I just was away from home for 14 days and I turned off my 50 gal electric water heater. May have saved me about $20-$30 on the electric bill.
I think it is more like $1, depending on your electric rates and age of your electric water heater:
I took a look at the cheapest new 50 gallon electric water heater at homedepot.com. It has a UEF of 0.93 and the Energy Guide shows an estimated annual kWh usage of 3493 kWh. Assuming those are based on the same test conditions, then 7% of that annual kWh usage is losses, or 245 kWh/year. That works out to a loss rate of 0.67 kWhr/day, or 95 BTU/hr, which we can assume worst case are all standby losses. I'm also going to assume that the operational delta T of the tank is 70F and that the actual tank volume is 45 gallons.
If I did my exponential decay math correctly, after 14 days the tank would have cooled off to only 21F above ambient. So to reheat it to 70F above ambient took (49 F)*(45 gal)*(8.33 lbs/gal) = 18400 BTUs, or 5.4 kWhrs. But you avoided 14*0.67 = 9.4 kWhrs of standby losses, so you saved a net 4 kWhrs. Depending on your electric rates, that's $0.40 to $1.
Cheers, Wayne