What is PERT?
Single-number estimates hide uncertainty: "four weeks" may mean three if all goes well and eight if it does not. PERT asks for all three and turns them into an expected time and a spread for every activity. Scheduled through the network with the critical path method, they give an expected project duration and, more usefully, the probability of finishing by any date. That turns "will we make it?" into "we have an 86% chance of making it".
PERT formulas
| Quantity | Formula |
|---|---|
| Expected time te | (o + 4m + p) ÷ 6 |
| Standard deviation σ | (p − o) ÷ 6 |
| Project duration T | Sum of te on the critical path |
| Project σ | √(sum of σ² on the critical path) |
| Probability of finishing by D | Φ((D − T) ÷ σ) |
PERT example
A team implementing a document management system estimates seven activities in weeks. Configuring workflows is the most uncertain (4, 6 or 12 weeks: te = 6.7, σ = 1.3). The critical path runs through requirements, vendor selection, configuration, validation and go-live, for an expected 20 weeks with a standard deviation of 1.8 weeks. Against a 22-week deadline, the chance of finishing on time is about 86%; for 95% confidence the team should commit to about 23 weeks, or reduce the uncertainty in the configuration work.
Tips for better estimates
- Ask the people who will do the work, and ask for the pessimistic case explicitly: what if things go wrong?
- Use history from similar projects where you can.
- Watch near-critical paths: PERT only counts the critical path's variance, so a parallel path with high uncertainty can still cause a delay.
- Plan the risks behind wide estimates with a PDPC.
How to use this PERT Chart tool
- List the activities. Add each activity with a code and name, and the codes of the activities that must finish first.
- Estimate three durations. For each activity enter optimistic, most likely and pessimistic durations. The tool calculates the expected time.
- Read the network. The PERT chart shows expected start and finish times and the critical path in red.
- Set a target date. Enter the deadline in the same time unit to see the chance of finishing on time.
- Check the confidence levels. Read the durations you can commit to with 80%, 90% or 95% confidence.
- Export. Export the PERT chart and the estimates to PDF, PNG or Excel.
Frequently asked questions
What is PERT?
PERT (Program Evaluation and Review Technique) is a project planning method developed for the US Navy Polaris program in 1958. Instead of one duration per activity, it uses three estimates (optimistic, most likely and pessimistic) to calculate an expected duration and a measure of uncertainty, and from those the probability of finishing the project by a given date.
What is the PERT formula?
Expected time te = (optimistic + 4 × most likely + pessimistic) ÷ 6. Standard deviation σ = (pessimistic − optimistic) ÷ 6, and variance = σ². These come from the beta distribution, which allows skewed estimates (a long pessimistic tail).
How do you calculate the probability of completing a project on time?
Find the critical path using the expected times. The project mean is the sum of te along that path, and the project variance is the sum of the variances of its activities. Then z = (target − mean) ÷ √variance, and the probability is the standard normal cumulative probability of z.
What is the difference between PERT and CPM?
CPM uses a single, fixed duration per activity and focuses on float and the critical path. PERT models uncertainty with three estimates and gives probabilities. Many tools, including this one, combine them: PERT estimates scheduled with the CPM forward and backward pass.
What are the limitations of PERT?
PERT uses only the critical path to estimate variance, so it can be optimistic when other paths are nearly critical. It assumes activities are independent and the total is roughly normal. Estimates are only as good as the people making them. For important deadlines, check near-critical paths too, or use a Monte Carlo simulation.
What is a PERT chart?
A PERT chart is the network diagram of the project: activities and their dependencies, usually showing the expected time of each activity and highlighting the critical path. This tool draws it with the duration probability curve underneath.