Turns in, turns out
Duration is one division. Count the turns the drive can give, divide by the turns the movement uses in an hour, and that is the run. Everything else on the page is working out one or other of those two numbers from things you can actually measure.
On the weight side, turns available comes from geometry. A 2.25 inch barrel with 0.05 inch line winds on a 2.30 inch working circle, which is 7.23 inches of line a turn. Sixty inches of fall with the line doubled through a pulley is 120 inches of line, so 16.6 turns. At twelve hours a turn that is 199 hours, eight and a third days — the classic eight day clock, and you can see how little margin the classic figure has.
The pulley doubles the line, not the fall
This is the point people get backwards. When the weight hangs on a loop of line through a pulley, the line pays out twice as fast as the weight falls. So the same case height gives twice the running time. That is why long duration clocks use compound pulleys and why the weight on an eight day longcase is usually hanging from a pulley while a thirty hour one hangs straight off the line.
The cost is at the other end, and it is not free. A doubled line halves what reaches the great wheel from the same weight, so the weight has to be heavier to give the same effect. Whether the movement, the seatboard and the case will take that is a question for somebody looking at the clock.
Winding day
An eight day clock wound every Sunday is running with about a sixth of its turns in reserve. On the defaults that is 14 turns used out of 16.6, leaving 2.6 turns and about a day and a quarter. Miss a Sunday and it stops on Monday afternoon. That margin is the honest reason a lot of eight day clocks are wound weekly rather than every eight days, and the page prints it as a number rather than as advice.
For a spring clock the same section shows how much of the barrel you are actually using. Running only the middle of a wind is a very different regime from running it to the end, and both the rate and the arc will tell you so.
The number that scales everything
Hours per turn multiplies straight through to the answer. Get it from a stopwatch and a chalk mark on the great wheel, not from what the clock is described as. If the run comes out twice or half what you expected, or twelve times, it is almost always because that figure came from an assumption about the train rather than from the train.
Not covered
Nothing here is about how much weight or how much spring. Duration is geometry; whether there is enough power to drive the train through the escapement is a matter of friction, depthing, pivot condition and the state of the oil, and none of that is visible from a drum diameter. A clock that stops after five days when the arithmetic says eight has a power problem, not a duration problem.
Questions people ask
How do I work out how long a weight driven clock will run?
Work out how much line the drum can take up, divide by the line one turn pays out, and you have the turns available. Divide those by the turns the movement uses an hour. A 2.25 inch drum with 0.05 line, 60 inches of fall and a doubled line gives 16.6 turns; at twelve hours a turn that is 199 hours, about eight and a third days.
Why does a pulley double the running time?
Because the weight hangs on a loop and falls half as far as the line pays out. The same case height therefore gives twice as much line off the drum and twice the run. The trade is at the other end: the same weight on a doubled line delivers half as much to the great wheel, so the weight has to be heavier, and whether the movement will take that is a bench question.
How many turns should a mainspring barrel give?
That is a number to measure rather than look up. Wind it fully, mark the barrel, run it down and count the turns until it stops keeping time — which is before the spring is slack, sometimes by a full turn. Count it again after a service, because a clean train and a dirty one give up at different points.
How much does the weight drop in a day?
One turn of the drum pays out its circumference, and the weight drops that divided by the number of lines carrying it. On the defaults, two turns a day on a 7.23 inch working circle is 14.5 inches of line and 7.2 inches of weight drop, which over eight and a third days uses the whole 60 inches of fall.
Is an eight day clock really good for eight days?
The arithmetic often says a little over eight, and that is the point. With the defaults it comes to 8.3 days, so winding every Sunday leaves about a day and a quarter in hand and missing one Sunday stops it. That thin margin is why weekly winding is the habit even on clocks nominally rated for longer.