Terminal Velocity Calculator
Enter mass, cross-sectional area, drag coefficient and fluid density — the terminal velocity solves instantly, with a live 3D scene showing the drag force catching up to weight and two charts of how v_t depends on mass and shape.
Reviewed by the ToolNestr Editorial Team — July 2026
Enter mass, area and drag coefficient (or pick a preset) — terminal velocity solves instantly.
Two ideas that trip students up
1. Drag catching up to weight
Near the top of the fall (upper sphere), the small blue drag arrow is much shorter than the grey weight arrow. At terminal velocity (lower sphere) the two arrows are equal — the net force is zero.
2. Terminal velocity vs mass, by shape
Each curve is vt ∝ √m for a different drag coefficient. More streamlined shapes (lower Cd) sit on higher curves — they need a faster fall before drag balances weight.
Terminal velocity graphs
How it works
The core idea in one line: a falling object speeds up only until drag grows large enough to exactly cancel its weight — after that, it falls at a constant terminal velocity set by its mass, shape and the fluid it moves through.
vt = √(2mg / (ρ·A·Cd))
terminal velocity from mass, area, drag coefficient & fluid density
Fdrag = ½·ρ·v²·A·Cd
drag force at speed v — equals weight (mg) at vt
Terminal velocity comes from setting drag force equal to weight: ½·ρ·v²·A·Cd = m·g. Solving for v gives the formula above. Because v_t ∝ √m, quadrupling the mass only increases terminal velocity by 2×; because v_t ∝ 1/√(A·Cd), a more streamlined or smaller-area shape falls proportionally faster.
Worked example 1 — skydiver, belly-down
Given: A 75 kg skydiver falls belly-to-earth with cross-sectional area A = 0.6 m², drag coefficient Cd = 0.7, through sea-level air (ρ = 1.225 kg/m³, g = 9.81 m/s²).
This matches the well-known belly-down skydiving terminal velocity of roughly 190–200 km/h.
Worked example 2 — a falling raindrop
Given: A spherical raindrop of radius r = 1.5 mm (water density 1000 kg/m³), drag coefficient Cd = 0.5, falling through air (ρ = 1.225 kg/m³).
Real raindrops of this size fall at roughly 6–9 m/s, which is why rain does not accelerate indefinitely on its way down.
Terminal velocity for different falling objects
Same air (ρ = 1.225 kg/m³) — mass, area and shape are what set the speed.
| Object | Masskg | Aream² | Cd | v_tm/s |
|---|---|---|---|---|
| Raindrop (3 mm) | 1.4 × 10⁻⁵ | 7.1 × 10⁻⁶ | 0.5 | 8.0 |
| Ping-pong ball | 0.0027 | 0.00126 | 0.5 | 8.3 |
| Baseball | 0.145 | 0.0043 | 0.3 | 42.4 |
| Skydiver, belly-down ★ | 75 | 0.6 | 0.7 | 53.5 |
| Skydiver, head-down | 75 | 0.18 | 0.7 | 97.6 |
★ Reference row. v_t ∝ √(m/(A·Cd)), so a denser, more streamlined object needs a much higher speed before drag balances its weight.
Where terminal velocity actually matters
🪂 Skydiving & parachutes
Skydivers control their fall speed by changing body position: spreading out increases A and slows the fall, tucking in reduces A and speeds it up. Opening a parachute suddenly multiplies A by 30–40×, collapsing terminal velocity from ~55 m/s to a safe landing speed of a few metres per second.
🌧️ Raindrop size and rainfall
Because v_t depends on mass and area in different ways, larger raindrops fall faster than smaller ones — meteorologists use terminal velocity to model how rain intensity and drop-size distribution relate to radar reflectivity.
🚗 Vehicle & equipment drop testing
Engineers computing the impact speed of a dropped tool, a cargo pallet under a drogue chute, or a re-entry capsule all start from the same drag-balance equation to size the required deceleration surface.
Common misconceptions
"Terminal velocity is the same for all objects."
False — it depends on mass, cross-sectional area, drag coefficient and the fluid’s density. A feather and a hammer have very different terminal velocities in air, even though they would fall together in a vacuum.
"Once an object reaches terminal velocity it stays exactly that speed forever."
It stays constant only while the conditions (mass, orientation, air density) stay constant. Change body position, altitude (air gets thinner), or deploy a parachute, and the object accelerates or decelerates toward a new terminal velocity.
"A heavier object always has a higher terminal velocity."
Not necessarily — v_t depends on the ratio m/(A·Cd), not mass alone. A heavy but very spread-out object (like a parachute canopy) can have a lower terminal velocity than a lighter, denser, more compact one.
"Terminal velocity means the object stops accelerating because gravity switches off."
Gravity keeps acting the whole time. Acceleration reaches zero because the upward drag force has grown to exactly cancel the downward weight — it is a balance of forces, not an absence of gravity.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 1 — §14.7, Drag Force and Terminal Speed (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 6, Drag Force and Terminal Speed.
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 6, Motion in Two Dimensions (resistive forces).
Standard sea-level air density ρ = 1.225 kg/m³ and g = 9.81 m/s² are used unless changed. Results are rounded for display.
How to use this calculator
Enter mass & area
Fill in the object’s mass (kg) and the cross-sectional area (m²) it presents to the airflow.
Choose a drag coefficient
Pick a preset shape or type a custom Cd; adjust fluid density if not falling through sea-level air.
Watch it settle
Use the 3D scene and charts to see the drag force grow until it matches weight at v_t.
Related tools
Frequently asked questions
What is terminal velocity?
Terminal velocity is the constant maximum speed a falling object reaches when air resistance (drag) grows large enough to exactly balance its weight. Once drag equals gravity the net force is zero, so acceleration stops and the object falls at a steady speed.
What is the formula for terminal velocity?
v_t = √(2mg / (ρ·A·Cd)), where m is mass, g is gravitational acceleration (9.81 m/s² on Earth), ρ is the fluid density (1.225 kg/m³ for sea-level air), A is the cross-sectional area facing the flow, and Cd is the dimensionless drag coefficient of the shape.
Why do a feather and a bowling ball fall at different speeds in air?
In a vacuum they would not — but in air, terminal velocity depends on mass, area and shape. A feather has huge area relative to its tiny mass, so drag balances its weight almost immediately at a low speed. A bowling ball is dense and compact, so it needs a much higher speed before drag catches up.
What is a typical human skydiving terminal velocity?
A skydiver in the standard belly-to-earth position reaches roughly 190–200 km/h (about 53–56 m/s). Falling head-down in a streamlined position sharply reduces the cross-sectional area and can push terminal velocity above 240 km/h (about 67–90 m/s or more).
Does terminal velocity depend on the height of the fall?
Not directly — it depends only on mass, shape, drag coefficient and fluid density, not on how far the object has fallen. Height only determines whether the object has had enough time and distance to actually reach that speed before landing.