PMP Example of PERT vs CPM Chart

PERT and the Critical Path Method (CPM) are two of the most widely used scheduling techniques in project management, and both appear on the PMP exam. PERT estimates how long each activity will take from three time estimates, while CPM finds the longest chain of dependent activities, the one that sets your project’s end date. In this guide, you’ll find clear explanations, worked examples of both methods and a side-by-side comparison to help you choose. You can also try our free Critical Path and PERT Network Builder just below the table of contents to map your own activities, find your critical path and check your odds of finishing on time.

Try our Free Critical Path and PERT Network Builder Below

This tool works in your browser. It calculates the early and late dates, the float and the critical path of your network as you type, and shows the results as a network diagram and a Gantt chart. Step-by-step instructions.

Instructions to use the calculator above:

1. Choose your method and time unit. Click “CPM (single duration)” to give each activity one duration, or “PERT (three estimates)” to enter Optimistic, Most likely and Pessimistic values. Use the “Time unit” menu to pick Hours, Days or Weeks, and every result and label updates to match.
2. List your activities and their dependencies. In the “Activities” tab, name each activity, open its “Predecessors” list to tick the activities that must finish first, and enter its duration or three estimates. In PERT mode, the tool shows the working for each duration, (O + 4M + P) / 6, and “Add activity” adds a new row. A red message flags any missing predecessor or circular dependency so you can fix it right away.
3. Read your critical path. The “Forward and backward pass” table shows ES, EF, LS, LF and total float for every activity, with critical activities marked in orange. The results panel shows your project duration and every critical path, and in PERT mode your chance of finishing by the “Deadline” you enter, with the Z-score worked out for PMP exam practice.
4. See your network and Gantt chart. Open the “Network diagram” tab to see each activity as a node in the standard PMP layout, with the critical path and its arrows in orange and activities with float in navy. The “Gantt” tab draws a bar for each activity from its early start, with a light extension after each non-critical bar showing how far it can slip.
5. Test delays and practice. In “What if an activity is late?”, pick an activity and enter a delay to see the new project duration and whether the critical path changes. Open the “Practice” tab to solve a random network, click “Check answer” to see the worked solution, then click “New question” to try another. Click “Copy results” to paste your schedule into an email, report or project plan.

Tip: your activities are saved in this browser, so you can close the page and pick up where you left off. Come back to the tool whenever a task slips or a new dependency appears instead of treating your schedule as a one-time exercise, since the critical path can change as the project moves. The tool opens with the party planning example from this article, so you can check its numbers against the worked examples further down this page. Loading a scenario replaces your activities, and “Reset to example” brings back the original example at any time.

PERT Formula Project Management

The PERT (Program Evaluation and Review Technique) formula is a project management tool used to estimate the time required to complete a project. It supports the creation of PERT charts—graphical timelines that show task sequences and dependencies. PERT charts are widely used in project planning because they clarify relationships between activities and help identify the sequence of tasks that affect project duration.

To apply the PERT formula, you gather three time estimates for each activity (optimistic, most likely, and pessimistic). These estimates are combined to calculate an expected duration for each activity and, ultimately, for the overall project schedule. Using these expected durations, you can build a PERT network, identify the critical path, and calculate the overall project completion time with greater confidence.

Benefits of PERT

Using the PERT formula helps project managers produce a clearer, more reliable estimate of a project’s timeline. Estimating the time required for each activity can be difficult, but PERT handles that uncertainty by combining three time estimates (optimistic, most likely and pessimistic) into a single expected duration. It also gives you a standard deviation, so you can see how much the schedule could vary, set realistic deadlines and decide how much schedule reserve to hold. The same three-point approach can be applied to cost estimates when you need a budget range rather than a single figure.

Example of PERT Formula in Project Management

So how does the PERT formula work? Let’s take a look at an example. 

• Say you are planning a party and you need to buy some supplies.
• You estimate that it will take you 3 hours to buy the supplies, but you want to account for any unforeseen delays.
• Using the PERT formula, you would first come up with an optimistic estimate (2 hours), a pessimistic estimate (4 hours), and a most likely estimate (3 hours). 

The PERT formula weights the most likely estimate four times: E = (O + 4M + P) / 6, where O is the optimistic estimate, M the most likely and P the pessimistic. For the party supplies, that gives E = (2 + 4 × 3 + 4) / 6 = 18 / 6 = 3 hours.

