Density altitude is lower in which scenario?

• A. 15°C at 7,000 ft PA
• B. -18°C at 9,000 ft PA
• C. 4°C at 5,500 ft PA
• D. -9°C at 3,000 ft PA

Answer: (B)

Density altitude is how high the air’s density corresponds to in the standard atmosphere. Cold air is denser, so cooler conditions lower density altitude, while warm air makes the density altitude higher. A handy way to estimate is DA ≈ PA + 120 × (OAT − ISA at that altitude). The ISA temperature drops with altitude, so you can compare each scenario quickly.

• At 7,000 ft, ISA is about 1°C; actual is 15°C, which is warmer than ISA by ≈14°C. That raises density altitude above the pressure altitude by roughly 1,680 ft, giving a DA around 8,700 ft.

• At 9,000 ft, ISA is about −3°C; actual is −18°C, which is 15°C cooler than ISA. That lowers density altitude below PA by about 1,800 ft, giving a DA around 7,200 ft.

• At 5,500 ft, ISA is about 4°C; actual matches ISA, so DA is about 5,500 ft.

• At 3,000 ft, ISA is about 9°C; actual is −9°C, which is 18°C cooler than ISA. That lowers density altitude by roughly 2,160 ft, yielding a DA around 840 ft.

Thus, the scenario with the coldest air at the lower elevation produces the lowest density altitude. In this set, that is the -9°C at 3,000 ft PA case.