Sum-of-Years-Digits Depreciation Calculator
Sum-of-years-digits (SYD) is an accelerated depreciation method that writes off more of an asset's cost in its early years and less as it ages. It works by applying a falling fraction to a fixed depreciable base, which is the cost minus the salvage value. The denominator of every fraction is the sum of the years' digits: for a 5-year asset that is 1 plus 2 plus 3 plus 4 plus 5, which equals 15, or more quickly the formula n times (n plus 1) divided by 2. The numerator is the remaining life at the start of each year, so the fractions run 5/15, 4/15, 3/15, 2/15 and 1/15, giving the largest deduction first. This calculator takes the asset cost, the salvage value and the useful life, then returns the SYD denominator, the first-year depreciation and the total depreciation over the asset's life. Because the fractions sum to one, the deductions always add up to the depreciable base and book value finishes exactly at salvage. The figures here are book depreciation; US federal tax depreciation generally follows the Modified Accelerated Cost Recovery System in IRS Publication 946. Every figure is computed deterministically, with a worked example and full schedule that reconcile exactly to the calculator.
Sum of the years digits weights early years more heavily. For a 5 year life the digits sum to 15, so a $10,000 asset with $1,000 salvage depreciates $3,000 (5/15 of 9,000) in year one.
Sum-of-years-digits formula
SYD denominator = n * (n + 1) / 2
depreciable base = cost - salvage
year k depreciation = (remaining life at start of year k / SYD) * base
remaining life in year 1 = n, in year 2 = n - 1, and so on
n = useful life in years
The denominator stays the same every year, but the numerator falls by one each year, so the fraction of the base charged shrinks over the asset's life. Because the fractions add up to one, the deductions sum to the full depreciable base and book value ends exactly at salvage.
Worked example
An asset costs 10,000, has a salvage value of 1,000 and a useful life of 5 years.
- SYD denominator = 5 * 6 / 2 = 15
- Depreciable base = 10,000 - 1,000 = 9,000
- Year 1: (5 / 15) * 9,000 = 3,000.00
- Year 2: (4 / 15) * 9,000 = 2,400.00
- Year 3: (3 / 15) * 9,000 = 1,800.00
- Year 4: (2 / 15) * 9,000 = 1,200.00
- Year 5: (1 / 15) * 9,000 = 600.00
- Total depreciation = 3,000.00 + 2,400.00 + 1,800.00 + 1,200.00 + 600.00 = 9,000.00
The SYD denominator is 15, the year 1 deduction is 3,000.00 and total depreciation is 9,000.00 (which equals cost minus salvage). These are the calculator's default inputs, so the results above match the widget exactly.
Default depreciation schedule
This schedule uses the default inputs: cost 10,000, salvage 1,000, 5-year life. The depreciable base is 9,000 and the denominator is 15.
| Year | Fraction | Depreciation | Ending book value |
|---|---|---|---|
| 1 | 5/15 | 3,000.00 | 7,000.00 |
| 2 | 4/15 | 2,400.00 | 4,600.00 |
| 3 | 3/15 | 1,800.00 | 2,800.00 |
| 4 | 2/15 | 1,200.00 | 1,600.00 |
| 5 | 1/15 | 600.00 | 1,000.00 |
| Total | 9,000.00 |
Method and recovery rules: US Internal Revenue Service, Publication 946.
Sum-of-years-digits depreciation calculator: frequently asked questions
What is the sum-of-years-digits (SYD) method?
Sum-of-years-digits is an accelerated depreciation method that charges more depreciation in early years and less later. Each year's deduction is a fraction of the depreciable base, where the numerator is the remaining life at the start of the year and the denominator is the sum of the years' digits. For a 5-year asset the fractions run 5/15, 4/15, 3/15, 2/15 and 1/15, so the first year takes the largest share.
How do you calculate the SYD denominator?
The denominator is the sum of the digits from 1 up to the useful life. For a 5-year life it is 1 + 2 + 3 + 4 + 5 = 15. A faster way is the formula n times (n + 1) divided by 2, which for 5 years gives 5 times 6 divided by 2 = 15. This single number is the denominator for every year of the schedule.
What is the depreciable base?
The depreciable base is the asset cost minus its salvage value, the part of the cost you actually write off over the asset's life. With a cost of 10,000 and salvage of 1,000, the base is 9,000. Every SYD fraction is applied to this base, so the deductions always add up to the base and book value finishes exactly at salvage.
How does SYD compare with declining balance?
Both are accelerated methods, but they front-load depreciation differently. Declining balance applies a fixed rate to a falling book value, while SYD applies a falling fraction to a fixed base. SYD is often a touch less aggressive than double declining balance in the first year and, unlike a simple declining balance schedule, it lands on salvage automatically without needing a final-year floor.
Is SYD allowed for US tax depreciation?
The figures here are book depreciation, used in financial statements. US federal tax depreciation generally uses the Modified Accelerated Cost Recovery System (MACRS), not SYD, with set recovery periods and official percentage tables. SYD is still useful for book purposes and for older assets, but for a tax return follow the rules and tables in IRS Publication 946.
Official sources
- Depreciation methods, recovery periods and MACRS tables: US Internal Revenue Service, Publication 946, How To Depreciate Property. As at 24 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 24 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.