S-curve cash flow calculator
An S-curve plots cumulative spend against time: slow at the start, fastest in the middle, slow at the end. Enter the contract value, the months and a shape to get planned spend per month and the cumulative percentage. The four shapes are planning approximations, not a standard curve.
On this page
What the four shapes are
The calculator spreads the contract value over whole months, up to 36. With N months, the cumulative share at month i is F(t) where t = i / N. Linear uses F = t, so every month is equal. Front-loaded uses F = 1 - (1 - t)^2, so more is spent early. Back-loaded uses F = t^2, so more is spent late. The S-curve uses the smoothstep function F = 3t^2 - 2t^3, which starts slowly, speeds up in the middle and slows towards the end.
These are simple planning approximations that we chose for convenience. They are not a standard or published construction curve, and a real job follows its own programme. Use them for a first cash-flow view, then replace them with a cost-loaded programme.
How the months add up
Each month's spend is the change in the cumulative amount, and the cumulative amount is rounded to the fils at each month. That way the months always add up to the contract value exactly, and the last month is closed out at 100%. A duration above 36 months is shown as 36.
A cumulative spend curve is also the baseline that actual cost is compared with, which is what the earned value calculator does at a review date. Research on early-phase cost forecasting uses cost S-curves in the same way, as a first estimate when detailed programme information is scarce.
From planned spend to cash
Planned spend is not the same as cash in or out. Money arrives through certificates, after the advance is recovered and retention is held back, and VAT follows the rules in the VAT calculator. Try the payment certificate calculator for a single period.
In SupaJack Construct the projects and tenders module records the payment terms, advance, retention and guarantees that drive each invoice, and interim payments handles the certificates. Read the interim payments guide and the tendering and costing guide for the commercial side, and see banking and budgets for budgets against actuals.
Worked example
A AED 1,200,000 contract over 6 months on the S-curve shape.
| Month | Planned spend (AED) | Cumulative (AED) | Cumulative % |
|---|---|---|---|
| 1 | 88,888.89 | 88,888.89 | 7.41% |
| 2 | 222,222.22 | 311,111.11 | 25.93% |
| 3 | 288,888.89 | 600,000.00 | 50.00% |
| 4 | 288,888.89 | 888,888.89 | 74.07% |
| 5 | 222,222.22 | 1,111,111.11 | 92.59% |
| 6 | 88,888.89 | 1,200,000.00 | 100.00% |
Worked example
A AED 1,200,000 contract over 6 months on the S-curve shape: the cumulative shares at months 1 to 6 are 7.41%, 25.93%, 50%, 74.07%, 92.59% and 100%. Month 1 is 1,200,000 x 0.074074 = AED 88,888.89, and month 2 is 311,111.11 - 88,888.89 = 222,222.22. The six months add up to exactly AED 1,200,000.00.
Questions people ask
What is an S-curve in construction?
A graph of cumulative cost or progress against time, usually slow at the start, fastest in the middle and slow near completion.
Is the S-curve here a standard curve?
No. The four shapes are planning approximations. Your own cost-loaded programme gives a better curve.
Why does the S-curve use 3t^2 - 2t^3?
It is the smoothstep function, a simple formula that starts slowly, speeds up and slows again. It is chosen for convenience, not as a rule.
How many months can I enter?
Up to 36 whole months. Longer durations are shown as 36.
Do the months add up to the contract value?
Yes. Each month is the change in a cumulative amount rounded to the fils, so the total is exact.
When would I choose front-loaded?
When mobilisation, procurement or early works are heavy and most of the cost falls in the first months.
When would I choose back-loaded?
When most of the cost comes late, for example finishes or commissioning on a long programme.
Is planned spend the same as invoicing?
No. Invoices follow certificates, with the advance recovered and retention held back.
Does it include VAT?
No. It spreads the figure you enter. Enter a value before VAT or after it, and keep to one.
Can I use it for the contract price or the cost?
Either. Enter the contract value to spread income, or the budgeted cost to spread spend.