You didn't mention if it was elec/gas etc.

But if it's electric, the total yearly average cost is around $500, So 500/365= $1.34 per day aprox.

I wouldn't sweat it. If you did you would need another shower/bath

 

It's tanked elec and only a couple years old. Probably just decent as far as efficiency. I was just thrown off guard at how much I had to turn my shower handle when it got cold. It has probably a 120 sweep and I have it limited to about 80 deg.... and it was nearly scalding when I set it. Now in the winter it just makes the cut.

Bathroom ventilation I know plays a huge role. I once had a ~25 sf bathroom with no vent and I used incredibly little hot water. When I installed an exhaust fan, showers got much hotter.

 

You're in Florida? I don't think you can reliably say your issue is from seasonal cold water. Perhaps run some diagnostics on your WH

 

If you want to save a bit of heating cost, let the water in the bath cool before draining.
that way the heat from the water will transfer into your home heat.

 

And humidity (although limited depending on the size of the house). I find most hotels/motels to be very dry in the winter up here. When I was travelling a lot and living out of hotel rooms, I used to fill the tub with hot water and leave the door open before I went to bed to hydrate the air in the unit.

 

There shouldn't be much loss in the plumbing, especially since you say it's very short. Sounds like you have two questions. First, why do you need a higher percentage of "hot" water in the winter, and second, what's the difference in cost between a bath and a shower.

If by "tanked" you mean it's a traditional water heater of sufficient capacity to fill the tub, then it should have a thermostat which keeps it always at the same temperature. So that isn't the difference. If it were a point-of-use, on-demand or otherwise "tankless" system, then the temperature of the incoming water would make a huge difference. Our water comes from reservoirs, and in late winter it enters the house not too far above freezing.

As for relative cost, that's pretty easy to estimate. Get a rough GPH estimate for your shower, either from the shower head spec sheet or by measuring how long it takes to fill a gallon jug. Likewise, estimate the volume of water you use in your bath. The difference in cost should be about the same ratio as the difference in water volume used.

 

I guess I threw in the shower comment without really tying it to the question. I was commenting on how much colder the water feels. There has to be some heat loss somewhere. It could be that the the cooler ambient air has a big effect. The house is probably 10 deg cooler - that makes me colder (requiring hotter water) and probably cools the water more between the shower head and me.

I have a traditional "tanked" water heater, so supply temp should be the same. It just seems like we're (me at least) using double the volume of hot water that we did in the summer.

 

Assuming you're looking for the electricity cost for your bath or shower, maybe this will help. To raise 50 gallons of water 50 degrees F (from 50F to 100F) requires 6.2 kWh. Excluding heat losses between the WH and the tub (which should be fairly minor), and electrical transmission losses (which are negligible).

Water heating calculator

 

I've had clients who wanted a soaking tub installed without an internal heater. I try to talk them out of it with the theory that the tub holds possibly 40 gallons of hot water. That's all you have available at any given time normally with a medium water heater. You deplete the water heater, it takes a while to get it all back, while your tub water is slowly getting tepid.

 

And remember your cold water, which is mixed with the hot at the valve, is also colder in the winter than summer, requiring your handle to be more towards the hot to get to your comfort zone .

 

How much does a hot bath cost?

That's a good question.

My tub, to the depth I would fill it (if I actually took a bath instead of shower) would hold 82 gallons.
It's December now, so I will put incoming water temperature at 50 deg and final temperature at 100 Deg.
That takes 10 kWhrs of energy. I have a gas water heater, so that would be 2.86 cubic meters assuming 95% efficiency (new condensing water heater).
2.86 cubic meters would cost me about $C1.43 = $US1.04

But wait, there's more.
Cost of the water and sewage charge is about $C.0145/gal, so 82 gallons cost $C1.19 = $US 0.87

So cost of a hot bath for me is about $C2.62 = $US1.91

 

It's December now, so I will put incoming water temperature at 50 deg and final temperature at 100 Deg.

Oh that's an excellent point. The cold water is a good deal colder than in the summer. I'll take some measurements throughout the year to see what the difference is.

 

Figure out how much water you use.
Get the water price for that quantity from your water bill if you have a public supply.
Measure the incoming water temperature.
Measure the water temperature you use for your shower.
Water weighs about 8.33 lbs. per gallon. Calculate the weight of the water you use.
Raising 1 pound of water 1 degree F uses 1 BTU of heat. Do the math: water weight x degrees raised = BTUs of energy used.
Electric water heater is 100% efficient. 1 kw = 3412 BTU. Figure out the electric usage and get the cost from your electric bill. Add 10% for standby and pipe losses.
Gas water heater: Gas is often sold by the therm, which is 100,000 BTU. Do the math then add 30% for an old tank water heater and piping, 20% for a newer tank water heater and 15% for a tankless.
Add the water cost to the heat cost. It will be reasonably close. I did the calculation for a 325,000 gallon swimming pool and it cost $2500 to replace the water and bring it up to temperature.
Our water lines are 4 feet deep and the temperature at that depth is fairly constant year round. Water is a little cooler in the winter. In warm climates with shallow water piping the water temperature varies more with the weather.

 

No clue about mixing valves at the tank. The shower I know is a pressure balance valve.

Here is the master bedroom heater in a garage closet. Shower is on other side of right wall and bath is on other side of back wall.

And here is other bedrooms heater.