CPM Network Diagram Calculator – Free Project Management Tool
CPM, Crashing & PERT Masterclass
Network Analysis, All 3 Float Types, Time-Cost Crashing, PERT Probability & Gantt Study Suite for CMA Professionals
Practice Library
Bulk Import (Excel)
Upload large projects instantly.
⚙️ Add Custom Activity
📥 Export Reports
Download Matrix for offline study.
Quick Analysis Insights
Interactive Network Diagram
Project Gantt Chart & Slack Map
Visual representation of the schedule. Striped bars represent Slack (Float) time.
Mathematical Float Ledger
Total, Free, and Independent Float — see the Formulas & Guide tab for what each one means.
| ID | Name | Dur. | Deps | ES | EF | LS | LF | Total Float | Free Float | Indep. Float | Action |
|---|
Crashing Data (Normal vs Crash)
⚙️ Add PERT Activity
Try a Sample
Probability of On-Time Completion
PERT Activity Ledger
| ID | Name | a | m | b | te | Variance | ES | EF | LS | LF | Float | Action |
|---|
How to Solve CPM Problems for Exams
The Critical Path Method (CPM) identifies the longest sequence of dependent activities to determine the shortest possible project completion time.
Earliest Finish (EF)
Latest Start (LS)
Total Float
Step-by-Step Solving Algorithm
Start from left to right. Activities with no predecessors start at Time 0.
Move left to right. Where activities converge, ES is the Maximum EF of all immediate predecessors.
Move right to left. Where activities diverge, LF is the Minimum LS of all immediate successors.
When two or more chains tie for the longest duration (zero float on both), the project has parallel critical paths. Shortening only one will not reduce the project duration.
The Three Types of Float
Float (or slack) measures spare time. Total Float is the most commonly tested, but Free and Independent Float matter when resources are shared across activities.
Total Float (TF)
Free Float (FF)
Independent Float (IF)
How long an activity can slip without delaying the entire project's finish date.
How long an activity can slip without delaying the earliest start of the next activity — useful for rescheduling without a ripple effect downstream.
How long an activity can slip without affecting any other activity's float at all — even if every predecessor finishes late and every successor starts early. The most conservative measure.
Crashing & Time-Cost Trade-off
Crashing means spending more money to finish an activity faster — used when a project must be compressed below its normal duration (e.g., to meet a contractual deadline or avoid penalty costs).
Cost Slope
Shortening a non-critical task doesn't shorten the project — it only eats into its own float.
One day at a time, until that activity hits its crash limit or a different activity becomes the new bottleneck.
You may need to crash one activity on each critical path simultaneously (or a shared activity common to both) to shorten the project by even a single day.
The cost-optimal duration is where Total Cost = Direct Cost + Indirect Cost is lowest. Crashing further raises direct costs faster than it saves in overheads.
PERT: Handling Uncertainty
CPM assumes each activity has one known duration. PERT (Program Evaluation and Review Technique) instead uses three time estimates to reflect real-world uncertainty, then finds the probability of meeting a target date.
Expected Time
Activity Variance
Project Std. Deviation
Find the critical path exactly as in standard CPM, but using each activity's te instead of a single fixed duration.
Add up σ² for only the critical activities, then take the square root to get the project's standard deviation.
Z = (Target Date − Expected Duration) ÷ σ. Look up (or let the tool calculate) the area under the normal curve up to that Z to get the probability of finishing on time.
