To make lifge easier, I've provided a Coil Making Calculator that will do much of the folowing maths for you. But for those interesting in number crunching, let's start with Power.
Physics gives us the formula P = IV (power = current x volts). So let's say the Voltage is 230 and the current is 10 Amps. This would give us a potential power rating of (230 x 10) 2300 Watts (2.3 KW).
Physics also gives us another useful Power formula which is P = I²R (Power = Current Squared x Resistance). So let's say our current is still 10 Amps and our resistance is 23 Ohms. This would give us a potential power rating of (10² x 23) 2300 Watts (2.3 KW).
If we don't know the voltage, we can turn to Ohms Law formula V = IR (Voltage = Current x Resistance). So with current of 10 Amps and resistance of 23 Ohms we could establish, in this example, a voltage of (10 x 23) 230 Volts.
If the resistance of a circuit is unknown, we can again turn to Ohms Law and rearrage the formula to give us R = V / I (Current = Volts / Resistance). So as an example, Volts of 230 divided by a Current of 10 Amps gives us (230 / 10) 23 Ohms.
Where could also rearrange the Power formula to calculate resistance, ie R = P / I² (Resistance = Power / Current Squared). So as an example, Power is 2300 Watts divided by a Current of 10 Amps squared gives us (2300 / 10²) 23 Ohms.
Just as with resistance, we can use Ohms Law and rearrage the formula to give us current with I = V / R (Current = Volts / Resistance). So as an example, Volts of 230 divided by a resistance of 23 Ohms gives us (230 / 23) 10 Amps.
Rearrange the Power formula to calculate current with I² = P / R (Current Squared = Power / Resistance). So as an example, Power is 2300 Watts divided by a resistance of 23 Ohms gives us (2300 / 23) 100 Amps - and when we get the square root of this it gives us 10 Amps.
The last thing we need to consider is the length of the wire. If you're making a coil, you'll need to calculate the resistance needed and from that it's a simple matter of calulating the length. L = R / r (which is a terrible made up formula meaning Length = Resistance / Resistance per unit length). For example, we know our resistance is 23 Ohms and I mentioned earlier the given resistance per meter on my wire is 1.73 Ohms (23 / 1.73) which gives us a length of wire of 13.2 metres required.
To make lifge easier, I've provided a Coil Making Calculator that will do much of this maths for you. To use it, click here.
Stretching The Coil
One last thing - before using the coil it must be stretched. If you fail to stretch it you've basically got a solid length of metal with no resistance.
Stretching is easy enough. Simple securely grab each end and pull. You may need to do this a few times. It's generally considered a bad idea to stretch the coil longer than three times its original (unstretched) length.