How Much Lighter Is a Stone Under Water?

How much lighter does a stone get once it is under water? For ordinary rock in fresh water, a bit more than a third. A 50 lb stone the size of a 2.25 gallon bucket weighs 31.22 lb while it is fully submerged, because the water is carrying 18.78 lb of it, or 37.6 percent. Pull it out and the missing pounds come straight back onto the rope.

That is the short answer. The longer one is more useful, because the share is not fixed. It moves with the fluid, it moves a great deal with the material, and it is the same number that decides whether something sinks at all, how far a spring scale drops and how a float bobs when you push it down. One ratio runs through all of it.

Where the 18.78 pounds go

Water does not know what the stone is made of. It only knows how much room the stone takes up. A submerged object pushes aside exactly its own volume of water, and the water pushes back up with the weight of what it lost. That is Archimedes' principle, and it is the whole mechanism.

A US gallon of fresh water weighs 8.345 lb. The stone fills 2.25 gallons, so the water pushes up with 18.78 lb, whether the stone weighs fifty pounds or five hundred. Its own weight only decides what is left over.

Broken down line by line, this is the arithmetic the buoyancy calculator runs:

The last row is the one to remember. A density of 2.663 times that of water, or 166.2 lb/ft³, is in the range of granite and much common rock. And the share carried is simply one divided by that ratio: 1 / 2.663 is 37.6 percent. Know the ratio, and you know the loss without weighing anything.

What if the conditions change?

What if it is in the ocean, not a lake?

Seawater is denser, about 1,025 kg/m³ against 1,000, so the same stone pushes aside 19.25 lb of it instead of 18.78. Under the sea it weighs 30.75 lb, and the water carries 38.5 percent. Half a pound makes no practical difference to a stone. The same 2.5 percent of extra lift matters far more to a swimmer or a boat, whose margin between floating and not is small to begin with.

Push the salt further and the gap opens. In Dead Sea water, at 1,240 kg/m³, the stone weighs 26.72 lb and nearly half of it, 46.6 percent, is carried. In gasoline, which is lighter than water, only 28.2 percent: 35.92 lb is left.

What if it is steel instead of stone?

Fifty pounds of steel takes up far less room. At 7,850 kg/m³ it fills only 0.7632 gallons, so the water can only push back with 6.369 lb. Under water it still weighs 43.63 lb. The share carried falls to 12.7 percent, because 1 / 7.85 is about an eighth.

That is why a stone feels surprisingly light when you lift it off a riverbed and a steel anchor does not. Same weight in air, very different weight in the water, and the only thing that changed is how much space each one occupies.

What if you weigh it with a luggage scale?

A hanging luggage scale is a spring, and a spring reads force by stretching. Suppose the spring inside is rated at 25 lbf/in. Hang the stone from it on the bank and the spring stretches 2 in. Lower the stone until it is fully under water, without letting it touch the bottom, and the stretch drops to 1.249 in.

The difference, 0.751 in, is the buoyant force in disguise: 18.78 lbf divided by the spring rate. Hooke's law is linear, so the spring does not care whether the missing force was taken by water or by a hand under the stone. It simply stretches in proportion to whatever is left. The energy the spring holds falls faster than the stretch, from 4.167 ft·lbf to 1.624 ft·lbf, because stored energy goes with the square of the stretch.

This is also the practical way to measure a stone's density at home. The reading in air divided by the drop gives the ratio directly: 50 / 18.78 comes to about 2.66, the same figure the table above arrived at from the volume.

What if the object floats and bobs?

Change the stone for something lighter than water, a float, and it no longer sinks. It settles at a depth, called the draft, where the water it pushes aside weighs exactly as much as it does. Push it down and let go, and it bobs.

