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There are multiple battery sizes that are the most commonly used ones, these are the AAA, AA, C, D and 9V batteries that can be either primary (single use) as well as rechargeable. But these batteries also have many other names, some of which are used by different manufacturers and in some countries the other names may be more popular than the typical types mentioned above.

AAA Alkaline Battery – MN2400, LR03, E92, 4203/4003, K3A, AM4, 824, LR03, 24A, R03 (carbon–zinc), 24D (carbon–zinc)
AAA Rechargeable Battery – HR03 (NiMH), MIGNON, MINI-STILO, 4003, E92, K3A, R0, UM4, KR03 (NiCd), ZR03 (NiOOH)

The typical capacity of an AAA size alkaline battery is around 1000-1200 mAh, for Carbon-Zinc batteries the capacity is around 500 mAh and the rechargeable AAA batteries of the NiMH type usually offer abound 800-1000 mAh capacity.

AA Alkaline Battery – MN1500, LR6, E91, 4206/4006, KAA, AM3, 815, LR6, R6 (carbon–zinc), 15D (carbon–zinc)
AA Rechargeable Battery – HR6 (NiMH), MICRO, STILO, 4006, E91, KAA, R6, UM3, KR6 (NiCd), ZR6 (NiOOH)

The typical capacity of an AA size alkaline battery is around 1500-2500 mAh, for Carbon-Zinc batteries the capacity is around 500-800 mAh and the rechargeable AA batteries of the NiMH type usually offer abound 1600-2900 mAh capacity.

C Alkaline Battery – MN1400, LR14, E93, 4014, KC, AM2, 814, LR14, R14 (carbon–zinc), 14D (carbon–zinc)
C Rechargeable Battery – HR14 (NiMH), BABY, MEZZA-TORCIA, 4014, E93, KC, R14, UM2, KR14 (NiCd), ZR14 (NiOOH)

The typical capacity of a C size alkaline battery can be up to about 8000 mAh, for Carbon-Zinc batteries the capacity can be up to about 4000 mAh and the rechargeable C batteries of the NiMH type usually offer abound 4500-6000 mAh capacity. Alternatively there are also special plastic adapters that can be used together with an AA battery to make a C size cell, though the capacity would be lower in this case than what a C size battery would normally provide.

D Alkaline Battery – MN1300, LR20, E95, 4020, KD, AM1, 813, LR20, 13D (carbon-zinc), R20 (carbon-zinc)
D Rechargeable Battery – HR20 (NiMH), HR20, MONO, TORCIA, 4020, E95, KD, R20, UM1, KR20 (Ni-Cd), ZR20 (NiOOH)

The typical capacity of a D size alkaline battery can be up to about 12000 mAh, for Carbon-Zinc batteries the capacity can be up to about 8000 mAh and the rechargeable D batteries of the NiMH type usually offer abound 2000-12000 mAh capacity. Alternatively there are also special plastic adapters that can be used together with an AA battery to make a D size cell, though the capacity would be lower in this case than what a D size battery would normally provide.

9V Alkaline Battery – MN1604, 6LR61, 522, 4022, K9V, 6AM6, A1604, 6LR61, 1604D (carbon‑zinc), 6F22 (carbon-zinc), 1604LC (lithium)
9V Rechargeable Battery – HR9V (NiMH), HR9V, E-BLOCK, TRANSISTOR, 422, 4022, 6F22, K9V, 6HR61, 6KR61 (NiCd), 11604 (NiCd)

The 9V batteries essentially consists of multiple cells to bring up the voltage higher – 6x 1.5V cells for carbon-zinc; 3 cells for Lithium; 6, 7 or 8 cells for NiMH (7.2V, 8.4V or 9.6V) using 1.2V cells. Alkaline batteries can go up to about 500-600 mAh capacity, 400 mAh for the carbon‑zinc, up to about 1200 mAh for lithium (non-rechargeable), 200–300 mAh for NiMH and about 100 mAh for NiCd.