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Terminal Velocity Calculator
Find the top speed of a falling object when air drag balances its weight, v = √(2mg/ρAC_d). Enter the mass, drag coefficient, frontal area and air density (or pick a preset) to see the terminal velocity, how long and how far it takes to reach 95% of it, and the full speed curve.
Last updated:
Sphere ≈ 0.47, skydiver belly-down ≈ 1.0, streamlined body ≈ 0.04–0.3
Frontal area from
kg/m³
m/s²
Enter your values to see the result.
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How to use the Terminal Velocity Calculator
- Enter the mass and its unit.
- Enter the drag coefficient (or start from a preset).
- Give the frontal area directly, or a diameter for round objects.
- Pick the air density for your altitude or a custom fluid.
- Read the terminal velocity, the time to 95% and the fall table and chart.
Terminal velocity formulas
| Quantity | Formula |
|---|---|
| Drag force | Fd = ½ ρ v² Cd A |
| Terminal velocity | vt = √(2 m g / (ρ A Cd)) |
| Speed after time t (from rest) | v(t) = vt tanh(g t / vt) |
| Distance after time t | d(t) = (vt² / g) ln cosh(g t / vt) |
| Time to 95% of vt | t = (vt / g) × artanh 0.95 ≈ 1.832 vt / g |
Typical drag coefficients
| Shape | Cd (approx.) |
|---|---|
| Flat plate facing the flow | 1.1 – 1.3 |
| Open parachute | 1.3 – 1.5 |
| Skydiver, belly-to-earth | 1.0 – 1.3 |
| Cube | 1.05 |
| Long cylinder, side-on | 0.8 – 1.2 |
| Smooth sphere | 0.47 |
| Golf ball (dimpled, at speed) | 0.25 – 0.3 |
| Streamlined body | 0.04 – 0.1 |
Air density by altitude (standard atmosphere)
| Altitude | Density (kg/m³) |
|---|---|
| Sea level | 1.225 |
| 1,000 m | 1.112 |
| 2,000 m | 1.007 |
| 3,000 m | 0.909 |
| 4,000 m | 0.819 |
| 5,000 m | 0.736 |
| 10,000 m | 0.414 |
Frequently asked questions
What is the formula for terminal velocity?
v_t = √(2 m g / (ρ A C_d)), where m is mass, g gravity, ρ the fluid density, A the frontal area and C_d the drag coefficient. It is the speed at which the drag force ½ρv²C_dA equals the weight mg.
How fast does a skydiver fall?
In a stable belly-to-earth position a typical skydiver reaches roughly 50–55 m/s (about 190–200 km/h, 120 mph). Head-down positions reduce the drag area and can exceed 70 m/s (250+ km/h).
How long does it take to reach terminal velocity?
Starting from rest with quadratic drag, v(t) = v_t tanh(g t / v_t). You reach 95% of v_t after t = 1.83 v_t / g; for a 53 m/s skydiver that is about 10 seconds and roughly 340 m of fall.
Why do heavier objects fall faster in air?
Terminal velocity grows with √(m / (A C_d)). Doubling the mass of an object with the same shape and size raises its terminal speed by about 41%. In a vacuum all objects fall at the same rate.
Why is terminal velocity higher at high altitude?
Air is thinner higher up, so ρ is smaller and the same drag needs a higher speed. At 10 km the air density is about a third of sea level, so terminal velocity is about 1.7 times higher.
Is the drag coefficient constant?
Only approximately. C_d depends on shape, orientation, surface roughness and the Reynolds number, so it can change with speed (the drag crisis of balls is an example). The calculator assumes a constant C_d.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.
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