MotionLab

Buoyant Force Calculator

Why ships float and submarines sink — the upward push of displaced fluid.

Fluid density (kg/m³)

Displaced volume (m³)

Gravity (m/s²)

Buoyant force (N)

490.5

F = ρVg

What you entered

Fluid density (kg/m³): 1000Displaced volume (m³): 0.05Gravity (m/s²): 9.81

1
F = ρ × V × g
1000 × 0.05 × 9.81= 490.5 N

Result

Buoyant force (N): 490.5

An object displacing 0.05 m³ of fluid (ρ = 1000 kg/m³) experiences a buoyant force of 490.5 N.

Buoyant force on submerged volumes in water

Archimedes' principle: the upward force equals the weight of fluid displaced, which is fluid density times volume times g. These use 9.81 m/s2.

Fluid density (kg/m3)	Volume displaced (m3)	Buoyant force (N)	Fluid
1000	0.001	9.810	Fresh water, 1 litre
1000	0.01	98.100	Fresh water, 10 litres
1000	1	9810.000	Fresh water, 1 cubic metre
1025	0.05	502.763	Seawater, 50 litres
1.225	1000	12017.250	Air, 1000 cubic metres

The force depends on the fluid displaced, not on what the object is made of - a kilogram of lead and a kilogram of cork displacing the same volume feel the same upward push, and only their weights differ. That is why an object floats when its average density is below the fluid's. The last row is why airships work: a thousand cubic metres of displaced air produces over 12 kilonewtons of lift, enough to hold up about 1.2 tonnes. Seawater at 1025 kg/m3 is denser than fresh, which is why swimmers float more easily in the sea.

Archimedes' eureka moment

The buoyant force equals the weight of the fluid displaced by the object — this is Archimedes' principle, and it explains why a steel ship floats (it displaces a huge volume of water) while a steel ball sinks (it displaces very little relative to its weight).

Neutral, positive, and negative buoyancy

If the buoyant force equals the object's weight, it hovers (neutral buoyancy) — submarines adjust this by filling or emptying ballast tanks, and scuba divers fine-tune it with a buoyancy compensator vest.

Frequently asked questions

A 0.5 m³ object is fully submerged in seawater (ρ = 1025 kg/m³). What buoyant force acts on it?

F_b = ρVg = 1025 × 0.5 × 9.81 = 5,028 N. If the object weighs less than 5,028 N (mass < 512 kg), it floats in seawater. Seawater's higher density vs fresh water (1025 vs 1000) gives about 2.5% more buoyancy.

How do submarines control their depth?

Submarines have ballast tanks that fill with water (increasing weight) to dive and expel water with compressed air (decreasing weight) to surface. At neutral buoyancy, the sub's total weight exactly equals the buoyant force, and it hovers at constant depth.

Why is it easier to float in the Dead Sea?

Dead Sea water has density ~1,240 kg/m³ (vs. ~1,025 for normal seawater) due to extreme salt content. The increased density produces ~21% more buoyant force, so your body displaces less water before the upward force matches your weight — you float higher.

How is this different from the buoyancy calculator?

This calculator directly computes F_b = ρVg and can compare it to weight. The buoyancy calculator may focus on whether an object sinks or floats. Both apply Archimedes' principle — use whichever inputs match your problem.

Does buoyancy work in gases too?

Yes — hot air balloons and helium balloons float because the surrounding air provides buoyant force. A hot air balloon heats air inside to lower its density below ambient air, creating net upward buoyancy. The same F = ρVg formula applies, just with air density (~1.225 kg/m³).