The one line of arithmetic under all of it
To land at a mixed temperature you need a fraction of hot equal to the target minus the cold, divided by the hot minus the cold. If the hot supply is 135, the cold is 55 and you want 104 at the head, the fraction is 49 over 80, which is about 61 percent. At a 2.0 GPM head that is 1.22 GPM of hot and 0.78 GPM of cold. Everything else on this page is that fraction applied to a flow, a duration or a tank.
The formula is a straight energy balance and it holds because water has effectively the same specific heat across this range. It is also the reason a mixed temperature can never exceed the hot supply: the fraction would have to be more than one, and there is no water hotter than hot to make up the difference. When a shower will not get hot enough, the answer is never at the mixing valve.
Why a hotter supply stretches the tank further
This is the part that catches people, because the tank holds the same gallons either way. What changes is how many of those gallons a shower consumes. From a 135 degree supply a 104 degree shower is 61 percent hot; from a 120 degree supply the same shower is 75 percent hot. On a 50 gallon tank with 75 percent counted as usable, that is 37.5 gallons of hot water lasting about 31 minutes in the first case and about 25 in the second, at the same 2.0 GPM and the same temperature at the head.
The energy has not appeared from anywhere. Each hot gallon from the hotter tank carries more heat, so fewer of them are needed for the same mixed result, and the arithmetic checks: 61 mixed gallons at a 49 degree rise is the same quantity of heat as 37.5 hot gallons at an 80 degree rise. Storing hotter is a way of storing more energy in the same volume, and effective capacity is what it buys.
What it also buys is a hotter tap, and that is a safety question rather than a capacity one. It is dealt with in its own section below, not folded into this one.
Cold supply temperature is a season, not a constant
Incoming water in most of the country swings by fifteen to twenty-five degrees between February and August, and the hot fraction moves with it in a way that is easy to feel and hard to attribute.
| Cold supply | Hot fraction for 104 °F from a 135 °F supply | Hot GPM at a 2.0 GPM head |
|---|---|---|
| 45 °F — deep winter mains | 66% | 1.31 |
| 55 °F — spring and autumn | 61% | 1.23 |
| 65 °F — summer | 56% | 1.11 |
| 75 °F — late summer, shallow lines | 48% | 0.97 |
That is a third more hot water per shower in February than in August for exactly the same shower, which is the real reason a heater that coped all summer starts running out in winter. It is also why the water heater sizing calculator asks for inlet temperature rather than assuming one, and why a sizing decision taken in July can be a size short.
Storage temperature, scald risk and where the decision belongs
Everything above says that a hotter supply gives more usable hot water from the same tank. That is true and it is only one side. Hotter stored water also arrives at every tap in the building hotter, and the time to a serious scald falls very steeply with temperature — steeply enough that the safe contact time at one setting can be a small fraction of the safe contact time a few degrees lower. Small children and older adults are burned faster than a healthy adult at the same temperature and are least able to move out of the way, which is why the risk is not distributed evenly across a household.
Pulling in the other direction, water held at lower temperatures sits in a range where bacteria including Legionella can multiply in stored water, and that risk rises in low-use buildings and in long dead-leg pipe runs. Neither concern is imaginary, and no single storage temperature resolves both.
The way the trade is normally engineered is to separate the two questions rather than compromise between them: store at whatever the bacterial side calls for, and bring the delivered temperature down at the outlet with a thermostatic mixing valve so the tank runs hot and the tap does not. That is a device selection and a plumbing modification, not a thermostat adjustment. This page deliberately names no temperature as safe, because the right answer depends on the system, who lives in the building and what your jurisdiction requires. Take it to a plumber who can look at the installation.
What tankless changes and what it does not
A tankless heater has no stored volume, so the runtime section of this page stops being about a tank and becomes a question of whether the unit can supply the hot fraction indefinitely. Put its capability in the recovery field expressed in gallons per hour — a unit good for 4 GPM at your temperature rise is 240 GPH — and set the tank size to zero. If the recovery figure exceeds the hot draw the water does not run out; if it does not, the unit modulates and the temperature at the head falls, which feels like the shower going cool rather than the shower stopping.
What tankless does not change is the wait. The volume of water in the pipe between the heater and the shower still has to be pushed out before hot arrives, and on a long run that is the same twenty or forty seconds it always was — sometimes longer, because the burner has to fire first. The recirculation payback calculator covers that delay and what removing it costs.
Questions people ask
How do I work out the hot to cold ratio for a target temperature?
Subtract the cold supply temperature from the target, then divide by the hot supply minus the cold supply. That gives the fraction of the flow that has to be hot; the rest is cold. For 104 at the head from 135 hot and 55 cold, it is 49 divided by 80, or 61 percent hot. Multiply by the flow rate for the split in GPM. The same formula runs backwards if you know the two flows and want the resulting temperature: multiply each temperature by its share of the flow and add them.
Why does my hot water run out faster in winter?
Because the incoming cold water is colder, so the same comfortable shower needs a larger share of hot. A 104 degree shower from a 135 degree supply is 61 percent hot when the mains are at 55 and 66 percent hot when they are at 45, which is roughly a tenth more hot water for an identical shower. The heater also has a larger temperature rise to work against, so its recovery rate falls at the same time. Two effects that both point the same way, in the same season, are why a system that was comfortable in September starts running short in January.
How long will a 50 gallon tank last in the shower?
Not 50 gallons worth, for two reasons. A tank does not deliver its full nominal volume at temperature, because cold entering the bottom mixes upward as you draw and the delivered temperature falls before the tank empties — seventy to eighty percent is a common working allowance. And the shower is only drawing the hot fraction, not the whole flow. A 50 gallon tank at 75 percent usable gives about 37.5 gallons of hot; a 2.0 GPM shower blended to 104 from a 135 supply draws 1.23 GPM of hot, so about 31 minutes, plus whatever the heater recovers while you stand there. Change the supply temperature and that number moves a long way.
Does a low-flow shower head save hot water or just water?
Both, in the same proportion. The hot fraction is set by the three temperatures and does not care about flow rate, so cutting the head from 2.5 to 2.0 GPM cuts the hot draw by the same twenty percent it cuts the total. The tank then lasts twenty-five percent longer at the same temperature, and the heat carried down the drain falls by a fifth. What a low-flow head does not change is the wait at the start, which gets slightly longer, because the same volume of cold sitting in the pipe now has to be pushed out at a lower flow rate.
What is a thermostatic mixing valve and do I need one?
It is a valve that blends hot and cold to a set delivered temperature and holds that temperature as the supply pressures and temperatures move around it, which an ordinary mixer does not. It is the standard way of separating storage temperature from delivery temperature, so a tank can be kept hot for the bacterial reasons while the water reaching a tap is not as hot as the tank. Whether one is required, where it goes, and what it is set to are decisions that depend on the installation, the occupants and your local requirements, and it is fitted into live water piping. That makes it a conversation with a plumber rather than a purchase, and this page will not name a setting for it.