Calculating the wattage of an appliance with radial velocity of domestic electrical meter There's a heater who's wattage I want to work out.
I notice when it is not plugged into the mains socket, the dial on the electric meter for the house spins at x rpm.
When it is plugged in, it spins at y rpm.
I know that each revolution on the electric meter represents n joules of energy.
Is it possible to work out the watttage of the heater with this information?  If not what should I measure to be able to do so. (The heater has no markings on it and there's no box)
 A: If the meter is linear in disk speed (it should be!) it is sufficient to measure its angular velocity for before and after the heater is turned on. The meter constant (Joules-per-round) must also be known, which you mentioned in your question is known for your meter.
For constant angular velocity, the work (energy) and power are defined as:
$$W = k \cdot \omega \cdot \Delta t \quad \text{and} \quad P = c \cdot k \cdot \omega$$
where $\omega$ is the angular velocity of the disk in $\text{rpm}$ (revolutions per minute, $\text{rev/min}$), $k$ is the meter constant in $\text{J/rev}$ (Joules per revolution), and $\Delta t$ is the time period in $\text{min}$ for which energy is measured. Note that the scaling factor $c = \frac{1}{60}$ in $\text{min/s}$ is introduced in order to get the units right, i.e. to transform $\text{J/min}$ to $\text{J/s}$ which is $\text{W}$. I suggest you evaluate the units yourself to confirm that work $W$ is in Joules and power $P$ is in Watts.
The power for the two scenarios (before and after the heater is turned on) is:
$$P_1 = \frac{1}{60} \cdot k \cdot \omega_1 \quad \text{and} \quad P_2 = \frac{1}{60} \cdot k \cdot \omega_2$$
From this it follows
$$P_2 = P_1 \frac{\omega_2}{\omega_1}$$
and the power difference is
$$\Delta P = P_2 - P_1 = P_1 \frac{\omega_2 - \omega_1}{\omega_1}$$
Since $P_1 = \frac{1}{60} \cdot k \cdot \omega_1$ the above equation is simplified into
$$\boxed{\Delta P = \frac{1}{60} \cdot k \cdot (\omega_2 - \omega_1)}$$
This equation gives the estimated heater power from the measured angular velocities in $\text{rpm}$. I suggest you estimate the power for different heater operating points, e.g. 50% and 100% of the maximum output power. In general, the more measurements, the better the estimate!
