Answer first
What this calculator tells you
Calculate depreciation, book value and accumulated depreciation for any year under the sum-of-the-years'-digits method. Front-load depreciation more gently than double-declining balance for an asset that loses value early. Formula: Depreciation in year n = (life − n + 1) ÷ [life × (life + 1) ÷ 2] × (cost − salvage). At the worked-example inputs, the depreciation in that year is $12,000. Holding every other input steady, moving purchase cost from $40,000 to $60,000 moves the result from $9,333 to $14,667.
Transparent method
The formula
Front-load depreciation more gently than double-declining balance for an asset that loses value early.
Worked example
Example inputs
How to interpret the result
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.
At the worked-example inputs the depreciation in that year is $12,000. It rises with purchase cost and falls as year to calculate, useful life and salvage value increase.
These are planning metrics, not audited accounting or a valuation opinion.
Before you rely on it
What to check
Confirm the method is allowed for your purpose. Tax rules often prescribe their own schedules, so this is mainly for book records.
The common error
Where people go wrong with sum-of-the-years'-digits depreciation calculator
Applying the fractions to the full purchase cost. Salvage value comes off first, and only the difference is spread across the years.
Sensitivity evidence
How purchase cost changes the depreciation in that year
Holding every other input at the worked-example value, moving purchase cost from $40,000 to $60,000 moves the depreciation in that year from $9,333 to $14,667: a spread of $5,333, or 44% of the worked-example result.
| Purchase cost | Depreciation in that year | Book value at year end | Total depreciation so far |
|---|---|---|---|
| $40,000 | $9,333 | $19,000 | $21,000 |
| $45,000 | $10,667 | $21,000 | $24,000 |
| $50,000worked example | $12,000 | $23,000 | $27,000 |
| $55,000 | $13,333 | $25,000 | $30,000 |
| $60,000 | $14,667 | $27,000 | $33,000 |
Every input, tested
Which input moves the depreciation in that year most
Of the 4 inputs, year to calculate moves the depreciation in that year most ($6,000 across the range tested) and salvage value moves it least ($267).
| Input | Tested from | To | Depreciation in that year at each end | Swing |
|---|---|---|---|---|
| Year to calculate | 1 | 3 | $15,000 to $9,000 | $6,000 (50%) |
| Useful life | 4.0 years | 6.0 years | $13,500 to $10,714 | $2,786 (23%) |
| Purchase cost | $45,000 | $55,000 | $10,667 to $13,333 | $2,667 (22%) |
| Salvage value | $4,500 | $5,500 | $12,133 to $11,867 | $267 (2.2%) |
Two variables at once
Depreciation in that year by purchase cost and salvage value
Across the grid the depreciation in that year runs from $9,067 to $14,933. Moving purchase cost from $40,000 to $60,000 shifts it by $5,333 at the middle column, and moving salvage value from $4,000 to $6,000 shifts it by $533 at the middle row, so purchase cost is the bigger lever here.
| Purchase cost \ Salvage value | $4,000 | $5,000 | $6,000 |
|---|---|---|---|
| $40,000 | $9,600 | $9,333 | $9,067 |
| $45,000 | $10,933 | $10,667 | $10,400 |
| $50,000 | $12,267 | $12,000 | $11,733 |
| $55,000 | $13,600 | $13,333 | $13,067 |
| $60,000 | $14,933 | $14,667 | $14,400 |
The highlighted cell is the worked example: $12,000.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Purchase cost | $50,000 | Enter the purchase cost used in this calculation. |
| Salvage value | $5,000 | Enter the salvage value used in this calculation. |
| Useful life | 5.0 years | Enter the useful life used in this calculation. |
| Year to calculate | 2 | Enter the year to calculate used in this calculation. |
| Depreciation in that year | $12,000 | |
| Book value at year end | $23,000 | |
| Total depreciation so far | $27,000 | |
Inputs, definitions and assumptions
Purchase cost
Enter the purchase cost used in this calculation. The prefilled worked-example value is $50,000.
Salvage value
Enter the salvage value used in this calculation. The prefilled worked-example value is $5,000.
