The original version of this paper was published here in May 2009: See S-curve/intro.htm This 4th Edition was submitted for publication in January 2019. It is copyright © Midori Media. Published here September 2019.

## Worked Example

To better understand how S-curves are generated, consider a simple Project consisting of five Tasks. The first Task is a Summary Task, and thus must be ignored. The remaining four Tasks are Detail Tasks. Please note that although this worked example will only consider Man Hours, the calculations shown below are identical if Cost is used in lieu of Man Hours.

A Baseline Schedule prepared using MS Project for the example project is shown below.

### Baseline Man Hours versus Time S‑curve

To generate a Baseline Man Hours versus Time S-curve, two sets of calculations are required.

The first set of calculations are performed for each Task in the Baseline Schedule.

(1)  Calculate the Duration in Days for each Task
Baseline Duration = Baseline Finish Date - Baseline Start Date + 1

(2)  Calculate Man Hours per Day for each Task
Baseline Man Hours per Day = Baseline Man Hours / Baseline Duration

These calculations are shown below.

 Task Name Baseline Start Baseline Finish Baseline Man Hours Baseline Duration (1) Baseline MH per Day (2) Task No. 1 01‑Feb‑2016 02‑Feb‑2016 12.0 2 6 Task No. 2 02‑Feb‑2016 04‑Feb‑2016 24.0 3 8 Task No. 3 03‑Feb‑2016 04‑Feb‑2016 30.0 2 15 Task No. 4 04‑Feb‑2016 05‑Feb‑2016 24.0 2 12 Totals 90.0
##### Table 4: Baseline S‑curve Calculation 1 of 2

The second set of calculations are performed for each Day in the Baseline Schedule.

(3)  Calculate the total Man Hours per Day for all Tasks

(4)  Calculate the Year To Date Total for Man Hours per Day for all Tasks

These calculations are shown below.

 Task / Date 01‑Feb‑2016 02‑Feb‑2016 03‑Feb‑2016 04‑Feb‑2016 05‑Feb‑2016 Task No. 1 6.0 6.0 -- -- -- Task No. 2 -- 8.0 8.0 8.0 -- Task No. 3 -- -- 15.0 15.0 -- Task No. 4 -- -- -- 12.0 12.0 Totals per Day (3) 6.0 14.0 23.0 35.0 12.0 YTD Totals (4) 6.0 20.0 43.0 78.0 90.0
##### Table 5: Baseline S‑curve Calculation 2 of 2

The Baseline S-curve is constructed by assigning the Baseline dates to the X axis, and the Year To Date (YTD) values to the Y axis. The resulting Baseline Man Hours versus Time S‑curve is shown below.

##### Figure 10: Baseline Man Hours versus Time S‑curve

Please note that the Totals per Day values may be used to generate a Baseline Man Hours Histogram by assigning the dates to the X axis, and the Totals per Day values to the Y axis, as shown below.

### Target Man Hours versus Time S‑curve

To generate the Actual and Target S-curves, a Production Schedule is required. For the purpose of this example, the Production Schedule will contain the same five Tasks (one Summary Task, four Detail Tasks) as the Baseline Schedule. Once again, the Summary Task must be ignored to ensure the calculations are accurate.

A Production Schedule for the example Project is shown below.

##### Figure 12: Sample Production Schedule

Note this schedule contains the Baseline data from the Production Schedule. This allows Baseline S‑curves to be generated from the Production Schedule.

To generate a Target Man Hours versus Time S‑curve, two sets of calculations are performed.

The first set of calculations are performed for each Task in the Production Schedule.

(1)  Calculate the Duration in Days for each Task
Duration = Finish Date - Start Date + 1

(2)  Calculate Man Hours per Day for each Task
Man Hours per Day = Man Hours / Duration

These calculations are shown below.

 Task Name Start Finish Man Hours % Complete Duration (1) MH per Day (2) Task No. 1 02‑Feb‑2016 03‑Feb‑2016 14.0 100% 2 7.0 Task No. 2 02‑Feb‑2016 05‑Feb‑2016 30.0 20% 4 7.5 Task No. 3 04‑Feb‑2016 06‑Feb‑2016 36.0 50% 3 12.0 Task No. 4 05‑Feb‑2016 07‑Feb‑2016 15.0 0% 3 5.0 Totals 95.0

### Target Man Hours versus Time S-curve (Continued)

The second set of calculations are performed for each Day in the Production Schedule.

(3)  Calculate the total Man Hours per Day for all Tasks

(4)  Calculate the Year To Date Total for Man Hours per Day for all Tasks

These calculations are shown below.

