Critical Path (CPM) Calculator
A six-activity project (A 3, B 4, C 2, D 5, E 3, F 2) takes 14 time units along the critical path A → B → D → F.
14
- Critical activities
- A → B → D → F
| Activity | Duration | ES | EF | LS | LF | Total float |
|---|---|---|---|---|---|---|
| A | 3 | 0 | 3 | 0 | 3 | 0 |
| B | 4 | 3 | 7 | 3 | 7 | 0 |
| C | 2 | 3 | 5 | 7 | 9 | 4 |
| D | 5 | 7 | 12 | 7 | 12 | 0 |
| E | 3 | 5 | 8 | 9 | 12 | 4 |
| F | 2 | 12 | 14 | 12 | 14 | 0 |
Step-by-step solution
- Forward pass: ES = max(EF of predecessors), EF = ES + duration
- Backward pass: LF = min(LS of successors), LS = LF − duration
- Total float = LS − ES; zero float marks the critical path
Critical Path (CPM) Formula
Total float = LS − ES = LF − EF
ES = max EF of predecessors; LF = min LS of successors
Worked Example
Six activities A–F with durations 3, 4, 2, 5, 3 and 2:
- Forward pass: ES = max(EF of predecessors), EF = ES + duration
- Backward pass: LF = min(LS of successors), LS = LF − duration
- Total float = LS − ES; zero float marks the critical path
| Activity | Duration | ES | EF | LS | LF | Total float |
|---|---|---|---|---|---|---|
| A | 3 | 0 | 3 | 0 | 3 | 0 |
| B | 4 | 3 | 7 | 3 | 7 | 0 |
| C | 2 | 3 | 5 | 7 | 9 | 4 |
| D | 5 | 7 | 12 | 7 | 12 | 0 |
| E | 3 | 5 | 8 | 9 | 12 | 4 |
| F | 2 | 12 | 14 | 12 | 14 | 0 |
GATE tip
Every network has at least one critical path; there may be several with zero float, and all must be monitored.
More Geomatics and Construction Management Calculators
-
Horizontal Curve Calculator
T = R tan(Δ/2), L = πRΔ/180
long chord 2R sin(Δ/2); E = R(sec Δ/2 − 1); M = R(1 − cos Δ/2)
Example: A 300 m curve deflecting 40°, with the PI at chainage 1000 m: Tangent length T = 109.191 m.
-
Photogrammetry Scale Calculator
S = f / (H − h)
relief displacement d = r h / H′ with H′ the height above the object base
Example: A 152 mm camera flying at 3000 m over ground at 500 m: Photo scale 1 : 16447.4.
Frequently asked questions
What is the difference between total and free float?
Total float delays the project end if exceeded; free float is the delay possible without delaying any successor’s early start.
How is CPM different from PERT?
CPM uses one deterministic duration per activity; PERT uses three time estimates and gives a probability of finishing on time.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Critical Path (CPM) Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/critical-path-calculator/
IEEE
Scientific Converters, "Critical Path (CPM) Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/critical-path-calculator/