About the Terminal Velocity Calculator
This terminal velocity calculator finds the steady speed a falling object settles at once air resistance grows large enough to cancel its weight. Enter the mass, the frontal (projected) area facing the airflow, the drag coefficient and the air density, and it returns the terminal velocity in m/s, km/h and mph, together with how long and how far the object falls before reaching 99% of that speed.
It is handy for skydiving and wingsuit curiosity, parachute and drone recovery sizing, physics coursework on drag, model rocketry, and questions like how fast raindrops or hailstones fall. Change the air density to see how much faster a skydiver falls in the thin air at exit altitude than near the ground. The chart compares the speed with drag against free fall in a vacuum.
The model uses quadratic (Newtonian) drag with a constant drag coefficient, which suits objects larger than a few millimetres moving through air. Very small particles such as dust or fog droplets follow Stokes' law instead, and deforming objects like large raindrops change shape and Cd as they fall.
With the default inputs, the terminal velocity is 51.13 m/s. Change any value above to recalculate instantly.
How to use the terminal velocity calculator
- 1Enter the mass and choose kg, g or lb.
- 2Enter the frontal area facing the airflow.
- 3Enter a drag coefficient (see the hints for common shapes).
- 4Adjust the air density for altitude or another fluid if needed.
- 5Read the terminal velocity and how long it takes to reach it.
Formula and method
A falling object accelerates until the drag force, F = ½·ρ·v²·C_d·A, equals its weight m·g. Setting the two equal and solving for v gives the terminal velocity. Because drag rises with the square of speed, heavier or more compact objects fall faster, and thinner air (lower ρ) raises the terminal speed.
With constant drag coefficient, the equation of motion has the exact solution v(t) = v_t·tanh(gt/v_t) and distance x(t) = (v_t²/g)·ln cosh(gt/v_t), starting from rest. The calculator uses these to find the time and distance to reach 99% of terminal velocity, and assumes density and gravity stay constant during the fall.
- v_t
- Terminal velocity (m/s)
- m
- Mass (kg)
- g
- Gravitational acceleration (m/s²)
- ρ
- Fluid (air) density (kg/m³)
- A
- Frontal area (m²)
- C_d
- Drag coefficient
Worked examples
Belly-to-earth skydiver, 80 kg
v_t = √(2 × 80 × 9.807 ÷ (1.225 × 0.7 × 0.7)) = √2,614 = 51.1 m/s ≈ 184 km/h (114 mph). It takes about 14 s and 520 m to get within 1% of that speed.
Head-down skydiver, smaller frontal area
Cutting the area to 0.3 m² gives v_t = √(1,569.1 ÷ (1.225 × 0.3 × 0.7)) = 78.1 m/s, about 281 km/h – why head-down flyers fall so much faster.
Same skydiver at 5,000 m altitude
The air at 5,000 m is only about 60% as dense, so v_t = √(1,569.1 ÷ (0.736 × 0.49)) = 66.0 m/s (237 km/h). Skydivers slow down as they descend into thicker air.
Parachute: 90 kg under a 25 m² round canopy
v_t = √(2 × 90 × 9.807 ÷ (1.225 × 25 × 1.3)) = √44.3 = 6.66 m/s, a landing speed similar to jumping off a 2.3 m wall.
2 mm raindrop treated as a sphere
A 2 mm water sphere has mass 4.19 mg and area 3.14 mm². With Cd = 0.47, v_t ≈ 6.7 m/s, close to measured speeds of about 6.5 m/s for drops this size.
Frequently asked questions
What is the terminal velocity formula?+
v_t = √(2mg / (ρAC_d)), where m is mass, g gravity, ρ the fluid density, A the frontal area and C_d the drag coefficient. It comes from setting drag force ½ρv²C_dA equal to weight mg.
What is the terminal velocity of a human?+
A skydiver in the stable belly-to-earth position falls at roughly 50–55 m/s (about 180–200 km/h or 120 mph). In a head-down position it rises to roughly 70–90 m/s (250–320 km/h).
Do heavier objects fall faster?+
In a vacuum, no – everything accelerates at g. In air, yes for the same shape and size: terminal velocity scales with the square root of mass, so a body four times as heavy reaches twice the terminal speed.
How long does it take to reach terminal velocity?+
Theoretically it is approached but never quite reached. A skydiver gets within about 1% of terminal speed after roughly 12–15 seconds and 450–550 m of fall, which this calculator shows as the 99% time and distance.
Why is terminal velocity higher at altitude?+
Drag is proportional to air density. At 4,000 m the air is roughly two-thirds as dense as at sea level, so a falling object must go faster to generate the same drag force that balances its weight.