 Task / Date 01‑Feb-2016 02‑Feb-2016 03‑Feb-2016 04‑Feb-2016 05‑Feb-2016 06‑Feb-2016 Task No. 1 7.0 7.0 -- -- -- -- Task No. 2 7.5 7.5 7.5 7.5 -- -- Task No. 3 -- -- 12.0 12.0 12.0 -- Task No. 4 -- -- -- 5.0 5.0 5.0 Totals per Day (3) 14.5 14.5 19.5 24.5 17.0 5.0 Year to Date Total (4) 14.5 29.0 48.5 73.0 90.0 95.0
##### Table 7: Target S‑curve Calculation 2 of 2

The Target S-curve is constructed by assigning the dates to the X axis, and the Year To Date (YTD) values to the Y axis. The resulting Target Man Hours versus Time S‑curve is shown below.

##### Figure 13: Target Man Hours versus Time S‑curve (showing Baseline S‑curve for Comparison)

Please note that the Totals per Day values may be used to generate a Target Man Hours Histogram by assigning the dates to the X axis, and the Totals per Day values to the Y axis, as shown below.

### Actual Man Hours versus Time S-curve

To generate an Actual Man Hours versus Time S‑curve, two sets of calculations are performed. Before these calculations may be performed, the Cut Off Date needs to be defined. This is the date the Project's Tasks were last physically inspected to determine their % complete status. For this example a Cut Off Date of the 4th of February, 2016 will be used.

The first set of calculations are performed for each Task in the Production Schedule.

(1)  Determine the Task Status: Finished, In Progress, Not Started.
•  Finished: Tasks that have a Finish Date prior to the Cut Off Date.
•  In Progress: Tasks that have started and have a Finish Date on or after the Cut Off Date.
•  Not Started: Tasks that have a Start Date after the Cut Off Date.

(2)  Calculate the Duration to Date based on the Task Status.
•  Finished: Duration To Date = Finish Date - Start Date + 1
•  In Progress: Duration To Date = Cut Off Date - Start Date + 1
•  Not Started: Duration To Date = 0

(3)  Calculate Man Hours to Date for Finished and Ongoing Tasks.
Man Hours to Date = (Man Hours x % Complete) / Duration to Date

As discussed above in the Target S‑curve calculations, the total Task Man Hours to complete the Task are required.

In this worked example, the Production Schedule contains total Task Man Hours.

The required calculations are shown below.

 Task Name Start Finish Man Hours % Complete Status (1) Duration to Date (2) MH x % completeDuration to Date (3) Task No. 1 02‑Feb-2016 03‑Feb-2016 14.0 100% Finished 2 7.0 Task No. 2 02‑Feb-2016 05‑Feb-2016 30.0 20% In Progress 3 2.0 Task No. 3 04‑Feb-2016 06‑Feb-2016 36.0 50% In Progress 1 18.0 Task No. 4 05‑Feb-2016 07‑Feb-2016 15.0 0% Not Started 0 0.0 Totals 95.0
##### Table 8: Actual S-curve Calculation 1 of 2

The second set of calculations is performed for each Day in the Production Schedule up to the Cut Off Date.

(4)  Calculate the total Man Hours to Date per Day for all Tasks

(5)  Calculate the Year To Date Total for Man Hours to Date per Day for all Tasks

These calculations are shown below.

 Task / Date 02‑Feb-2016 03‑Feb-2016 04‑Feb‑2016 05‑Feb-2016 06‑Feb-2016 07‑Feb-2016 Task No. 1 7.0 7.0 -- -- -- -- Task No. 2 2.0 2.0 2.0 -- -- -- Task No. 3 -- -- 18.0 -- -- -- Task No. 4 -- -- -- -- -- -- Totals per Day (4) 9.0 9.0 20.0 -- -- -- YTD Totals (5) 9.0 18.0 38.0 -- -- -- Cut Off Date:   04-Feb-2016
##### Table 9: Actual S‑curve Calculation 2 of 2

The resulting Actual Man Hours versus Time S‑curve is shown in Figure 15.

##### Figure 15: Actual Man Hours versus Time S‑curve (showing Baseline S‑curve for Comparison)

Please note that the Totals per Day values may be used to generate an Actual Man Hours Histogram by assigning the dates to the X axis, and the Totals per Day values to the Y axis, as shown in Figure 16.

##### Figure 16: Actual Man Hours versus Time Histogram (showing Baseline Histogram for Comparison)

The Baseline, Actual, and Target S-curves may be combined, as shown in Figure 17.