CPM Calculator

What is CPM?

Critical Path Method (CPM) mathematical analysis establishes the Early Start (ES), Early Finish (EF), Late Start (LS), and Late Finish (LF) parameters for network tasks.

Formula

Forward Pass: EF = ES + Duration - 1 (or EF = ES + Duration)
Backward Pass: LS = LF - Duration + 1 (or LS = LF - Duration)
Float: TF = LS - ES = LF - EF

Variables Explanation

- ES: Early Start date.
- EF: Early Finish date.
- LS: Late Start date.
- LF: Late Finish date.
- D: Activity duration.

How to Calculate

1. Perform Forward Pass starting from Day 1 to derive ES and EF.
2. Set project completion as LF for the final activity.
3. Perform Backward Pass working back to Start to derive LS and LF.
4. Compute Total Float (LS - ES).

Worked Example

Activity B: Duration = 6 Days. Predecessor EF = Day 10.
Forward Pass: ES = Day 11. EF = 11 + 6 - 1 = Day 16.
Backward Pass (LF = Day 20): LS = 20 - 6 + 1 = Day 15.
Total Float = 15 - 11 = 4 Days.

Practical Construction & Project Controls Use

Used by planning engineers to verify Primavera P6 scheduling engine outputs, audit logic integrity, and perform hand-calculated delay checks.

Understanding the Result

Output provides exact 4-date scheduling limits. If LS = ES and LF = EF, the task lies on the critical path.

Limitations & Assumptions

Calculates single-activity node dates. Full project networks require iterative pass calculation across all network nodes.