Expected Service Time Calculator

Expected Service Time Inputs

Scenario label

Time unit

Quick note

The calculator normalizes probabilities when totals differ from one.

Row	Service Time	Probability	Action
1
2
3
4
5

Example Data Table

Scenario	Service Time	Probability	Weighted Time
Fast request	2 minutes	0.10	0.20
Typical request	4 minutes	0.25	1.00
Moderate request	6 minutes	0.30	1.80
Long request	8 minutes	0.20	1.60
Complex request	10 minutes	0.15	1.50
Totals		1.00	6.10 minutes

Formula Used

E[T] = Σ (tᵢ × pᵢ)

E[T²] = Σ (tᵢ² × pᵢ)

Var(T) = Σ (pᵢ × (tᵢ - E[T])²)

CV = Std Dev / E[T]

Here, tᵢ is a service-time outcome and pᵢ is its probability. The calculator first checks the probability total. When the total differs from one, it converts entered values into normalized probabilities. This preserves the shape of the distribution and still returns a valid expected service time.

How to Use This Calculator

Enter a scenario label if you want a named case.
Select the time unit that matches your service data.
Add service-time outcomes and their corresponding probabilities.
Press Submit to show the result above the form.
Review the summary metrics, distribution table, and probability chart.
Use CSV or PDF export to save the calculation.

Why Expected Service Time Matters

Expected service time gives one average value for uncertain service outcomes. It supports staffing analysis, queue studies, simulation input design, and operating-policy comparisons. Variance and standard deviation add extra insight because two systems can share one average but behave very differently in practice.

Expected Service Time Inputs

Example Data Table

Formula Used

How to Use This Calculator

Why Expected Service Time Matters

Related Calculators