Checking the transmission fluid when the engine is running is important because:

• When the engine is running, the transmission fluid heats up and expands to its normal operating temperature and pressure, giving a more accurate reading of the fluid level. If checked when the engine is off and cold, the fluid will settle and give an inaccurate, often lower reading because the fluid drains out of components like the torque converter into the pan.
• The running engine activates the transmission pump, circulating the fluid throughout the transmission system (including the torque converter, cooler, and clutch packs). This circulation ensures the fluid is properly distributed and reflects the actual operating level.
• Checking with the engine running while the fluid is at operating temperature also provides diagnostic information from the fluid's color, consistency, and smell, which can indicate transmission health or issues.
• For automatic transmissions, the fluid level depends on pressure and circulation, which only occurs when the engine is on. Manual transmissions typically require checking fluid levels with the engine off.

In summary, checking transmission fluid with the engine running ensures an accurate fluid level reading under normal operating conditions and helps in detecting potential transmission problems before they become severe.