Useful life
Enter the useful life used in this calculation. The prefilled worked-example value is 5.0 years.
Year to calculate
Enter the year to calculate used in this calculation. The prefilled worked-example value is 2.
How to use this calculator
- 1Verify the inputs. Gather purchase cost, salvage value, useful life and year to calculate from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the depreciation in that year at $12,000. Store your own version of it as Scenario A.
- 3Test one change. Start with year to calculate, the input with the biggest effect here: moving year to calculate from 1 to 3 takes the depreciation in that year from $15,000 to $9,000, a swing of 50% of the worked-example figure.
- 4Check the extremes. At half the example year to calculate (1) the depreciation in that year is $15,000; at double (4) it is $6,000.
People also ask
Frequently asked questions
How do you calculate sum-of-the-years'-digits depreciation?
Depreciation in year n = (life − n + 1) ÷ [life × (life + 1) ÷ 2] × (cost − salvage). Enter purchase cost in dollars, salvage value in dollars and useful life in years. At the worked-example inputs the depreciation in that year is $12,000.
What does the sum-of-the-years'-digits depreciation result mean?
Front-load depreciation more gently than double-declining balance for an asset that loses value early. At the worked-example inputs the depreciation in that year is $12,000. It rises with purchase cost and falls as year to calculate, useful life and salvage value increase.
How much does purchase cost change the depreciation in that year?
Holding every other input at the worked-example value, moving purchase cost from $40,000 to $60,000 moves the depreciation in that year from $9,333 to $14,667, a spread of $5,333.
What are the limits of this sum-of-the-years'-digits depreciation calculator?
These are planning metrics, not audited accounting or a valuation opinion. The tables on this page test purchase cost only from $40,000 to $60,000; a value outside that range is not tabulated here.
Which input moves the depreciation in that year most in the sum-of-the-years'-digits depreciation calculator?
Ranked by how far each moves the depreciation in that year across the range tested: year to calculate ($6,000, 50%), useful life ($2,786, 23%), purchase cost ($2,667, 22%) and salvage value ($267, 2.2%).
If I double year to calculate in the sum-of-the-years'-digits depreciation calculator, does the depreciation in that year double?
Doubling it from 2 to 4 takes the depreciation in that year from $12,000 to $6,000, which is 0.50 times the worked-example figure. So it falls instead of rising. Halving it to 1 gives $15,000.
How much does salvage value matter in the sum-of-the-years'-digits depreciation calculator?
The worked example uses $5,000. With the other inputs left at the worked example, moving salvage value from $4,500 to $5,500 takes the depreciation in that year from $12,133 to $11,867, a swing of 2.2% of the worked-example figure.
How much does useful life matter in the sum-of-the-years'-digits depreciation calculator?
The worked example uses 5.0 years. Holding every other input at its worked-example value, moving useful life from 4.0 years to 6.0 years takes the depreciation in that year from $13,500 to $10,714, a swing of 23% of the worked-example figure.
How much does year to calculate matter in the sum-of-the-years'-digits depreciation calculator?
The worked example uses 2. With the other inputs left at the worked example, moving year to calculate from 1 to 3 takes the depreciation in that year from $15,000 to $9,000, a swing of 50% of the worked-example figure.
Which inputs change the book value at year end in the sum-of-the-years'-digits depreciation calculator?
At the worked-example inputs it is $23,000. Purchase cost takes it from $21,000 to $25,000, salvage value takes it from $22,700 to $23,300, useful life takes it from $18,500 to $26,429 and year to calculate takes it from $35,000 to $14,000.
Which inputs change the total depreciation so far in the sum-of-the-years'-digits depreciation calculator?
At the worked-example inputs it is $27,000. Purchase cost takes it from $24,000 to $30,000, salvage value takes it from $27,300 to $26,700, useful life takes it from $31,500 to $23,571 and year to calculate takes it from $15,000 to $36,000.
What does a debt-to-equity ratio tell a lender?
How much of the business is funded by borrowing compared with the owners' money. Higher ratios mean more risk to the lender, and what is normal differs a great deal between industries.
Sources and evidence
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