The information transfer through a single neuron is a fundamental information processing in the brain and computing the information channel capacity is important to understand the information processing in the brain. The problem is difficult since the capacity depends on various issues, such as coding, characteristics of the communication channel and optimisation over input distributions. In this letter, two different models are considered. The temporal coding model of a neuron as a communication channel assumes the output is $\tau$ where $\tau$ is a gamma-distributed random variable corresponding to the inter-spike interval, that is, the time it takes for the neuron to fire once. The rate coding model is similar; the output is the actual rate of firing over a fixed period of time. Theoretical studies prove that the distribution of inputs, which achieves the channel capacity, is a discrete distribution with finite mass points for temporal and rate coding under a reasonable assumption. This allows us to compute numerically the capacity of a neuron. Numerical results are in a plausible range based on biological evidence to date.