Terminal Velocity Calculator

The Terminal Velocity Calculator finds the maximum steady speed a falling object reaches once air resistance balances gravity — using only its mass, drag coefficient and cross-sectional area. Pick a skydiver, raindrop, cat, bowling ball or feather, or enter your own object, choose the medium (air, water or honey), and the tool computes the terminal velocity from \(v_t = \sqrt{2mg / (\rho A C_d)}\), then shows exactly how long and how far the object must fall to actually reach it.

What Is Terminal Velocity?

Terminal velocity is the constant speed a falling object eventually reaches when the upward drag force from the surrounding fluid grows large enough to exactly cancel the downward force of gravity. With zero net force, acceleration stops (Newton's first law) and the object continues to fall at that steady maximum speed. Anything dropped in air — a skydiver, a hailstone, a leaf — settles toward its own terminal velocity, set by how heavy it is versus how much drag its shape and size produce.

In a vacuum there is no fluid and therefore no drag, so there is no terminal velocity: a feather and a hammer fall together, exactly as astronaut David Scott demonstrated on the Moon during Apollo 15.

Terminal Velocity Formula

Terminal velocity comes from setting the drag force equal to the weight. The quadratic drag force is \(F_d = \tfrac{1}{2}\rho v^2 A C_d\); setting \(F_d = mg\) and solving for \(v\) gives:

where:

• \(v_t\) — terminal velocity (metres per second)
• \(m\) — mass of the object (kilograms)
• \(g\) — gravitational acceleration, \(9.80665\ \text{m/s}^2\) on Earth
• \(\rho\) — density of the fluid (about \(1.225\ \text{kg/m}^3\) for sea-level air)
• \(A\) — cross-sectional area facing the flow (square metres)
• \(C_d\) — drag coefficient, a dimensionless number that depends on shape (≈0.5 for a sphere, ≈1.0–1.3 for a flat plate or spread skydiver)

How Long Does It Take to Reach Terminal Velocity?

An object dropped from rest does not reach terminal velocity instantly — it approaches it smoothly along a hyperbolic-tangent curve and, strictly, never quite touches 100%:

The characteristic time \(\tau = v_t/g\) tells you how quickly the approach happens. In practice, physicists say an object has "reached terminal velocity" once it is within a percent or two of it. This calculator reports the exact time and fall distance to hit both 95% and 99% of your object's terminal velocity, using \(t_f = \tau\,\operatorname{arctanh}(f)\) and \(x_f = \tfrac{v_t^2}{2g}\ln\!\big(1/(1-f^2)\big)\). A belly-to-earth skydiver, for example, needs roughly 10 seconds and about 330 metres of fall to reach 95%.

Terminal Velocities of Common Objects (in Air)

What Affects Terminal Velocity?

How to Use This Calculator

1. Choose an object: Select a preset such as a skydiver, raindrop or bowling ball, or choose "Custom Object" to enter your own.
2. Enter mass, drag and area: For a custom object, type its mass, drag coefficient and cross-sectional area and pick the units (kg/g/lb and m²/cm²/ft²).
3. Pick the medium: Choose sea-level air, thin high-altitude air, water or honey — this sets the fluid density.
4. Click Calculate: The tool applies \(v_t = \sqrt{2mg / (\rho A C_d)}\) and shows the result instantly.
5. Explore the result: Read the terminal velocity in m/s, km/h, mph and Mach, watch the fall animation and tanh approach curve, see how long and far it takes to reach terminal velocity, and follow the step-by-step working.

Frequently Asked Questions

What is terminal velocity?

Terminal velocity is the constant, maximum speed a falling object reaches when the upward drag force from the air (or other fluid) exactly balances the downward pull of gravity. At that point the net force is zero, so the object stops accelerating. For a belly-to-earth skydiver this is roughly 190 km/h.

How do you calculate terminal velocity?

Terminal velocity equals the square root of (2 × mass × gravity, divided by the product of fluid density, cross-sectional area and drag coefficient): \(v_t = \sqrt{2mg / (\rho A C_d)}\). Gravity is \(9.81\ \text{m/s}^2\) and sea-level air density is about \(1.225\ \text{kg/m}^3\). Heavier or more compact objects fall faster; larger or draggier ones fall slower.

Does a heavier object reach a higher terminal velocity?

Yes. Terminal velocity grows with the square root of mass, so for the same shape a heavier object falls faster. This differs from a vacuum, where every object accelerates at the same rate. With air resistance a bowling ball reaches a much higher terminal velocity than an equally sized beach ball.

How long does it take to reach terminal velocity?

An object dropped from rest approaches terminal velocity along a tanh curve and never quite reaches 100%. It typically hits about 95% within a few seconds. A human skydiver reaches roughly 95% after around 10 seconds and 330 metres of fall. This calculator reports the exact time and distance to reach 95% and 99% for your object.

What is the terminal velocity of a human?

A skydiver falling belly-to-earth has a terminal velocity of about 53 m/s — roughly 190 km/h or 120 mph. In a head-down dive, with a much smaller frontal area, that can rise to around 90 m/s or more. A wingsuit trades vertical speed for a slower, glide-like descent.

Why do a feather and a hammer fall at the same rate on the Moon?

Terminal velocity only exists when there is a fluid to create drag. On the airless Moon there is no air resistance and no terminal velocity, so every object accelerates together — as the Apollo 15 feather-and-hammer demonstration showed. On Earth the feather's large area and tiny mass give it a very low terminal velocity, so it flutters down slowly.

Additional Resources

• Terminal Velocity - Wikipedia
• Drag Coefficient - Wikipedia