Sum-of-the-Years’-Digits (SYD) Depreciation Calculator with Schedule
Calculate sum-of-the-years’-digits (SYD) depreciation: the digits total, each year’s fraction and expense, a full schedule with a partial first year, and a comparison with straight-line.
How it works
Sum of the years’ digits SYD = n × (n + 1) ÷ 2 (n = useful life in years) · Depreciation in year k = (cost − salvage) × (n − k + 1) ÷ SYD · with a partial first year of m months, each fiscal year takes m/12 of one asset year plus (12 − m)/12 of the previous one
Sum-of-the-years’-digits (SYD) is an accelerated depreciation method that writes off more of an asset’s cost early in its life. Add the digits of the useful life (for 5 years, 5 + 4 + 3 + 2 + 1 = 15, or n × (n + 1) ÷ 2). Each year’s depreciation is the depreciable base (cost minus salvage) times a fraction: the remaining life at the start of the year over that sum, so 5/15, then 4/15, 3/15, 2/15 and 1/15. The expense falls by the same amount every year and the asset ends exactly at its salvage value, with no switch needed. SYD sits between straight-line and double declining balance: faster than straight-line in the early years, but usually gentler than 200% declining balance in year one. If the asset went into service partway through the fiscal year, each asset year straddles two fiscal years, so each fiscal year blends two fractions; the schedule then runs one extra, partial year. The straight-line column in the schedule shows how much faster SYD front-loads the expense compared with the straight-line depreciation calculator.
Worked example
A $10,000 asset with a $1,000 salvage value and a 5-year life: the digits add up to 5 × 6 ÷ 2 = 15 and the depreciable base is $9,000. Year 1 = $9,000 × 5/15 = $3,000; year 2 = $9,000 × 4/15 = $2,400; year 3 = $1,800; year 4 = $1,200; year 5 = $600. The expense drops by $9,000 ÷ 15 = $600 a year, totals $9,000 and leaves a book value of $1,000. Straight-line would be $1,800 every year.
Sources: Wikipedia: Depreciation (SYD example: $1,000, $100 salvage, 5 years) · Deltek: Sum of years digit example ($160,000, $10,000 salvage, 5 years) · MathWorks: depsoyd (13,000 cost, 1,000 salvage, 10-year schedule)
Frequently asked questions
How do you calculate sum-of-the-years’-digits depreciation?
Add the years of useful life (n × (n + 1) ÷ 2), subtract salvage from cost, and multiply that base by the remaining life over the sum each year. For a $160,000 asset with a $10,000 salvage value and 5-year life, the base is $150,000 and the sum is 15, so year 1 is $150,000 × 5/15 = $50,000, then $40,000, $30,000, $20,000 and $10,000.
What is the sum of the years’ digits for 10 years?
55, because 10 × 11 ÷ 2 = 55. The first-year fraction is 10/55 (18.2%) and the last is 1/55. For 7 years the sum is 28 and for 3 years it is 6.
How does SYD handle a partial first year?
Each asset year is split across fiscal years. If the asset is in service for 4 months of the first fiscal year, that year gets 4/12 of the first asset year’s depreciation, the next fiscal year gets 8/12 of the first asset year plus 4/12 of the second, and so on, with a final partial year at the end.
Is SYD faster than double declining balance?
Usually not in year one. For a 5-year asset, SYD takes 33.3% of the depreciable base in year 1, while double declining takes 40% of the full cost. In later years SYD can be larger. Both are faster than straight-line in the early years.
Can I use SYD for taxes?
Many countries and US tax rules (MACRS) prescribe their own methods, so SYD is mainly used for financial statements and accounting courses. Check your local tax rules or ask an accountant before using it on a return.
Related calculators
For accounting and tax decisions, follow your accounting standards and tax rules or ask an accountant; tax depreciation can differ from this schedule.