Estimation answers the question every project manager fears: how big is this software, how long will it take, and how many people will it need? Two size measures dominate. Lines of code (LOC) counts what programmers write, but it depends on the language and cannot be known before coding. Function points count what users see: inputs, outputs, inquiries, files and interfaces. Because function points are counted from requirements, they can be estimated before a single line is written, and they do not change when the language changes.
COCOMO turns size into effort. The Basic COCOMO formula is Effort = a × (Size)^b person-months, where Size is in thousands of lines of code (KLOC) and the constants a and b depend on the project mode: organic (small, experienced team, familiar problem), semi-detached (medium complexity), or embedded (tight constraints, for example flight control software). The exponent b is larger than 1, which is the key insight: effort grows faster than size. Doubling a project more than doubles the effort, because communication and coordination grow with team size.
Worked example — reading a COCOMO estimate. A 20 KLOC embedded project uses a = 3.6 and b = 1.20. First compute 20^1.20. Since ln 20 ≈ 2.996, multiply by 1.20 to get ≈ 3.595, and e^3.595 ≈ 36.4. Effort ≈ 3.6 × 36.4 ≈ 131 person-months. The same 20 KLOC in organic mode (a = 2.4, b = 1.05) would give about 2.4 × 20^1.05 ≈ 2.4 × 23.7 ≈ 57 person-months. The mode matters as much as the size: identical code, very different effort, because the constraints differ.