Terminal Velocity Calculator
Terminal velocity is the steady speed a falling object reaches when fluid drag exactly balances its weight, so it stops accelerating. Pick a shape and fluid preset or enter your own numbers to find that maximum speed in m/s, km/h and mph, plus how long it takes to get there, the drop distance, and the drag force at terminal velocity.
Formula
Worked example
80 kg skydiver, A = 0.7 m², C_d = 1.0, ρ = 1.225 kg/m³, g = 9.80665: v_t = √(2 × 80 × 9.80665 ÷ (1.225 × 0.7 × 1.0)) = √(1569.1 ÷ 0.8575) ≈ 42.8 m/s (about 154 km/h). Reaching 95% of that takes about 8 s and a fall of roughly 245 m.
What terminal velocity actually means
When an object falls through a fluid it accelerates under gravity, but the drag force pushing back grows with the square of speed. Terminal velocity is the speed at which that drag exactly equals the weight, leaving zero net force: from that moment the object stops accelerating and falls at a constant speed. This calculator solves the steady-state balance mg = ½·ρ·A·C_d·v² for v, giving the terminal velocity directly. The result is the fastest the object will ever fall in those conditions, it never exceeds this value no matter how long the drop continues.
Shape and fluid presets
Drag depends heavily on shape, so the shape preset fills in a representative drag coefficient: about 0.47 for a smooth sphere, 1.05 for a face-on cube, 1.28 for a flat plate, and as low as 0.04 for a streamlined teardrop. A belly-to-earth skydiver sits near 1.0 while a head-down dive drops to about 0.7, which is part of why head-down falls are so much faster. The fluid preset sets the density: air at sea level is 1.225 kg/m³, thin high-altitude air is far less, and water is about 998 kg/m³, roughly 800 times denser, which is why objects fall so slowly through water. Choose the Custom option in either menu to type an exact value.
Time, distance and drag force
Reaching terminal velocity is not instant. The speed approaches it along a curve v(t) = v_t·tanh(g·t/v_t), creeping closer but never quite touching the limit, so we report the time and the drop distance to reach 95% of terminal velocity as a practical marker. The characteristic time is τ = v_t/g, and 95% arrives at about 1.83·τ. The calculator also shows the drag force at terminal velocity, which by definition equals the weight, m·g, since the two are perfectly balanced. The live curve plots the whole approach so you can see how quickly the object stops accelerating.
Assumptions and limits of the model
The equation assumes the quadratic drag regime that applies to large, fast objects, where the drag coefficient is roughly constant. It does not capture the linear (Stokes) drag that dominates for very small particles like dust or fog droplets, where viscosity rules instead. Fluid density is treated as constant, yet air density falls with altitude, so a high-altitude jumper actually reaches a higher terminal velocity up high and slows as the air thickens nearer the ground. The drag coefficient itself drifts with shape, surface texture and speed, so treat the output as a well-grounded estimate rather than an exact figure.
Typical terminal velocities
| Object | m/s | km/h | mph |
|---|---|---|---|
| Raindrop (large) | 9 | 32 | 20 |
| Skydiver (parachute open) | 5 | 18 | 11 |
| Skydiver (belly-to-earth) | 55 | 198 | 123 |
| Skydiver (head-down) | 90 | 324 | 201 |
| Bullet (falling, spent) | 100 | 360 | 224 |
Approximate values in air at sea level; actual speeds vary with shape and conditions.
Frequently asked questions
What is the formula for terminal velocity?
Terminal velocity is v_t = √(2·m·g ÷ (ρ·A·C_d)), where m is mass, g is gravitational acceleration (9.80665 m/s² on Earth), ρ is the fluid density, A is the cross-sectional area facing the airflow, and C_d is the drag coefficient. It comes from setting weight equal to drag and solving for speed.
How long does it take to reach terminal velocity?
Speed approaches terminal velocity along v(t) = v_t·tanh(g·t/v_t), getting ever closer but never exactly reaching it. A practical marker is 95% of terminal velocity, which arrives at about 1.83·v_t/g seconds. For a belly-down skydiver near 43 m/s that is roughly 8 seconds and about 245 metres of fall. This calculator reports both the time and the distance.
Why do heavy and light objects have different terminal velocities?
In a vacuum all objects fall at the same rate, but in air a heavier object needs a higher speed before drag grows enough to balance its larger weight. Because the relationship is a square root, mass has a muted effect: doubling the mass only raises terminal velocity by about 41%, not 100%.
How does altitude or a different fluid affect terminal velocity?
Terminal velocity is inversely proportional to the square root of fluid density. Thin, high-altitude air gives a higher terminal velocity than sea-level air, then the object slows as it descends into denser air. Water is roughly 800 times denser than air, so the same object falls dramatically slower in water. Use the fluid preset to switch between air, altitude and water.