Sum-of-the-years’-digits (SYD) is an accelerated depreciation method with a pleasingly regular shape: the charge is largest in year 1 and falls by exactly the same dollar amount every year after. It sits between straight-line and double declining balance in aggressiveness, and unlike declining-balance methods it lands precisely on salvage value with no switch or plug. This calculator shows each year’s fraction, handles assets placed in service mid-year, and builds the full book value schedule.
How to use the SYD calculator
- Enter the asset cost and salvage value.
- Enter the useful life in whole years.
- Choose the months in service in the first fiscal year.
The schedule’s “fraction” column shows exactly which share of the depreciable base each fiscal year receives.
Sum-of-the-years’-digits formula
n is the useful life. The fractions (n − k + 1)/SYD add up to exactly 1, which is why the method always depreciates the full base.
Worked example
A printing press costs $52,000, has a $4,000 salvage value and a 7-year life. SYD = 7 × 8 ÷ 2 = 28, and the base is $48,000.
| Year | Fraction | Depreciation | Ending book value |
|---|---|---|---|
| 1 | 7/28 | $12,000.00 | $40,000.00 |
| 2 | 6/28 | $10,285.71 | $29,714.29 |
| 3 | 5/28 | $8,571.43 | $21,142.86 |
| 4 | 4/28 | $6,857.14 | $14,285.71 |
| 5 | 3/28 | $5,142.86 | $9,142.86 |
| 6 | 2/28 | $3,428.57 | $5,714.29 |
| 7 | 1/28 | $1,714.29 | $4,000.00 |
Each year drops by $48,000 ÷ 28 = $1,714.29, and the final year’s charge is that same amount.
Partial first year
SYD fractions belong to asset years, which run from the date the asset was placed in service. When that does not match the fiscal year, each fiscal year takes a slice of two asset years. If the press arrives with 9 months left in the fiscal year:
- Fiscal year 1: 9/12 × $12,000 = $9,000.00
- Fiscal year 2: 3/12 × $12,000 + 9/12 × $10,285.71 = $10,714.29
- Fiscal year 3: 3/12 × $10,285.71 + 9/12 × $8,571.43 = $9,000.00
- … and fiscal year 8 picks up the last 3/12 × $1,714.29 = $428.57
The schedule spans eight fiscal years but still totals exactly $48,000.
Where SYD fits
SYD suits assets whose usefulness declines steadily: production equipment that slows down, vehicles whose repair costs climb each year, or rental equipment that commands lower prices as it ages. Compared with double declining balance on the same asset, SYD typically records less in year 1 but more in the middle years. For an even charge, use straight-line, and to compare all of these on one screen, open the depreciation calculator.
Estimates for planning, coursework and bookkeeping, not accounting or tax advice.
Frequently asked questions
What is the sum-of-the-years'-digits formula?
Depreciation for a year = (cost − salvage) × remaining useful life at the start of the year ÷ SYD, where SYD = n(n + 1) ÷ 2. For a 7-year life, SYD = 28 and the fractions are 7/28, 6/28, … 1/28.
Why is it called sum of the years' digits?
Because the denominator is the sum of the digits of each year of the life: for 5 years, 5 + 4 + 3 + 2 + 1 = 15. The numerators count down through the same digits.
How does SYD compare with double declining balance?
Both are accelerated, but SYD falls by the same dollar amount every year, while DDB falls by the same percentage. SYD usually starts lower than DDB, declines more evenly and always ends exactly at salvage value without a switch.
How do I handle a partial first year?
Allocate each asset year across fiscal years. With 9 months in service in fiscal year 1, that year gets 9/12 of the first asset-year charge; fiscal year 2 gets the remaining 3/12 plus 9/12 of the second asset-year charge, and so on.
Is SYD allowed for US tax purposes?
Not for most property placed in service after 1986, which must use MACRS. SYD remains acceptable for financial reporting under US GAAP and is common in accounting courses.