# Sum of Years Digits Depreciation Calculator

## Calculator Use

Use this calculator to calculate an accelerated depreciation using the sum of years digits method. Depreciation is taken as a fractional part of a sum of all the years.

## Inputs

- Asset Cost
- the original value of your asset or the depreciable cost; the necessary amount expended to get an asset ready for its intended use
- Salvage Value
- the value of the asset at the end of its useful life; also known as residual value or scrap value
- Useful Life
- the expected time that the asset will be productive for its expected purpose
- Placed in Service
- select the month and enter the year the asset started being used for its intended purpose
- Year
- enter 1 or 4 digits; enter a four digit year to use your actual years
**OR**enter a 1 to list years using digits 1 through the last year

## Sample Full Depreciation Schedule

Cost: $125,000.00, Salvage: $15,000.00

Life: 7 years, First Year: 5 months

Year Start

Depreciable

Percent

Expense

Depreciation

Year End

(5/12) x (7/28)

[(7/12) x (7/28)] + [(5/12) x (6/28)]

[(7/12) x (6/28)] + [(5/12) x (5/28)]

[(7/12) x (5/28)] + [(5/12) x (4/28)]

[(7/12) x (4/28)] + [(5/12) x (3/28)]

[(7/12) x (3/28)] + [(5/12) x (2/28)]

[(7/12) x (2/28)] + [(5/12) x (1/28)]

(7/12) x (1/28)

## Sum of Years' Digits Depreciation Formulas

The sum of years digits method is accelerated depreciation. Depreciation is taken as a fractional part of a sum of all the years. For example, if an asset has a life of 5 years the sum of years is 1+2+3+4+5 = 15. Fractional parts are built with the year as the numerator and the sum of years as the denominator but, in reverse order. Year 1 is 5/15 * depreciable cost, Year 2 is 4/15 * depreciable cost, Year 3 is 3/15 * depreciable cost, etc. Since the sum of all fractions will equal 15/15, the total depreciation over the life of an asset will be 1 * depreciable cost = depreciable cost.

Calculating the sum of years can be simplified with the formula (Life * (Life + 1)) / 2 so you do not need to actually add up all the years.

- Depreciable Cost = Original Cost - Salvage Value = (Cost - Salvage)
- Fraction for a Given Period = (Life - Period + 1) / ((Life * (Life + 1)) / 2)
- Depreciation in Any Period:
- = Fraction for Given Period * Depreciable Cost
- = [(Life - Period + 1) / ((Life * (Life + 1)) / 2) ] * (Cost - Salvage)
- = ((Cost - Salvage) * (Life - Period + 1) * 2 / (Life) / (Life +1))

- Partial year depreciation, when the first year has M months requires a bit of manipulation since the period fraction used and the years in which the depreciation are taken will overlap. If we have an asset with a life of 5 years and the service for the first year is only 4 months:
- First year depreciation fraction = (4/12) x (5/15)
- Second year depreciation fraction = [(8/12) x (5/15)] + [(4/12) x (4/15)]
- Etc .....
- And, a life, for example, of 5 years will be depreciated across 6 years.

## Microsoft® Excel® Functions Equivalent: SYD

The Excel equivalent function for Sum of Years' Digits Method is **SYD(cost,salvage,life,per)** will calculate the depreciation expense for any period. For a more accelerated depreciation method see, for example, our Double Declining Balance Method Depreciation Calculator.

(Microsoft® and Excel® are registered trademarks of Microsoft Corporation)

**Cite this content, page or calculator as:**

Furey, Edward "Sum of Years Digits Depreciation Calculator"; from *https://www.calculatorsoup.com* - Online Calculator Resource.