Sum of Years Digits Calculator

How it is calculated

For an asset with useful life n whole years, the tool first sums the digits: S = n × (n + 1) ÷ 2. The depreciable base is cost − salvage. In year y the remaining life at the start of the year is n − y + 1, so expense = base × (n − y + 1) ÷ S. Accumulated depreciation is the sum of the expenses for years 1 to y, and book value = cost − accumulated. Life and year are rounded to whole numbers, the year must lie between 1 and the life, the life can be at most 1,000 years, and salvage may not exceed cost; otherwise nothing is shown. The tool applies the full-year convention, with no part-year adjustment for assets bought mid-year, and gives one chosen year at a time.

Common mistakes

• Depreciating the full cost. SYD applies to cost minus salvage, so the machine can never be written down below its salvage value.
• Entering the year as a calendar year (such as 2026) instead of the year number of the asset's life (1, 2, 3...). A value above the life gives no result.
• Using the percentage of year 1 for every year. The fraction falls each year (5/15, 4/15, 3/15, 2/15, 1/15 for a 5-year life).
• Forgetting that book value is based on cost, not on the depreciable base: it ends at the salvage value, not at zero.
• Assuming it matches tax depreciation. Tax rules differ by country and often use their own schedules, so this tool shows the accounting method only.