Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the erlang distribution calculator works
F(x)=1−e^(−λx)Σⱼ₌₀^(k−1)(λx)^j/j!, with integer shape k≥1.
Erlang is the gamma special case with integer shape and has a direct waiting-time-to-the-kth-event interpretation.
Worked example
Erlang Distribution example
Shape 2 and rate 1 give cumulative probability 1−3e⁻² at x=2.
F(x)=1−e^(−λx)Σⱼ₌₀^(k−1)(λx)^j/j!, with integer shape k≥1.
Supported inputs
Precision and limits
Model and design
The underlying event process must have independent exponential gaps with a constant rate; rate and time units must be reciprocal.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Erlang is the gamma special case with integer shape and has a direct waiting-time-to-the-kth-event interpretation.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
Continue calculating