Torricelli Velocity Calculator
How fast does water jet out of a hole in a tank? Torricelli's law turns the depth below the surface into the exit speed.
One height, the exit speed
Enter the fluid height above the opening (and gravity) and the calculator returns the efflux velocity from v = √(2gh) — no density, viscosity, or hole size needed.
What is a Torricelli velocity calculator?
Depth below the surface in, exit speed out
A Torricelli velocity calculator tells you how fast an ideal fluid shoots out of an opening some distance below its free surface. Discovered by Evangelista Torricelli in 1643, the law is a direct consequence of energy conservation: the pressure head of the fluid column above the hole converts into kinetic energy, so the fluid leaves at exactly the speed it would reach falling freely through that same height. That makes it the go-to estimate for water draining from a tank, a jet from a dam outlet, fluid through an orifice, or the reach of a garden water feature.
Enter the fluid height above the opening to get the efflux velocity instantly — gravity is pre-filled at 9.81 m/s².
One short formula, built from the height h above the opening and the gravitational acceleration g.
v = √(2 × g × h)The product 2gh is the squared speed an object gains falling through height h, so taking its square root gives the exit speed. Notice what is absent: the fluid's density never appears, and neither does the size of the opening. Only the depth below the surface and gravity set the speed.
Suppose the water surface sits 2 m above a small hole, on Earth (g = 9.81 m/s²).
Combine 2, g, and h
2 × 9.81 × 2 = 39.24 — twice gravity times the height.
Take the square root
√39.24 ≈ 6.264184 m/s — the speed of the jet leaving the hole.
Sanity check
A stone dropped 2 m reaches the same 6.26 m/s, because both come from √(2gh).
The efflux velocity is how fast fluid leaves the opening at the instant it has that head above it. For a 2 m head the jet exits at about 6.26 m/s — fast enough to throw a noticeable arc of water. The single most useful insight is that the speed depends only on the depth below the surface, not on how wide the hole is or what fluid you use: water, oil, and mercury all leave a 2 m head at the same 6.26 m/s. Because the relationship is a square root, doubling the depth only multiplies the speed by about 1.41, not by 2 — so a tank that is four times deeper produces a jet only twice as fast. As a tank drains, h shrinks and the jet slows, which is why the stream from a draining bucket droops toward the end. Use the result to size a drain, estimate how far a spout will throw, or judge how quickly a vessel empties.
Torricelli's law is exact for an ideal fluid, but real flows lose a little to friction.
Ideal fluid, small hole, open to the air
The formula assumes an ideal (frictionless, incompressible) fluid, a hole much smaller than the tank cross-section, and an opening vented to the atmosphere. Real openings lose speed to viscosity and edge turbulence — a sharp-edged orifice delivers roughly 60–97 % of the ideal velocity depending on its shape (the discharge coefficient). The result is also the instantaneous speed at the current height h: as the tank drains, h falls and the jet slows, so use the live height for a snapshot, not the whole emptying. For a pressurised tank, add the extra pressure head before applying the formula.