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

Sum-of-the-Years'-Digits Depreciation: worked example

Purchase cost	$160,000
Salvage value	$10,000
Useful life	5.0 years
Year to calculate	2
Depreciation in that year	$40,000
Book value at year end	$70,000
Total depreciation so far	$90,000

Sum-of-the-Years'-Digits Depreciation: formula

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

IRS Publication 946: How To Depreciate Property · AccountingCoach: sum-of-years digits example

Common error: Applying the fractions to the full purchase cost. Salvage value comes off first, and only the difference is spread across the years.

Purchase cost, salvage value and useful life are the same as in other methods, and the year to calculate picks which year's expense to show. Multiply the depreciable amount by the year's fraction. Its numerator is remaining life in that year.

Its denominator is the sum of the year digits. For five years, 5 + 4 + 3 + 2 + 1 = 15. Use it when an asset loses value faster early but not as sharply as double-declining balance implies.

Sum-of-the-Years'-Digits Depreciation: changing Purchase cost

Purchase cost	Depreciation in that year	Book value at year end	Total depreciation so far
$128,000	$31,467	$57,200	$70,800
$144,000	$35,733	$63,600	$80,400
$160,000 (example)	$40,000	$70,000	$90,000
$176,000	$44,267	$76,400	$99,600
$192,000	$48,533	$82,800	$109,200

Sum-of-the-Years'-Digits Depreciation: compare input ranges

Input	Tested from	To	Depreciation in that year: low input	Depreciation in that year: high input	Swing
Year to calculate	1	3	$50,000	$30,000	$20,000 (50%)
Useful life	4.0 years	6.0 years	$45,000	$35,714	$9,286 (23%)
Purchase cost	$144,000	$176,000	$35,733	$44,267	$8,533 (21%)
Salvage value	$9,000	$11,000	$40,267	$39,733	$533 (1.3%)

Sum-of-the-Years'-Digits Depreciation: individual input comparisons

Input	Value	Depreciation in that year	Book value at year end	Total depreciation so far
Purchase cost	$128,000	$31,467	$57,200	$70,800
	$144,000	$35,733	$63,600	$80,400
	$160,000	$40,000	$70,000	$90,000
	$176,000	$44,267	$76,400	$99,600
	$192,000	$48,533	$82,800	$109,200
Salvage value	$8,000	$40,533	$68,800	$91,200
	$9,000	$40,267	$69,400	$90,600
	$10,000	$40,000	$70,000	$90,000
	$11,000	$39,733	$70,600	$89,400
	$12,000	$39,467	$71,200	$88,800
Useful life	3.0 years	$50,000	$35,000	$125,000
	4.0 years	$45,000	$55,000	$105,000
	5.0 years	$40,000	$70,000	$90,000
	6.0 years	$35,714	$81,429	$78,571
	7.0 years	$32,143	$90,357	$69,643
Year to calculate	0	$50,000	$110,000	$50,000
	1	$50,000	$110,000	$50,000
	2	$40,000	$70,000	$90,000
	3	$30,000	$40,000	$120,000
	4	$20,000	$20,000	$140,000

Sum-of-the-Years'-Digits Depreciation: combined input changes

Purchase cost / Salvage value	$8,000	$10,000	$12,000
$128,000	$32,000	$31,467	$30,933
$144,000	$36,267	$35,733	$35,200
$160,000	$40,533	$40,000	$39,467
$176,000	$44,800	$44,267	$43,733
$192,000	$49,067	$48,533	$48,000

Sum-of-the-Years'-Digits Depreciation: which assumptions move the result?

The depreciation weight declines as the asset moves through its stated life. For the entered $150,000 depreciable basis and five-year life, the first-year charge is $50,000 and the third-year charge is $30,000. Book value and cumulative depreciation reconcile the intervening charges separately. This arithmetic schedule does not establish whether a tax authority permits the chosen accounting method.

Changing useful life changes both the denominator's sum of digits and the weight assigned to the selected year. At year two, a four-year life produces $45,000 of depreciation; a six-year life produces about $35,714. Cost and salvage remain fixed. A revised estimate of useful life is therefore different from simply advancing the year within an unchanged depreciation schedule.

Sum-of-the-Years'-Digits Depreciation: values and definitions

Quantity and definition	Value used
Purchase cost	$160,000
Salvage value	$10,000
Useful life	5.0 years
Year to calculate	2
Depreciation in that year	$40,000
Book value at year end	$70,000
Total depreciation so far	$90,000

Sum-of-the-Years'-Digits Depreciation: half and double Year to calculate

Year to calculate	Depreciation in that year
1	$50,000
2	$40,000
4	$20,000

The method is less common than straight-line or MACRS and is mainly used for book reporting. Tax depreciation follows its own rules. Choosing an accelerated method reduces reported profit in the early years, which can affect covenants and comparisons with businesses that use straight-line.

Check the entire sequence of fractions

AccountingCoach uses equipment costing $160,000, a $10,000 residual estimate and a five-year useful life. The allocable difference is $150,000. Adding the year digits gives 15, so the annual weights are 5/15, 4/15, 3/15, 2/15 and 1/15.

Expenses are respectively $50,000, $40,000, $30,000, $20,000 and $10,000. Those fractions sum to one and the expenses sum to the allocable amount. This is why the original acquisition cost cannot be substituted for the cost less residual value.

After the second year, accumulated depreciation is $90,000 and carrying amount is $70,000. The decreasing numerator creates an equal dollar reduction from one annual charge to the next, unlike the declining-balance method’s percentage of a changing carrying amount. Keep full years and any partial-year convention separate.

This example allocates book cost; it does not establish a federal tax deduction or forecast a sale price.

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The sum-of-the-years'-digits method takes the largest slice of depreciation in the first year and steps down by an equal amount each year after. For a five year life the digits add to 15, so year one takes 5/15 of the depreciable amount, year two 4/15 and so on. On $45,000 of depreciable cost, year two is $12,000, and the book value after two years is $23,000.

The full schedule on the $50,000 example runs $15,000, $12,000, $9,000, $6,000 and $3,000 across the five years, a steady step of $3,000 each year, with book value falling to $35,000, $23,000, $14,000, $8,000 and $5,000.

Confirm the method is allowed for your purpose. Tax rules often prescribe their own schedules, so this is mainly for book records.

Compare with the straight-line and double-declining-balance calculators, and the units of production page for usage-based expense. The equipment lease versus buy calculator uses depreciation in the buy case. Confirm the method with your accountant to keep your books consistent.

Depreciation methods compared

When is SYD better than straight-line?

When the asset produces more value or loses more resale value in its early years, so the expense should be heavier at the start.

Does SYD depreciate below salvage value?

No. The fractions add to one, so total depreciation equals cost minus salvage, and book value ends at salvage.

How is the sum of the years' digits calculated?

Add the digits from one to the useful life; for five years that is 15. Each year's fraction is the remaining life divided by that sum.

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