A flow calculator based on queuing theory. Adjust the inputs on the left to see how cycle time, utilization, and wait time respond. Use it to find the balance that works for your team — whether you run Scrum, Kanban, or continuous delivery.
As your team gets busier, wait time grows nonlinearly. The dot shows where you are now.
This calculator does not invent its numbers. Every metric on the calculator tab is derived from two foundational results in queuing theory, with documented assumptions. The math is laid out below so you can see what is going on under the hood.
The first equation is an identity. For any stable queueing system — regardless of arrival distribution, service distribution, or queue discipline — the average number of items in the system equals the arrival rate times the average time spent in the system (Little, 1961; Little, 2011).
L = λ × W
In flow terms:
WIP = Throughput × Cycle Time
The calculator uses this to compute cycle time directly from the team's work-in-progress and throughput:
Cycle Time = WIP ÷ Throughput
The second equation estimates the average time an item waits in queue before being worked on. For a single-server queue with general arrival and service distributions (denoted G/G/1), Kingman (1961) showed that the wait time can be approximated as the product of three factors — variability, utilization, and service time. This is sometimes called the VUT formula in operations research (Hopp & Spearman, 2008).
Wq ≈ V × U × T
The U term is what produces the nonlinear "wall" in the chart on the calculator tab. As ρ approaches 1, U explodes toward infinity — at 90% utilization U is 9, at 95% it is 19, at 99% it is 99.
The two predictability dropdowns in the calculator hide a technical concept: the coefficient of variation (CV), defined as the standard deviation divided by the mean. The mapping used is:
| Dropdown choice | CV value | Interpretation |
|---|---|---|
| Very steady, almost like clockwork | 0.25 | Near-deterministic |
| Somewhat predictable, with bumps | 0.5 | Mild variability |
| Random and unpredictable | 1.0 | Memoryless (Poisson-equivalent) |
| Very bursty | 1.5 | Burstier than random |
A CV of 0 means perfectly deterministic; 1.0 corresponds to an exponential distribution (the textbook "random arrivals" case); values above 1 indicate burstier-than-random behavior such as sprint planning or traffic spikes.
Utilization (ρ) is computed from the inputs as:
ρ = arrival rate per day ÷ team capacity per day
Walking through what the calculator does with the default inputs (20 items in progress, 5 items per week arrival, 3 days per item, 5 people, "somewhat predictable" for both variability dimensions):
Every number shown on the calculator tab traces through these steps. There is no fudge factor or hidden adjustment.