Critical Path Method (CPM) Calculator

What is the critical path method?

The critical path method (CPM) takes the durations of the activities in a project and the dependencies between them and finds the earliest time the project can finish. The longest chain of activities through the network is the critical path. If any activity on that chain slips, the project slips by the same amount.

How the calculation works

• Forward pass: the early start of an activity is the largest early finish among its predecessors. Early finish = early start + duration.
• Project duration: the largest of all early finishes.
• Backward pass: the late finish of an activity is the smallest late start among its successors. Late start = late finish − duration.
• Total float = late start − early start. It is how far the activity can slip without delaying the project.
• Free float = earliest start among the successors − early finish. It is how far it can slip without delaying any successor.

Activities with zero total float are critical.

How to use it

Give each activity an ID, enter its duration, and in the predecessors column list the IDs of the activities that must finish first, separated by commas. The result updates with every change. The 14 activity construction project shown at first is a well known example from operations research textbooks: the answer is 44 weeks with the critical path A B C E F J L N.

Error messages

If a predecessor ID is not in the list, the tool tells you which row refers to which missing ID. If the activities form a loop where they wait for each other (A waits for B and B waits for A), it shows the chain in the loop. Such a network has no schedule.

Limits

Only finish to start links are supported: an activity starts when its predecessors have finished. There are no lags, no start to start links, no resource limits, no calendar and no holidays. Time is counted in a single unit such as working days or weeks. Durations are taken as certain, and the three point estimates of PERT are outside the scope of this tool.