So your PERT estimate for buying the party supplies is 3 hours. The standard deviation, (P − O) / 6 = (4 − 2) / 6 = 0.33 hours, tells you how uncertain that estimate is: the narrower your range, the more confident you can be.

The free network builder above opens with this example extended into a small party plan: plan guest list (2 hours), book venue (4 hours), buy party supplies (3 hours), send invitations (1 hour) and decorate (3 hours). Its critical path is plan guest list, book venue, decorate, for a total of 9 hours, and with a project standard deviation of 1 hour you have about an 84% chance of being ready within 10 hours.

Numbers check: guest list O 1, M 2, P 3; venue O 2, M 4, P 6; supplies O 2, M 3, P 4; invitations O 0.5, M 1, P 1.5; decorate O 1, M 3, P 5. Variances on the critical path: 0.11 + 0.44 + 0.44 = 1, so σ = 1 hour and Z = (10 − 9) / 1 = 1, which is 84%.

CPM Formula Explained in Project Management

The Critical Path method is a popular project management technique used to schedule and organize complex projects. The method is based on the concept of the longest path through a network of activities. This path is referred to as the Critical Path, and it represents the minimum amount of time needed to complete the project. A critical path has the following attributes:

• It has no slack or float time.
• It consists of dependencies between tasks.
• It links together all the tasks in the project.

Benefits of CPM

The Critical Path Method (CPM) is a project-management technique for identifying the sequence of activities that determines a project’s minimum completion time. CPM highlights which tasks have zero slack and therefore cannot be delayed without extending the overall schedule. It also helps pinpoint activities most likely to cause delays, exposing potential bottlenecks and risks. With a clear understanding of the critical path, project managers can prioritize resources, monitor high-impact tasks more closely, and take targeted actions to keep the project on schedule.

Example of CPM

To create a critical path, first identify the dependencies between tasks and then sequence tasks according to those dependencies. Next, determine which activities have float (slack) and which are critical. Critical tasks have zero float and directly affect the project’s minimum completion time.

Let’s find the critical path for a small project: building a garden shed. The table lists each activity, its duration in days and its predecessors, the activities that must finish before it can start. All dependencies are finish-to-start.

Activity	Duration (days)	Predecessors
A: Prepare site	3	None
B: Pour foundation	4	A
C: Build frame	6	B, F
D: Install roof	3	C, G
E: Order materials	2	None
F: Deliver materials	4	E
G: Build doors and windows	3	F

Step 1: list every path. There are three paths from start to finish:

• A → B → C → D: 3 + 4 + 6 + 3 = 16 days
• E → F → C → D: 2 + 4 + 6 + 3 = 15 days
• E → F → G → D: 2 + 4 + 3 + 3 = 12 days

The longest path, A → B → C → D, is the critical path, so the project takes 16 days.

Step 2: run the forward pass. Start at day 0 and work from left to right. Each activity’s early start (ES) is the latest early finish (EF) of all its predecessors, and EF = ES + duration. For example, Build frame (C) must wait for both Pour foundation (B, EF 7) and Deliver materials (F, EF 6), so C starts at day 7 and finishes at day 13. Install roof (D) waits for C (EF 13) and G (EF 9), so it runs from day 13 to day 16.

Step 3: run the backward pass. Start at the project end, day 16, and work from right to left. Each activity’s late finish (LF) is the earliest late start (LS) of all its successors, and LS = LF − duration. For example, Deliver materials (F) feeds both C (LS 7) and G (LS 10), so F must finish by day 7 and start by day 3 at the latest.

Step 4: calculate the float. Total float = LS − ES, which always equals LF − EF. A, B, C and D have zero float, which confirms the critical path. Order materials (E) and Deliver materials (F) have 1 day of float, and Build doors and windows (G) has 4 days, so G could start up to 4 days late without moving the 16-day finish. A delay longer than an activity’s float does move the end date: if Deliver materials slipped by 2 days, the path E → F → C → D would take 17 days and become the new critical path.

In the diagram, each activity is a node in the standard PMP layout: early start, duration and early finish on top, late start, total float and late finish at the bottom. The critical path and its arrows are orange, and activities with float are navy. You can load this exact network in the free tool above by clicking “PMP exam network”, then try the “What if an activity is late?” panel yourself.

