Sum of Years' Digits — Sum
This little formula calculates the "sum of digits," which is the bottom number (the denominator) used in the sum-of-years'-digits depreciation method. On its own it isn't a rate or a dollar amount—it's just a total you compute once so you can reuse it every year.
To calculate it, take the asset's useful life in years, called n, and add together every whole number from n all the way down to 1. So SD = n + (n−1) + (n−2) + … + 1. For example, if n is 5, you add 5 + 4 + 3 + 2 + 1. There's also a quick shortcut: n × (n + 1) ÷ 2 gives the same answer without adding each number by hand.
Read the result simply as a single fixed number for that asset. The larger the useful life, the larger this sum becomes. A project manager calculates it as the very first step when setting up an accelerated depreciation schedule, because every year's depreciation rate is built on top of it.
Think of it like counting the total number of steps on a staircase before you start climbing—you tally them up once at the bottom, and that single count guides how you measure each step you take afterward.
Say an asset has a useful life of 5 years. Adding the digits: 5 + 4 + 3 + 2 + 1 = 15. Using the shortcut to check: n × (n + 1) ÷ 2 = 5 × 6 ÷ 2 = 30 ÷ 2 = 15. Same answer. That 15 now becomes the denominator for every year's rate: 5/15 in year one, 4/15 in year two, and so on. You calculate it just once and use it for the entire depreciation schedule.
Every PMP formula explained free — plus worked examples and practice in PMP Math, and full timed mocks in the simulator.