How do you calculate sum-of-the-years'-digits depreciation?
Short answer
Multiply the depreciable amount, which is cost minus salvage value, by a fraction each year. The numerator is the asset's remaining life at the start of that year, and the denominator is the sum of the digits from 1 to the life, which equals life × (life + 1) ÷ 2. Charges fall each year and total exactly cost minus salvage.
Sum-of-the-years'-digits (SYD) is an accelerated method: it charges more depreciation early in an asset's life and less later, without ever going below salvage value.
What is the SYD formula?
Depreciation in year n = (cost − salvage) × (life − n + 1) ÷ (life × (life + 1) ÷ 2)
The denominator is the sum of the digits 1 through life. For a 5-year life it is 1 + 2 + 3 + 4 + 5 = 15, and the fractions for the five years are 5/15, 4/15, 3/15, 2/15 and 1/15.
What does a worked example look like?
An asset costs 10,000, has a salvage value of 1,000 and a 5-year life, so the depreciable amount is 9,000.
| Year | SYD fraction | SYD | Straight-line | Double-declining |
|---|---|---|---|---|
| 1 | 5/15 | 3,000 | 1,800 | 4,000 |
| 2 | 4/15 | 2,400 | 1,800 | 2,400 |
| 3 | 3/15 | 1,800 | 1,800 | 1,440 |
| 4 | 2/15 | 1,200 | 1,800 | 864 |
| 5 | 1/15 | 600 | 1,800 | 296 |
| Total | 9,000 | 9,000 | 9,000 |
All three methods depreciate the same 9,000 over the life. They differ only in timing. Straight-line is (cost − salvage) ÷ life every year. Double-declining balance charges 2 ÷ life, here 40%, on the opening book value and is capped so that book value never falls below salvage. That is why year 5 is 296 and not 518.40: only 296 remains above salvage.
What are the usual conventions and limits?
These figures take a full year of depreciation in the year the asset is placed in service. Partial-year and mid-month conventions, impairments and disposals are not modeled, and tax depreciation such as MACRS follows its own tables. Use this for book depreciation and confirm treatment with a qualified accountant. This page is arithmetic, not accounting or tax advice.
The fixed asset register and depreciation schedule calculates all three methods for up to 60 assets over lives of 1 to 10 years.