Project buffer & PERT estimator
The project buffer and PERT estimator turns a best case, a most likely case and a worst case for each task into an expected duration, a project buffer sized from how uncertain each estimate is, and an optional contingency reserve. It is for anyone planning a chain of tasks who wants a buffer they can explain. It runs in your browser and exports the plan to Mermaid.
1. Task estimates (days)
Optimistic (O), most likely (M) and pessimistic (P) durations for each task on the critical path, in the order they happen.
| Task Name | Opt (O) | Likely (M) | Pess (P) | PERT (t_e) | |
|---|---|---|---|---|---|
| 3.3 d | |||||
| 5.3 d | |||||
| 6.7 d | |||||
| 3.5 d |
2. Schedule
Updates as you typeThe Mermaid code appears here once the page's script runs.How the numbers are calculated
A single estimate ("five days") hides how sure you are. Three estimates per task keep that information, and the calculator uses it twice: once for the expected duration and once for the buffer.
1. Expected duration: PERT
PERT, developed for the US Navy's Polaris programme in the late 1950s, weights the three estimates towards the most likely one:
σ is a rough standard deviation: the wider the gap between the best and the worst case, the less you know about the task. The expected duration of the whole chain is the sum of the t_e of its tasks.
2. Project buffer: root sum of squares
Instead of padding every task, the buffer goes once, at the end of the chain. If the tasks' overruns are independent, they don't all happen together, so the spreads add as squares:
Two standard deviations cover about 95% of outcomes if the total behaves like a normal distribution, which is a reasonable approximation for a chain of several tasks and a poor one for two or three. If the tasks share a cause of delay (the same reviewer, the same unknown API), they are not independent and this buffer is too small.
This is not the 50% rule
Critical Chain Project Management, as Eliyahu Goldratt described it in Critical Chain (1997), sizes the buffer differently: cut each task's estimate roughly in half and put half of what you cut into a shared project buffer, so the buffer ends up at about half the length of the chain. That rule ignores how uncertain each task is. Root sum of squares uses it, and for chains of many tasks gives a much smaller buffer. This calculator uses root sum of squares; if you want the 50% rule, the buffer is half of the expected total.
3. Contingency reserve
The buffer only covers the uncertainty you wrote into the estimates. The contingency slider adds a percentage of the expected duration for everything else: scope that grows, people who are away, suppliers who are late. There is no formula for that number; it is a judgement call, and the calculator keeps it separate so you can see how much of the total it is.
We wrote more about buffers, and how Andamio handles them per task, in Why your project needs buffer time built in, and about what Andamio does and doesn't calculate along the chain in our post on the critical path.
Frequently asked questions
How is the project buffer calculated?
The buffer is 2 × √(σ₁² + σ₂² + … + σₙ²), where each task's σ is (P − O) / 6. It goes once, at the end of the chain, instead of padding every task. Two standard deviations cover about 95% of outcomes if the total behaves like a normal distribution.
How is this different from the 50% rule?
The 50% rule of Critical Chain Project Management cuts each estimate roughly in half and puts half of what was cut into a shared buffer, so the buffer ends up about half the length of the chain. It ignores how uncertain each task is. Root sum of squares uses that uncertainty and, for chains of many tasks, gives a much smaller buffer. This calculator uses root sum of squares; for the 50% rule, take half of the expected total.
When is the buffer too small?
When the tasks share a cause of delay, such as the same reviewer or the same unknown API: their overruns are not independent, and root sum of squares assumes they are. It is also a poor approximation for a chain of only two or three tasks.
What does the contingency reserve add?
A percentage of the expected duration for everything the estimates don't cover: scope that grows, people who are away, suppliers who are late. There is no formula for that number, so it is a judgement call, and the calculator keeps it apart so you can see how much of the total it is.
Does it send my estimates anywhere?
No. The calculation runs in your browser and nothing you type is sent to a server. The Mermaid export is text on the page, which you copy yourself.