CPM formulas to remember for the PMP exam:

• Forward pass: ES = latest EF of all predecessors (0 for the first activities), EF = ES + duration
• Backward pass: LF = earliest LS of all successors (the project end for the last activities), LS = LF − duration
• Total float = LS − ES = LF − EF
• Critical path = the activities with zero total float
• PERT: E = (O + 4M + P) / 6, and the standard deviation σ = (P − O) / 6

PERT vs CPM

Both of these methods can be useful in different situations, but there are also some key differences between PERT and CPM charts:

• PERT (Program Evaluation and Review Technique) is a probabilistic method that uses optimistic, most likely, and pessimistic estimates to calculate expected task durations and quantify schedule uncertainty. It is particularly useful when historical data or expert estimates are available for similar tasks and when projects involve significant uncertainty or complex dependencies.
• The Critical Path Method (CPM) is a deterministic scheduling technique that identifies the longest sequence of dependent activities (the critical path) to determine the project’s minimum completion time. CPM is well-suited to projects where task durations are more certain or when a clear, fixed schedule is required.
• In practice, PERT is often applied to larger, high-uncertainty projects with multiple interdependent tasks, because it captures variability and schedule risk. CPM is commonly used for smaller or more routine projects with straightforward dependencies, where a single, deterministic timeline is sufficient.

Video About the Difference Between PERT and CPM

Watch this concise explainer to quickly understand how PERT and CPM differ, when to use each method, and how they complement one another in project scheduling. The video breaks down key concepts with clear examples so you can apply them to your next project planning session.

Conclusion

PERT and CPM are complementary scheduling tools: PERT adds probabilistic estimates to account for uncertainty, while CPM identifies the deterministic critical path and highlights tasks with zero slack. Use PERT when project durations are uncertain or expert judgment and risk analysis are needed; choose CPM for clearer, routine projects where fixed durations and resource prioritization matter. In practice, combining both approaches often yields the best results—use PERT to quantify schedule risk and CPM to manage day-to-day execution and resource allocation.

By understanding each method’s strengths, project managers can create realistic timelines, anticipate delays, and focus attention on tasks that truly influence delivery. Applying these techniques thoughtfully improves planning accuracy, reduces surprises, and increases the likelihood of on-time project completion.

Frequently Asked Questions

What is the PERT formula?

The Program Evaluation and Review Technique (PERT) is a probabilistic network-analysis method used to estimate activity durations and overall project timelines. For each task, PERT uses three time estimates—optimistic, most likely, and pessimistic—to calculate an expected duration. Although PERT does not guarantee perfect accuracy, its three-point approach improves the reliability of schedule forecasts and helps project managers account for uncertainty.

What is the Critical Path Method?

The Critical Path Method (CPM) is a deterministic scheduling technique that identifies the longest sequence of dependent activities, which determines the minimum project duration. CPM models task dependencies and sequencing to reveal which activities are critical (have zero float) and therefore cannot be delayed without extending the project finish date.

What are the main differences between CPM and PERT?

• Focus: CPM is deterministic and emphasizes the critical sequence that sets the project’s minimum completion time. PERT is probabilistic and emphasizes estimating durations under uncertainty.
• Estimates: CPM typically uses single-point duration estimates. PERT uses three-point estimates (optimistic, most likely, pessimistic) to derive an expected duration and quantify schedule uncertainty.
• Typical use cases: CPM is commonly applied in projects with well-understood task durations (e.g., construction or routine engineering). PERT is better suited to research-driven or high-uncertainty projects where task durations are uncertain.
• Outcome: CPM highlights critical tasks and float for resource prioritization; PERT provides a probabilistic view of likely completion times and schedule risk.

How should I choose between CPM and PERT?

Use CPM when task durations are reliable, and you need a clear, deterministic schedule for execution and resource planning. Use PERT when activity durations are uncertain, and you want to quantify schedule risk and probable completion dates. In many projects, combining both approaches—using PERT to estimate durations and CPM to identify the critical path—yields the best results.

Suggested articles:

• PERT Formula Examples & PERT Calculator
• Critical Path Method Scheduling: What? Why? and How?
• Free Project Estimation Template with 6 Options