A float is a volume, not a capacity
Put a sealed box in fresh water and it sinks until the water it has pushed out of the way weighs the same as everything sitting on it. That is the whole mechanism. Fresh water is 62.4 pounds per cubic foot, so a cubic foot of float under the surface holds up 62.4 pounds, and a float that is half under is holding up half of what it would hold up fully under.
Which is why the useful readout is freeboard rather than weight. You cannot see a pound. You can see, from thirty feet away, that the deck used to sit a hand-width above the water and now sits two fingers above it, and that observation is a direct measurement of how much displacement you have left. A dock tells you it is loaded up long before anything on it fails, and it tells you in inches.
The defaults, worked all the way through
Four floats at 48 by 30 by 16 inches. Each is 23,040 cubic inches, which is 13.333 cubic feet, so the set is 53.33 cubic feet. Fully submerged in fresh water that is 53.33 times 62.4, or 3,328 pounds of displacement — the ceiling, and a number the dock never actually reaches because the deck goes under first.
The dead load is 900 pounds of frame and decking plus four floats at 60 pounds, so 1,140 pounds. Dividing by 62.4 gives 18.27 cubic feet that have to go under water. The plan area of four floats each 48 by 30 inches is 40 square feet, so the floats sit 18.27 divided by 40 equals 0.457 feet down — 5.48 inches — leaving 10.52 inches of the 16 inch float above water.
Add 800 pounds of people and gear and the total is 1,940. That needs 31.09 cubic feet under, which over 40 square feet is 9.33 inches of draft and 6.67 inches of freeboard. Every inch the floats go down is 40 square feet times 62.4 divided by 12, or 208 pounds, so the last two inches of that freeboard are worth about 416 pounds. That is the number worth carrying around: on this dock, one inch is roughly two hundred pounds.
Ratings, and what a rating actually says
A float sold as an 830 pound float is making a claim about its displacement. Eight hundred and thirty pounds divided by 62.4 is 13.30 cubic feet, which is the 13.33 cubic foot box above to within a quarter of a percent. If a stated rating and the physical volume disagree, one of two things is happening: the rating is quoted at some partial submersion rather than at full, or the float is not the shape of the box it appears to be. This page shows both numbers and refuses to draw a conclusion from the gap, because reconciling them is the maker job and not arithmetic.
Salt water changes the answer by about two and a half percent — 64 pounds per cubic foot instead of 62.4 — which is small and goes the friendly direction. Brackish water sits between the two and varies with the tide and the river, which is a reason to work from the lower figure rather than the flattering one.
Where the even-load assumption breaks
The draft calculation divides the load over the whole plan area, and that is only true if the load is spread over the whole plan area. It usually is not. Four people on one corner of a section put most of the added weight into one float, which goes down much further than the average says, while the far float comes up and stops contributing. A dock that reads six inches of freeboard on paper can put a corner rail in the water with nobody having exceeded any total.
The same thing happens with a point load that lives on the dock permanently — a bench, a locker, a fish cleaning table, a cradle for a small boat. It is in the dead load total and it is also in one place, and the arithmetic here sees only the first of those.
Anything built in, on or over water is permitted work in most places, and the permission usually comes from more than one desk. The state environmental or natural resources agency, the Army Corps of Engineers district for the waterway, the local building department, and on many lakes the utility or authority that holds the shoreline licence all have a say, and what each one wants is different from one state and one waterbody to the next. None of it is on this page. Start with the state agency and the Corps district for the water you are on, and get a marine contractor who works that lake or that stretch of river involved before the arithmetic turns into an order.
Questions people ask
How many dock floats do I need?
That question has no arithmetic answer, because it depends on a freeboard you choose and a load you choose, and neither comes from a calculator. What arithmetic gives you is the chain: each cubic foot of float under fresh water holds 62.4 pounds, so total the dead weight and the live load you want to carry, divide by 62.4 to get the cubic feet that must go under water, and compare that with the volume you are proposing to put down there. The gap between that submerged volume and the total volume of the floats is your freeboard, expressed as a volume. Deciding how much of that gap you want to keep is a judgement about wake, wind, ice and what the dock is for, and it belongs to whoever is responsible for the structure.
What is freeboard on a floating dock and why does it matter more than weight?
Freeboard is the height of the deck, or the top of the float, above the water surface. It matters more than a weight figure because it is the one thing you can actually observe, and it is a direct reading of how much displacement is left in reserve. A float does not fail at a weight; it goes further under as weight goes on, and it keeps going until either the deck is awash or something in the frame gives. Since the relationship is linear, freeboard also converts straight back into pounds: multiply the plan area of the floats by 62.4 and divide by 12 and you have the pounds per inch of settlement, which on a typical eight by ten section is a couple of hundred.
Does salt water hold a dock higher than fresh?
Slightly. Salt water runs about 64 pounds per cubic foot against 62.4 for fresh, so the same float displaces about two and a half percent more, and the same dock floats about two and a half percent shallower. On a section drawing nine inches that is a bit over two tenths of an inch. It is worth getting right in the arithmetic and it is never the thing that decides a design. Brackish water sits between the two and moves with the tide and the river stage, so if you are on it, the honest choice is to work at the fresh water figure and treat the extra as something you do not count on.
Why does one corner go under when the total load is nowhere near the limit?
Because the total load was never the thing that mattered at that moment. The draft arithmetic spreads the load over the whole plan area of every float, and a group of people standing on one corner does the opposite of that: most of the added weight goes into the nearest float, which settles far more than the average, while the float diagonally opposite unloads and stops carrying its share. The section tips, the low corner takes water over the deck, and the totals on paper are all still comfortable. Distribution is not in this arithmetic and it is often the thing that decides how a dock behaves.
Can this tell me whether my dock is safe or overloaded?
No, and it does not try. It runs two divisions on numbers you supplied and reports the result. Whether the flotation is adequate, whether the frame will take the load that flotation implies, whether the freeboard suits your water, whether the floats are attached in a way that holds under an uneven load, and whether the whole thing is right for the ice and wake it will see are all questions about a specific structure in a specific place. They belong to a marine contractor or an engineer who can look at it. Building over water is also permitted work in most places, and the permitting bodies frequently have their own requirements about what may be built and how.