Carry Forward is the amount unspent on an award that has originally been budgeted for prorated spending over the lifespan of a sponsored award; it is often recalculated as a running balance that is spread over the remaining life of the award. 

The process of calculating Carryforward:

The Anticipated Total Amount is divided by Project - # Months to determine the Anticipated $ per Month.  For the first month, the Anticipated $ per Month is carried to Adj Anticipated.  Expenses are subtracted from Adj Anticipated.  This value is Carryover.  Carryover is divided by the number of months remaining on the grant.  This value is Allocated to Future Months.  For the first month, Allocated to Future Months is carried over to Running Allocations. Running Allocations for the first month is carried to the second month as Reallocated to Anticipated.  This value is added to the Anticipated $ per Month to calculate the Adj Anticipated.  Expenses are subtracted from Adj Anticipated to calculate Carryover.  Carryover is divided by the number of months remaining.  This value is Allocated to Future Months.  Allocated to Future Months is added to the Running Allocation.  The new Running Allocation value is carried to the third month as Reallocated to Anticipated.

The "rolling balance" of what dollars expensed was anticipated to have been spent on a pro-rated calendarization over the lifetime of a grant, and the remaining dollars to be spent on that grant per its budgeted amount

The Carryover dollars divided by the number of Months Remaining in  the Grant's lifecycle.  For example, Carryover = ($15,054); Number of Months Remaining = 47; Allocated to Future Months = ($15,054)/47 = ($320)

A pro-rated amount ( by month) of the expected average spend on a grant based on its lifecycle starting at month 1

The resultant of actual grant expenses subtracted from the Adjusted anticipated (planned expenses) dollars

the difference, in months, between the Award Effective Date and the Final Expiration Date.

A Running Allocation from the previous fiscal month; a carry over amount that is redistributed

A Running Sum of Allocated dollar amounts on a grant, distributed evenly to Future Months.