pretty close to 1 square inch for 250W
4sqin for 1kw
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To calculate the no load current from transformer & core loss is also calculated.
It is the current transformer core meant for metering.
there are several losses in a transformer that prevent it from attaining 100% efficiency. One is core loss, which can be divided into Hysteresis losses, Eddy currents and Magnetostriction loses. see for more details http://en.wikipedia.org/wiki/Transformer#Energy_losses
A 'core type' transformer core is one in which the primary windings and secondary windings are placed around each of the limbs, as opposed to a 'shell type' core, in which the two windings are placed across the centre core. A core-type core is a magnetic circuit equivalent to an electric series circuit, whereas a shell-type core is equivalent to an electric parallel circuit. This is better answered with a diagram, so I suggest that you do a search on the internet.
The transformer core is ferromagnetic in order to focus and concentrate the magnetic fields generated in the windings. This improves coupling and increases inductance.