone8+ 6" 27 2.79 Machine = .202 kg iPhone8 5" 25 1.82 Machine = .148 kg iPhone7+ 6" 40 2.90 Machine = .188 kg iPhone7 5" 27 1.96 Machine = .138 kg iPad Mini 8" 70 5.12 Machine = .30 kg iPad Pro 10" 111 8.13 Machine = .47 kg Mac Air 11" 137 Machine = 1.08 kg Mac Air 13" 194 Machine = 1.34 kg MacBook 12" 149 Machine = .92 kg Mac Pro 13" 209 Machine = 1.37 kg Mac Pro 15" 301 Machine = 1.83 kg
Energy Power Lifetime kJoule Watts hours iPhone 8 5" 25 .50 14 iPhone 8+ 6" 27 .54 14 iPad Mini 8" 70 1.9 10 iPad Pro 10" 111 3.1 10 Mac Air 11" 137 3.8 10 Mac Air 13" 194 5.4 10 Mac Pro 13" 209 5.8 10 Mac Pro 15" 301 8.4 10
Voltage = V Volts Charge = C Coulombs Time = T seconds Electric current = I = C/T Amperes (Amps) Electric power = P = VI Watts Energy = E = PT Joules = CV JoulesBattery energy is often given in "Watt hours" or "Ampere hours".
1 Watt hour = 3600 Joules = 1 Watt * 3600 seconds
1 Amp hour = 3600 Coulombs = 1 Coulombs/second * 3600 seconds
A battery with a voltage of 3.7 Volts that delivers
1 Ampere for 1 hour has an energy of
Energy = 1 Ampere * 3.7 Volts * 3600 seconds = 13320 Joules
Energy/Mass Power/Mass Recharge Year Anode Cathode Market fraction of MJoule/kg Watt/kg Lithium-ion batteries Lithium air 6.12 No Future Li O2 Aluminum air 4.68 200 No 1970 Al O2 Lithium thionyl 2.00 700 No 1973 Li SOCl2 Zinc air 1.59 No 1932 Zn O2 Lithium-ion sulfur 1.44 670 Yes Future Li S 0 Lithium metal 1.01 400 No 1976 Li MnO2 Lithium-ion CoNiAlO2 .79 Yes 1999 Li CoNiAlO2 .10 Lithium-ion CoNiMnO2 .74 1200 Yes 2008 Li CoNiMnO2 .29 Lithium-ion CoO2 .70 200 Yes 1991 Li CoO2 .29 Lithium-ion Mn2O4 .54 1200 Yes 1999 Li Mn2O4 .10 Lithium-ion FePO4 .47 1200 Yes 1996 Li FePO4 .22 Alkaline .40 Yes 1992 Zn MnO2 NiMH .34 1000 Yes 1990 MH NiO(OH) Lead acid .15 180 Yes 1881 Pb PbO2 NiCd .14 200 Yes 1960 Cd NiO(OH)
MJoules/kg Recharge 1932 Zinc air 1.59 N 1949 Alkaline .59 N 1973 Lithium thionyl 1.8 N 1976 LiMnO2 1.01 N 1989 LiFeS2 1.07 N 1989 Aluminum air 4.68 N Lab Lithium air 6.1 N 1881 Lead acid .14 Y 1901 NiFe .09 Y 1960 NiCd .14 Y 1975 NiH2 .23 Y 1991 Lithium-ion .95 Y 1992 Rechargeable alk. .4 Y Lab Lithium sulfur 1.44 Y
The largest energy storage stations are "pumped hydro" stations, where water is pumped to an elevated reservoir when energy is available and returned to the lower reservoir when energy is needed. The cheapest system types are pumped hydro and underground compressed air. For small-scale energy storage such as homes, batteries are the cheapest option. The types of energy storage are:
Cost Cost Efficiency Cycles kJ/$ Watt/$ Pumped hydro 26 .7 .8 Infinite Pump water to an elevated reservoir Air, underground 60 1.0 .7 Infinite Compress air Air, above ground 9 .5 .7 Infinite Compress air Battery, Li-ion 10 10 .9 1000 Battery, Lead acid 10 10 .9 1000 Flywheel .45 .5 .85 Infinite Gasoline 30000 2.0 .35 - Using a generator with 2 Watts/$ Solar cell - .5 - - Wind turbine - .25 - - Blade diameter = 2.5 meters
The largest energy storage systems for each type of storage are:
