# Terminal Velocity Calculator

Calculate terminal velocity of a falling object using vt = sqrt(2mg/ρCdA). Accounts for mass, drag coefficient, cross-section area, and air density.

## What this calculates

Terminal velocity is the maximum speed a falling object reaches when the drag force from air resistance equals the gravitational force pulling it down. At terminal velocity, the net force is zero and the object falls at a constant speed. This calculator uses the formula vt = sqrt(2mg / (ρCdA)) to find that speed.

## Inputs

- **Mass** (kg) — min 0 — Mass of the falling object.
- **Drag Coefficient (Cd)** — min 0 — Dimensionless drag coefficient of the object shape.
- **Cross-Section Area** (m²) — min 0 — Projected frontal area perpendicular to the direction of fall.
- **Air Density (ρ)** (kg/m³) — min 0 — Air density. Standard sea-level value is 1.225 kg/m³.

## Outputs

- **Terminal Velocity** (m/s) — vt = sqrt(2mg / (ρCdA))
- **Terminal Velocity** (km/h) — Terminal velocity in kilometers per hour
- **Terminal Velocity** (mph) — Terminal velocity in miles per hour

## Details

When an object falls through a fluid (like air), two forces act on it: gravity pulling it down and drag pushing it up. As the object accelerates, drag increases with the square of velocity. Eventually drag equals gravity, acceleration drops to zero, and the object reaches terminal velocity.

The formula vt = √(2mg / (ρCdA)) shows that terminal velocity depends on mass (m), gravitational acceleration (g = 9.81 m/s²), air density (ρ), drag coefficient (Cd), and cross-sectional area (A). Heavier objects or those with smaller frontal areas fall faster, while larger drag coefficients or denser air slow the fall.

A skydiver in a belly-to-earth position (Cd ≈ 1.0, A ≈ 0.7 m²) reaches about 55 m/s (200 km/h). In a head-down dive (smaller A), terminal velocity can exceed 80 m/s (290 km/h). A golf ball (Cd ≈ 0.47, small A, low mass) has a terminal velocity of about 32 m/s. Understanding terminal velocity is essential in skydiving, aerospace engineering, meteorology, and sedimentation analysis.

## Frequently Asked Questions

**Q: What is terminal velocity?**

A: Terminal velocity is the constant speed a falling object reaches when the force of air resistance (drag) equals the force of gravity. At this point, acceleration is zero and the object falls at a steady rate.

**Q: What is the terminal velocity of a human?**

A: A skydiver in a spread-eagle position reaches about 55 m/s (200 km/h or 120 mph). In a head-down streamlined dive, terminal velocity can reach 80+ m/s (290 km/h or 180 mph). Felix Baumgartner exceeded 370 m/s at high altitude where air density is much lower.

**Q: Does a heavier object fall faster?**

A: In a vacuum, all objects fall at the same rate. In air, a heavier object of the same shape and size will have a higher terminal velocity because gravity pulls harder while drag remains the same at a given speed. This is why a bowling ball falls faster than a beach ball.

**Q: What is the drag coefficient?**

A: The drag coefficient (Cd) is a dimensionless number representing how much air resistance an object's shape creates. A streamlined shape like a teardrop has Cd around 0.04, a sphere about 0.47, and a flat plate perpendicular to flow about 1.17.

**Q: Why does terminal velocity depend on air density?**

A: Denser air creates more drag at any given speed. At higher altitudes where air is thinner, terminal velocity is higher because the object must fall faster before drag equals gravity. This is why high-altitude skydivers reach much higher speeds.

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Source: https://vastcalc.com/calculators/physics/terminal-velocity
Category: Physics
Last updated: 2026-04-21