What is an S Curve in Capital Projects?

Jacob Gibbs
Jacob Gibbs
March 20, 2024

Firstly, what the hell is an S Curve?

'S Curve' is a well-known term used in the construction industry to reference a graphical representation, characterized by a unique S-shaped curve, of project progress, costs, or other key metrics over time, characterized by a unique S-shaped curve. Most capital projects will feature an S curve on the project's dashboard!  

A sample of a typical S curve graph.
A sample of a typical S curve graph.

S curves are vital for project management, planning, and monitoring, visually depicting the expected versus actual progress, expenditure, or resource utilization across the project lifecycle. Let's delve into the technical aspects of an S curve and incorporate the mathematical underpinnings of the its calculation as we gain a comprehensive understanding of its role in modeling capital project expenditure, and driving decision making.

The Essence of S Curves in Project Management

An S curve graphically represents the cumulative progress of variables like costs, labor hours, or materials against time, forming an "S" shape. This shape mirrors the typical project lifecycle: a slow start, rapid progress during the middle phase, and a slowdown as completion approaches.

  • Initiation Phase: This phase signals the project's commencement, characterized by the initial setup activities and the mobilization of resources. The S curve at this point exhibits a flat trajectory, indicating a slow start with minimal progress and financial expenditure.
  • Construction Start-up: As the project transitions from initiation to the construction start-up phase, you can see a sharp escalation in project activities. This phase is crucial for allocating significant resources, encompassing the bulk of construction efforts. The steep ascent of the S curve during this period signifies a vigorous allocation of labor, materials, and capital, driving the project forward with momentum.
  • Construction Maturity: Advancing further, the project reaches a phase of construction maturity, where activities achieve a consistent rhythm. The S curve begins to level, reflecting a plateau in the expenditure and resource utilization rate. This stage represents a controlled progression towards the project's completion, with the curve's gradient evening out as it nears its targeted objectives and milestones.
  • Decline towards Completion: In the final stretch, the project enters a phase of decline toward completion, characterized by a reduction in active construction tasks. The S curve mirrors this transition by flattening at its peak, indicating the completion of most tasks and decreased expenses and labor involvement. This phase encapsulates the project's journey from its inception, through a peak of intense activity, to a gradual conclusion.

Here's a real example of an S Curve on a capital works program. You can see historical actuals in green and then forward cash flow in blues (committed), dark blue (uncommitted), and yellow (risk).

Here's a real example of an S Curve on a capital works program. You can see historical actuals in green and then forward cash flow in blues (committed), dark blue (uncommitted), and yellow (risk).

S curves provides client side project managers with the insights needed to ensure successful project delivery, thanks to its visibility. It's easy to see the workload peaks, where risk exists in the project, and how far behind.

Technical Foundations for modeling an S Curve and the S Curve Formula

The mathematical formula representing an S curve is best derived from logistic or cumulative distribution functions, providing a quantified view of progress over time. A generalized form of the S curve equation can be expressed as:

A mathematical equation with numbers and symbolsDescription automatically generated


  • y is the cumulative progress or cost at time x,
  • L is the curve's maximum value, representing the total project cost or completion percentage, is the curve's maximum value, representing the total project cost or completion percentage,
  • e is the base of the natural logarithm,
  • k is the curve's steepness, indicating how aggressive the construction will be,
  • x is time, and
  • x0​ is the inflection point's time, where the curve shifts from concave to convex, showing the commencement of construction.

Baselining S Curves: A Technical Perspective

It is also good practice to show an S curve plotted against the planned progress (baseline) against the actual progress. Constructing an S curve baseline should start with a detailed project plan, from which a baseline projection is created from the first principles or the formula above. As the project progresses, actual data is integrated, with the S curve serving to analyze performance and guide adjustments.

Mastt provides cash flow baselining functions and detailed under/over graphical representations of the planned vs. actual progress.

Advanced Techniques and Considerations

  • Earned Value Management (EVM): Combining S curve analysis with EVM offers a comprehensive view of project performance.
  • Scenario Analysis: Utilizing S curves for different project scenarios aids in risk management, providing insights into potential outcomes.
  • Continuous Updating: The utility of an S curve relies on the regular integration of actual project data, with real-time updates crucial for maintaining accuracy.

Challenges in S Curve Utilization

The effectiveness of S curve analysis depends on the accuracy and the timeliness of updates. For large, multifaceted projects, keeping an accurate S curve requires sophisticated software like Mastt, and skilled analysts such as dedicated project controllers.

S curves are widely used in modern capital project management. Reporting an S curve on a dashboard is crucial in project management, particularly in visualizing project health and progress. It offers a quick, visual snapshot of where the project stands in relation to its planned schedule and budget. This lets stakeholders immediately grasp the project's status without delving into complex datasets. By comparing the actual progress and expenditure against planned values, an S curve highlights variances and trends, making better decisions.

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