GWatt hours California, San Luis Pumped hydro 126 Tennessee, Raccoon Mtn. Pumped hydro 36 Virginia, Bath County Pumped hydro 31 California, Kern County Compressed air 3 Alabama, McIntosh CAES Compressed iar 2.9 Arizona, Solana Thermal salt 1.7 Spain, Andasol Thermal salt 1.03 Australia, Hornsdale Battery, Li-ion .129 California, Primus Power Battery, ZnCl .075 Japan, Hokkaido Project Battery, Li-ion .060 China, National Wind Battery, Li-ion .036 New York, Beacon Flywheel .005
The average American home uses 1400 Watts of electricity. 1 GWatt hour is enough to power 30000 homes for 1 day.
For small scale energy storage such as an off-grid home, a generator can help. They typically cost ½ $/Watt.
Data on cost of energy storage
A house can use either grid electricity, a gasoline generator, or a system of solar cells and batteries. Grid electricity is cheapest, gasoline is slightly more expensive, and solar cells and batteries are much more expensive.
House, electrical power = 1000 Watts Typical for a small house Energy for one day = 86 MJoules Li-ion battery Energy/$ = .01 MJoule/$ Generator efficiency = .3 Generator cost = 2 Watts/$ Solar cell cost = .5 Watts/$ Solar cell average power = 50 Watts/meter2 Cost of grid electricity = 36 MJoules/$ Gasoline energy per mass = 48 MJoules/kg Gasoline cost per mass = .5 $/kg Gasoline energy per dollar = 96 MJoules/$ Cost, 1 year of grid electricity= 870 $ Cost, 1 year of gasoline = 1090 $ 1 year of gasoline to supply a 1 kWatt generator Cost, 1000 Watt generator = 500 $ Cost, 1000 Watt solar cell = 2000 $ Cost, battery, 1 day of energy = 8600 $ 1 Day at 1 kWatt
A single battery is a "cell" and a set of cells is a "pack". Packs are used to multiply the energy and power of cells.
Battery packs are notorous for catching fire, but cell technology has reached the point where it's now possible to make safe battery packs, and the design is simple enough so that anyone can construct their own packs.
Cells can be combined in series and/or parallel. Connecting in series multiples voltage, and voltage is helpful for achieving high power in a motor.
Connecting in series is easier than in parallel. If it's possible to achieve the required power without parallelization then one should do so, and this is usually possible with modern cells.
Series packs have the advantage that the cells can easily be extracted and charged individually, and cells can be interchanged between packs. One can also construct a set of series packs and swap them in like gun clips.
High power electric bikes use a voltage of 72 Volts. If we use one series array of C cells then a pack provides 4440 Watts and 1.2 MJoules. Any electric device requiring less than this much power can be powered by a series pack.
The properties of a modern high-power cell are:
Type = "C" Voltage = 3.7 Volts Energy = 60 kJoules Power = 155 Watts Mass = 92 grams Energy/mass = 650 kJoules/kg Power/mass =1680 Watts/kg Current = 42 Amperes Manufacturer = "Basen"When the cells are connected in series the values for voltage and power are:
Cells Voltage Power Volts kWatts 1 3.7 .15 2 7.4 .30 3 11 .45 Electric kick scooter 4 15 .60 6 24 .90 Electric bike 10 36 1.5 20 72 3.0 Compact electric car 96 356 15.0 Large electric car
Electric bike motors use either 36, 48, or 72 Volts. The following table shows how to build a battery pack for each motor power.
