What is the sum-of-the-years'-digits formula?

Depreciation in year t = (cost − salvage) × (life − t + 1) ÷ [life × (life + 1) ÷ 2].

How do you calculate the sum of the years' digits?

Add 1 + 2 + … + n, or use n(n + 1) ÷ 2. For a 10-year life it is 55.

Why use SYD instead of straight-line?

It matches higher depreciation to the early years, when many assets lose value fastest and are most productive.

Does SYD reach the salvage value exactly?

Yes. The yearly fractions sum to 1, so the full depreciable base is written off.

Sum-of-the-Years'-Digits Depreciation

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Sum-of-the-Years'-Digits Depreciation Calculator

The sum-of-the-years’-digits method is an accelerated depreciation method that charges more in the early years and less later, but in a smoother pattern than declining balance: the annual charge falls by the same amount every year. Add the digits of the useful life (for 5 years, 1 + 2 + 3 + 4 + 5 = 15, or n(n + 1) ÷ 2), and each year depreciate the fraction remaining life ÷ that sum of the depreciable base.

Formula

Depreciation_t = (Cost − Salvage) × Life − t + 1SYD SYD = Life × (Life + 1)2

Where

t: year number (1 for the first year)
Life: useful life in years
SYD: sum of the years’ digits, 1 + 2 + … + Life

Calculator

Asset cost

Salvage (residual) value

Useful life (years)

Result and step-by-step solution

First-year depreciation

4,090.91

Falls by 409.09 each year, to 409.09 in year 10.

Sum of the years’ digits
10 × 112 = 55
Depreciable base
30,000.00 − 7,500.00 = 22,500.00
Year 1
22,500.00 × 1055 = 4,090.91
Year 2
22,500.00 × 955 = 3,681.82

Schedule

Year	Book value at start	Depreciation	Accumulated	Book value at end
1	30,000.00	4,090.91	4,090.91	25,909.09
2	25,909.09	3,681.82	7,772.73	22,227.27
3	22,227.27	3,272.73	11,045.45	18,954.55
4	18,954.55	2,863.64	13,909.09	16,090.91
5	16,090.91	2,454.55	16,363.64	13,636.36
6	13,636.36	2,045.45	18,409.09	11,590.91
7	11,590.91	1,636.36	20,045.45	9,954.55
8	9,954.55	1,227.27	21,272.73	8,727.27
9	8,727.27	818.18	22,090.91	7,909.09
10	7,909.09	409.09	22,500.00	7,500.00

How to use the formula

In the first year of a 5-year asset the fraction is 5/15, then 4/15, 3/15, 2/15 and 1/15. The fractions add up to exactly 1, so the asset is depreciated exactly to its salvage value, with no need for a switch to straight-line.

The default reproduces Excel’s SYD example: a 30,000 asset with a 7,500 salvage value and a 10-year life. The sum of the digits is 55 and the depreciable base 22,500, so year 1 is 22,500 × 10/55 = 4,090.91 and year 10 is 409.09; the charge falls by 409.09 each year. The method is less common today than double declining balance but still appears in accounting courses and in some leasing contracts.

Frequently asked questions

What is the sum-of-the-years’-digits formula?: Depreciation in year t = (cost − salvage) × (life − t + 1) ÷ [life × (life + 1) ÷ 2].
How do you calculate the sum of the years’ digits?: Add 1 + 2 + … + n, or use n(n + 1) ÷ 2. For a 10-year life it is 55.
Why use SYD instead of straight-line?: It matches higher depreciation to the early years, when many assets lose value fastest and are most productive.
Does SYD reach the salvage value exactly?: Yes. The yearly fractions sum to 1, so the full depreciable base is written off.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.