Connecting a 12V relay to Arduino

Step 4 Calculating R1

You can find the value of hfe in your datasheet:
Mine says for BC548 its 75 at 10mA at 10V. Its not very precise cause its very difficult to build transistor with a accurate hfe.

hfe = Ic / Ib

We know hfe and Ic so lets calculate Ib:

Ib = Ic / hfe

For BC548:

Ib = 0.03 A / 75
Ib = 0.0004 A => 0.4 mA

Due to Ohms Law:

R1 = U / Ib
R1 = 5V / 0.0004 A
R1 = 12500 Ohm
This is not very accurate to so we use 10kOhm.