Beta of a bipolar transistor is equal to:

In a bipolar junction transistor (BJT), alpha represents the common-base current gain (Collector Current divided by Emitter Current), while beta represents the common-emitter current gain (Collector Current divided by Base Current). Because the emitter current is the sum of the collector and base currents, these two gains are mathematically connected. The formula relating them is beta = alpha / (1 - alpha). Since alpha is typically very close to 1 (for example, 0.99), the denominator (1 - alpha) becomes a very small number. This small denominator results in a large beta value (e.g., 99), matching the typical high current gain seen in practical common-emitter configurations. Distractors involving multiplication or addition are mathematically incorrect. They fail to model the fundamental transistor current relationship where a tiny base current controls a much larger collector current.