Power Volts Cells Series Parallel Current Cell max Cell Cell Cell Cell brand kWatt Amperes Amperes Amphours $ type .75 36 10 10 1 21 30 2.0 5 A Sony VTC4 1.5 48 13 13 1 31 60 4.5 8 C Basen 3 72 20 20 1 42 60 4.5 8 C Basen 6 72 40 20 2 83 120 4.5 8 C Basen 12 72 80 20 3 167 180 4.5 8 C Basen Cells Total number of cells, equal to the number of cells connected in series times the number of cells connected in parallel. Series Number of cells connected in series. For example, 20 batteries with 3.6 volts each connected in series produces a voltage of 72 Volts. Parallel Number of cells connected in parallel. Current Current required to provide given power Cellmax Maximum current of a cell
Cobalt is the dominant cost for lithium-ion batteries, and copper is the dominant cost for solar cells, wind turbines, and electric motors.
Lithium-ion batteries can be made with or without cobalt, although cobalt is required if you want large energy/mass.
The critical metals are copper, lithium, cobalt, nickel, neodymium, silver, and rare Earths. Cobalt and rare Earths are a concern because they're scarse (42% of cobalt goes to batteries) and because they come from politically unstable regions.
The metal content of various devices is:
Cost Mining Reserves Battery Battery SolarCell SolarCell Wind Wind Motor Motor $/kg Bkg/yr Bkg kg/MJoule $/MJoule kg/kWatt $/kWatt kg/kWatt $/kW kg/kWatt $/kWatt Lithium 20 .6 30 .023 .46 - - - - - - Cobalt 30 .12 7 .20 6.0 - - - - - - Nickel 15 2.2 80 .20 3.0 - - - - - - Copper 6 18 700 - - 5 30 4 24 .036 .22 Neodymium 25 .01 .6 - - - - .014 .28 .0062 .16 Silver 450 .026 .53 - - .034 15 - - - -
All lithium-ion batteries contain lithium and most contain an equal number of lithium and cobalt atoms. Lithium-ion batteries typically contain an equal number of lithium and cobalt atoms. A cobalt atom is substantially more massive than a lithium atom and so batteries have much more cobalt mass than lithium mass. Cobalt reserves are smaller than lithium reserves and so we will run out of cobalt before we run out of lithium.
For a typical car battery, the cobalt cost is:
Energy = 100 MJoules Cobalt cost per MJoule = 6.0 $/MJoule Cobalt cost = 600 $
If we make 1 billion electric cars then the total cobalt mass is:
Energy = 100 MJoules Cobalt mass per MJoule = .2 kg Cobalt mass per car = 20 kg Number of cars = 1 billion cars Total cobalt mass = 20 Bkg Cobalt mining = .12 Bkg/year Cobalt reserves = 7 Bkg
The cobalt required far exceeds annual mining and it even exceeds reserves. Not all batteries will be able to have cobalt.
All lithium-ion batteries contain lithium and they can also contain cobalt, manganese, nickel, and aluminum. Only lithium (20 $/kg) and cobalt (30 $/kg) are expensive enough to matter. Batteries with high energy/mass require cobalt. The battery types are:
Energy/Mass Market Commer- MJoule/kg frac cialized Lithium-ion LiS 1.44 0 Future Lithium-ion LiCoO2 .95 .29 1991 Lithium-ion LiNiCoAlO2 .79 .10 1999 Lithium-ion LiNiCoMnO2 .74 .29 2008 Lithium-ion LiMn2O4 .54 .10 1999 Lithium-ion LiFePO4 .47 .22 1996 Alkaline .40 1992 Nickel metal hydride .34 1990 Lead acid .15 1881 Nickel cadmium .14 1960
Lithium-iBatteries typically cost 100 $/MJ. "Market fraction" is for lithium-ion batteries only.