How should 8051 UART baud-rate error be calculated before changing the oscillator?

Use the baud-generator equation for the exact device, UART mode and selected timer clock. Calculate the nearest available integer divider, then compute the actual baud rate. Percentage error is 100 × (actual - target) / target. Include oscillator tolerance when assessing the transmitter and receiver together.

For example, an actual rate of 9,615 bit/s against a 9,600 target is about +0.156% error. That arithmetic alone does not establish a universal allowable limit; frame length, receiver implementation and the other endpoint's error matter. Consult both devices' specifications and test the intended operating range.

Verify the transmitted bit time with a logic analyzer or oscilloscope and use a recognizable byte pattern. Check framing settings and electrical levels separately from the baud calculation. A USB serial adapter operating at the wrong voltage can create failures that no divider adjustment will fix.