About the Critical Path Calculator
This critical path calculator applies the critical path method (CPM) to a list of project activities. Enter each task’s ID, its duration and the tasks that must finish before it can start. The calculator runs a forward pass to find every task’s earliest start and finish, a backward pass to find the latest start and finish that will not delay the project, and from those works out total float, free float and the critical path.
The critical path is the longest chain of dependent tasks — the sequence that sets the shortest possible project duration. Any delay to a critical task delays the whole project, while tasks with float can slip by that amount without moving the finish date. Project managers, construction schedulers, event planners and students studying operations management use CPM to decide where to focus resources and which tasks to crash.
Durations can be in any unit (hours, days or weeks) as long as you use the same unit throughout. Dependencies are finish-to-start with no lag, the standard CPM assumption. If your durations are uncertain, estimate them first with a PERT three-point estimate.
With the default inputs, the project duration (selected unit) is 15. Change any value above to recalculate instantly.
How to use the critical path calculator
- 1Give each task a short ID such as A, B, C or 1, 2, 3.
- 2Enter one task per line: ID, duration, then the IDs of the tasks it depends on.
- 3Use the same time unit for every duration and select it from the list.
- 4Read the project duration and the critical path at the top.
- 5Use the float column to see which tasks can slip and which cannot.
Formula and method
The forward pass processes tasks in dependency order. A task with no predecessors starts at time 0; otherwise its earliest start (ES) is the latest earliest finish (EF) among its predecessors, and EF = ES + duration. The largest EF is the minimum project duration.
The backward pass starts from that project finish. A task with no successors has a latest finish (LF) equal to the project duration; otherwise LF is the smallest latest start (LS) among its successors, and LS = LF − duration. Total float (LS − ES) is how far a task can slip without delaying the project; free float is how far it can slip without delaying any successor. Tasks with zero total float are critical, and the chain of critical tasks linked end-to-start is the critical path. All links are finish-to-start with zero lag.
- d
- Task duration
- ES / EF
- Earliest start / earliest finish
- LS / LF
- Latest start / latest finish
- TF
- Total float (slack) = LS − ES
Worked examples
Six-task project
A runs 0–3. B runs 3–8 and D 8–12, while C runs 3–5 and E 5–11. F needs both D and E, so it starts at 12 and finishes at 15. The A–B–D–F chain has zero float; C and E each have 1 day of float.
Two parallel critical paths
B and C both take 4 days after A finishes at day 2, so both end at day 6 and D finishes at day 7. Every task has zero float, giving two critical paths: A–B–D and A–C–D. Delaying either B or C would delay the project.
Website launch in weeks
Requirements (R) take 2 weeks, design (D) 3 and build (B) 5, reaching week 10. Content (C) only needs until week 6, so it has 4 weeks of float. Testing (T) runs weeks 10–12 and launch (L) ends at week 13.
Frequently asked questions
What is the critical path in project management?+
It is the longest sequence of dependent tasks from project start to finish. Its length is the shortest time in which the project can be completed, and every task on it has zero float, so any delay to one of them delays the whole project.
What is the difference between total float and free float?+
Total float is how long a task can be delayed without delaying the project finish date. Free float is how long it can be delayed without delaying the earliest start of any task that follows it. Free float is always less than or equal to total float.
Can a project have more than one critical path?+
Yes. When two or more chains of tasks have the same, longest duration, they are all critical. Projects with several critical paths are riskier because a delay on any of them pushes out the finish date.
How do you shorten the critical path?+
Either crash critical tasks by adding resources so they finish sooner, or fast-track by overlapping tasks that were planned in sequence. Shortening a non-critical task does not help, and once a critical path is shortened another path may become critical.
What is the difference between CPM and PERT?+
CPM uses a single fixed duration for each task, while PERT uses optimistic, most likely and pessimistic estimates to produce an expected duration and a measure of uncertainty. You can calculate PERT estimates first and then enter them here as durations.