Antenna gain relative to input power
An antenna gain of 2.54dBi means it has 2.54dB greater launch power in its maximum direction than does an isotropic antenna. That's what the 'i' in dBi means, taking as a reference the isotropic antenna. 

A physical isotropic antenna doesn't exist, it's what you get if you theoretically spread all your input power evenly over the full \$4\pi\$ steradians around it. Thus even a simple dipole has a gain of about +3dBi in its maximum directions.

If the input power is 1 watt, then it outputs +2.54dBW/\$4\pi\$ per steradian in its maximum direction. If the input power is 4 watts, it outputs +8.56dBW/\$4\pi\$ steradian. An increase of 4x in power is an increase of 6.02dB