Here the arithmetic turns out to be the spring's. For a float with straight sides, every extra inch it is pushed down displaces more water, so the water acts like a spring whose stiffness is the weight of water per inch of depth. Put that into the spring formula and the mass cancels out: the period of the bob is T = 2π × √(draft / g), the same sag rule that governs a weight hanging on a real spring. A float sitting 4 in deep bobs once every 0.6395 s. At 2 in deep it is 0.4522 s, at 8 in deep 0.9044 s: four times the draft, twice the period.

Pushed 1 in down and released, with that 0.64 s period, the float passes its resting level a quarter of a cycle later, after 160 ms, at its top speed of 0.8181 ft/s. At the top and the bottom of each bob it is accelerating at 0.2496 g, about a quarter of the pull of gravity. A real float bobs a little slower than this, because it has to push some of the surrounding water along with it, and in practice the bobbing usually fades quickly. The simple model is still the right first estimate.

What if you want to float the stone on drums?

Turn the question around. To hold the stone up at the surface, something has to give back the 31.22 lb it weighs under water. A sealed container does it by pushing aside 3.741 gallons of fresh water, so a single 5 gallon pail would do it with room to spare, less the weight of the pail itself.

The same arithmetic sizes a raft or a small dock. Each drum gives the weight of its own volume in water, at 8.345 lb per gallon, before its own weight and whatever sits on it:

Those are the figures at the moment the top of the drum goes under, which is exactly where nobody wants a raft to sit. Subtract the drums themselves and the deck, then plan to use only part of what is left, so there is freeboard for waves, people moving around and the day somebody brings a cooler.

All the cases side by side

The table puts the same 50 lb weight in every situation above, with the reading the 25 lbf/in luggage scale would show in each. The share column is the one that explains the rest.

Read down the share column and the pattern is plain. It depends on the fluid's density divided by the object's, and on nothing else: not on the weight, not on the shape, not on gravity. Put the whole scene on the Moon and every force in the table shrinks by the same factor, while the percentages stay exactly where they are.

So, how much lighter?

For most rock in fresh water, about 37 to 38 percent, a little more in the sea and a lot more in very salty water. For steel, barely an eighth. The quick rule is to divide one by the object's density relative to water, and that single ratio also tells you whether it will float, how far a spring scale will drop and, for a float, how fast it will bob. If you only remember one thing, remember that water weighs the space, not the thing.

Tools discussed in this article

Buoyancy Calculator - Archimedes' principle for any sealed object in nine fluids: the buoyant force, whether it floats or sinks, how deep it sits, how much more it can carry, and what it weighs under water, in gallons, cubic feet, pounds or metric. Ready-made for a 55 gallon drum and the other sizes in the table above.

Hooke's Law Calculator - the force, the spring constant or the stretch, from the other two, in lbf/in, N/mm or N/m, with the energy stored, the sag and bounce of a hung mass, and the same load on springs in series or in parallel.

Simple Harmonic Motion Calculator - position, velocity and acceleration of any oscillator at any moment, from its amplitude and its period or frequency, with the whole cycle tabulated in eighths and the energy split into potential and kinetic.

More Physics tools

Pendulum Period Calculator - the other classic oscillator, with the exact period at any amplitude.

Force Calculator - weight and mass kept apart, the step before comparing a weight with a lift.

Work Calculator - the work it takes to haul a load up through the water and then out of it.

Potential Energy Calculator - what a lifted stone holds once it is out of the water and climbing.

Kinetic Energy Calculator - the energy of a bobbing float at the moment it passes its resting level.

Momentum Calculator - mass times velocity, and what a collision cannot destroy.

Mechanical Power Calculator - how fast a winch has to do the lifting work, in watts and horsepower.

Torque Calculator - the turning force a winch handle or a fastener demands.

Kinetic Friction Calculator - what a surface takes back when a load is dragged instead of lifted.

Thermal Expansion Calculator - how much a length or a volume grows with temperature, liquids included.

Specific Heat Calculator - the energy it takes to warm a mass of water, or anything else, by a given amount.

Thermal Conductivity Calculator - heat loss through a wall, with the R-value in both unit systems.