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Fuel Trim is the adjustment the engine computer (PCM) makes to the fuel mixture to maintain a balanced air/fuel ratio. Fuel trim is usually displayed as a PERCENTAGE reading on a scan tool.

For lowest emissions, the engine computer tries to keep the fuel mixture balanced around 14.7 to 1 (14.7 parts of air to one part fuel). If the air/fuel ratio is less than 14.7 to one (say 12 to 1), the fuel mixture is RICH. A rich fuel mixture can produce more power (up to a point) but it also increases fuel consumption and emissions. Conversely, if the fuel mixture is greater than 14.7 to one (say 16 to one), it is LEAN. A lean fuel mixture reduces fuel consumption but can also increase emissions if the air/fuel mixture is so lean that it fails to ignite and causes lean misfire.

The engine computer monitors the air/fuel ratio via the oxygen sensor(s) in the exhaust manifold(s). An oxygen sensor is essentially a RICH or LEAN indicator. When the engine is running lean (too much air and not enough fuel), the O2 sensor generates a low voltage signal that tells the engine computer more fuel is needed. When the engine is running rich (too much fuel and not enough air), the O2 sensor produces a higher voltage signal that tells the engine computer the engine is getting too much fuel and to cut back the fuel delivery. On vehicles that have an Wide Ratio Air/Fuel sensor (WRAF) or A/F sensor, the sensor tells the computer the exact air fuel sensor so the computer can increase or decrease the fuel delivery as needed.
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Accurate fuel trim values require an accurate feedback signal from the Oxygen sensor, otherwise the engine computer has no way of knowing whether the fuel mixture is running rich or lean.

When a cold engine is first started, it may take 10 to 30 seconds or more for the heaters inside the oxygen sensors to warms the sensors up to operating temperature. Until that point is reached and the fuel feedback control system goes into "closed loop", the fuel mixture is fixed at a predetermined value so no fuel trim adjustments are made. But once the Oxygen sensors are hot and the coolant temperature is high enough for the computer to go into closed loop, the computer starts to generate fuel trim values and make adjustments in the fuel mixture.

When the engine is shut off, the fuel trim values are retained in the computer's memory so the next time the vehicle is driven it can pick up where it left off. Erasing the computer's memory with a scan tool or by disconnecting the battery or the PCM power supply to clear codes also wipes the fuel trim values, which means the computer has to start learning the fuel adjustments all over again the next time the engine runs.