PERT/CPM Calculator (Critical Path Method)

Find out how long a project will really take and which tasks cannot slip. Combine PERT three-point estimates with the Critical Path Method to compute expected duration, the critical path, slack and the early and late schedule for every activity.

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What are PERT and CPM?

PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method) are complementary project-scheduling techniques. Both model a project as a network of activities with dependencies, and both identify the critical path, the longest chain of dependent tasks, which determines the shortest possible project duration.

CPM uses a single, deterministic time estimate for each activity and is well suited when task durations are well known. PERT adds uncertainty by using three estimates per activity, optimistic, most likely and pessimistic, and combines them into an expected duration and a variance, which is useful when durations are uncertain.

Together they answer the central scheduling questions: how long the project will take, which activities are critical (have zero slack and cannot slip without delaying the project), and how much slack the non-critical activities have. This lets managers focus attention on the tasks that actually control the finish date.

In plain terms: A project is a web of tasks that depend on each other. PERT/CPM finds the critical path, the chain of tasks that sets the finish date, so you know exactly which tasks can't slip. PERT also handles uncertainty by using three time guesses per task (best, likely, worst) instead of one.

Key Concepts

Critical Path

The longest path of dependent activities through the network. Its length is the shortest time the project can finish, and its tasks have zero slack.

PERT Three-Point Estimate

Each activity gets optimistic (a), most likely (m) and pessimistic (b) times, combined into an expected duration to reflect uncertainty.

Slack (Float)

The amount a non-critical activity can be delayed without delaying the project. Critical activities have zero slack.

Key Formulas

PERT expected time t_e = (a + 4m + b) / 6

Activity variance = ((b − a) / 6)²

Slack = late start − early start (= late finish − early finish)

Critical path = path with zero slack (longest through the network)

Using the Schedule

The critical path is where management attention belongs: delaying any critical activity delays the whole project, while non-critical activities can absorb some delay up to their slack. Focusing acceleration efforts on critical tasks is the only way to shorten the overall schedule.

PERT's expected times and variances let you estimate the probability of finishing by a given date, not just a single-point deadline. This acknowledges that real projects are uncertain, and it helps set realistic commitments and buffers.

Assumptions & Validation

Defined Activities & Dependencies

Activities and their precedence relationships are correctly identified.

If violated: Revisit the network; a missing dependency invalidates the critical path.

Reasonable Estimates

Duration estimates (single or three-point) are realistic.

If violated: Improve estimates; PERT's three points help capture uncertainty.

Stable Network

The activity network does not change during analysis.

If violated: Re-run the analysis when scope or sequence changes.

⚠️ Check assumptions first

The critical path is only as valid as the dependency network behind it. A single missing or wrong precedence relationship can put the wrong tasks on the critical path and mislead the whole schedule. Get the activity dependencies right first. Remember too that PERT's expected duration is an estimate with variance, not a guaranteed date, and that the critical path can shift as activities progress.

When NOT to Use PERT/CPM Calculator

Simple Task Lists

For a short list of tasks with no complex dependencies, a Gantt chart alone may suffice.

Resource Leveling

PERT/CPM schedules by time and dependency; for balancing limited resources, resource-leveling tools are needed.

Ongoing Flow Work

For continuous, repetitive work rather than a one-off project, Kanban and flow metrics fit better.

Industry Applications

Project Scheduling

Determine the expected duration and critical path of a project from its activity network.

Deadline Risk

Use PERT variances to estimate the probability of meeting a target completion date.

Acceleration Planning

Identify which critical activities to shorten (crash) to compress the schedule efficiently.

Improvement Project Timing

Schedule the phases of a DMAIC or design project and find where delay would hurt most.

Frequently Asked Questions

What is the critical path?

The critical path is the longest chain of dependent activities through a project network. Its total length equals the shortest possible time in which the project can be completed. Activities on the critical path have zero slack, meaning any delay to them delays the entire project. Identifying the critical path tells managers exactly which tasks control the finish date and therefore deserve the most attention.

What is the difference between PERT and CPM?

CPM uses a single deterministic time estimate for each activity and suits projects where durations are well known. PERT uses three estimates per activity, optimistic, most likely and pessimistic, to compute an expected duration and a variance, making it better for projects with uncertain durations. Both identify the critical path; PERT adds the ability to reason about schedule uncertainty and probability of on-time completion.

How is the PERT expected time calculated?

The PERT expected time for an activity is a weighted average of three estimates: optimistic plus four times the most likely plus pessimistic, all divided by six. This weighting gives the most likely estimate the greatest influence while still accounting for the best and worst cases. The associated variance, based on the spread between optimistic and pessimistic, quantifies the uncertainty in that activity's duration.

What is slack or float?

Slack, also called float, is the amount of time a non-critical activity can be delayed without delaying the overall project. It is calculated as the difference between an activity's late and early start times. Critical activities have zero slack, so they cannot slip at all, while non-critical activities have positive slack that provides scheduling flexibility, up to the point where a delay would make them critical.

Can the critical path change during a project?

Yes. As activities are completed ahead of or behind their estimates, the balance of slack across the network shifts, and a path that was not critical can become critical. This is why the schedule should be re-analyzed as the project progresses. Monitoring the critical path over time ensures management attention stays on the activities that currently control the finish date.

How does PERT/CPM relate to a Gantt chart?

PERT/CPM provides the scheduling logic, the dependencies, critical path and slack, while a Gantt chart is a visual timeline that displays activities and their durations against a calendar. The two are complementary: PERT/CPM determines the critical path and float, and a Gantt chart presents the resulting schedule in an easy-to-read bar format. Many projects use the analysis to build and manage the Gantt view.

Find the Critical Path and Real Duration

Compute expected duration, critical path and slack from your network. Free during Beta.