 Online Calculators

# Sum of Years Digits Depreciation Calculator

Sum-of-Years' Depreciation
Placed in service:

## 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. Create and print schedules.

## 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

Depreciation Schedule
Year

Book Value
Year Start
Total Cost
Depreciable
Depreciation
Percent
Depreciation
Expense
Accumulated
Depreciation
Book Value
Year End
2011
\$125,000
\$110,000.00
10%
(5/12) x (7/28)
\$11,458
\$11,458
\$113,542
2012
\$113,542
\$110,000.00
24%
[(7/12) x (7/28)] + [(5/12) x (6/28)]
\$25,863
\$37,321
\$87,679
2013
\$87,679
\$110,000.00
20%
[(7/12) x (6/28)] + [(5/12) x (5/28)]
\$21,935
\$59,256
\$65,744
2014
\$65,744
\$110,000.00
16%
[(7/12) x (5/28)] + [(5/12) x (4/28)]
\$18,006
\$77,262
\$47,738
2015
\$47,738
\$110,000.00
13%
[(7/12) x (4/28)] + [(5/12) x (3/28)]
\$14,077
\$91,339
\$33,661
2016
\$33,661
\$110,000.00
9%
[(7/12) x (3/28)] + [(5/12) x (2/28)]
\$10,149
\$101,488
\$23,512
2017
\$23,512
\$110,000.00
6%
[(7/12) x (2/28)] + [(5/12) x (1/28)]
\$6,220
\$107,708
\$17,292
2018
\$17,292
\$110,000.00
2%
(7/12) x (1/28)
\$2,292
\$110,000
\$15,000

## 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" at https://www.calculatorsoup.com/calculators/financial/depreciation-sum-of-years.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: November 15, 2023