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Terminal Velocity Calculator

Physics

Calculate an object's terminal velocity in free fall using mass, gravity, air density, cross-sectional area, and drag coefficient. Instant results.

Reviewed by the thecalcu.com team · Last updated July 24, 2026

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Terminal Velocity

42.762
Terminal Velocity
153.942

This calculator computes your Terminal Velocity, Terminal Velocity from the values you enter.

Inputs
MassGravitational AccelerationAir (Fluid) DensityCross-Sectional AreaDrag Coefficient
Outputs
Terminal VelocityTerminal Velocity

What is a Terminal Velocity?

The Terminal Velocity Calculator computes the maximum steady falling speed of an object in a fluid (typically air), using v = √(2mg ÷ (ρACd)). Enter the object's mass, the local gravitational acceleration, the fluid's density, the object's cross-sectional area, and its drag coefficient, and the calculator instantly returns the terminal velocity in both m/s and km/h.

Terminal velocity is the point at which a falling object stops accelerating because drag force has grown to exactly balance gravity. It's a key concept across skydiving, meteorology, and fluid dynamics.

Why Use a Terminal Velocity Calculator?

Terminal velocity depends on five interacting variables, and manually solving the square root formula for different body positions, masses, or altitudes is tedious to do by hand repeatedly.

This calculator updates instantly as you adjust any input, making it easy to compare scenarios, like how body position (via area and drag coefficient) changes a skydiver's terminal speed, or how altitude (via air density) affects it.

The step-by-step breakdown shows the exact substitution, useful for physics coursework, meteorology estimates, or sanity-checking real-world skydiving and parachute data.

Who Should Use This Calculator?

Physics students studying drag force, fluid resistance, and free-fall dynamics.

Skydiving and parachuting enthusiasts estimating how body position or gear changes affect fall speed.

Meteorology students and researchers estimating the terminal velocity of raindrops, hailstones, or falling particles.

Engineers designing parachutes, drop-test equipment, or objects meant to fall predictably through air or fluid.

Science teachers demonstrating how drag force grows with speed until it balances gravity.

What Insights Does This Calculator Give You?

Terminal velocity, the primary result, showing the steady-state falling speed once drag balances gravity, in both m/s and km/h.

Sensitivity to body position, by changing area and drag coefficient, you can see directly how a streamlined dive versus a spread-eagle position changes fall speed dramatically.

Altitude effects, by adjusting air density, you can model how terminal velocity increases as a falling object descends from thin high-altitude air into denser air near the ground.

How to use this Terminal Velocity calculator

  1. Enter the mass, the mass of the falling object, in kilograms.

  2. Enter gravitational acceleration, defaults to 9.8 m/s² for Earth's surface; adjust for other bodies or altitudes if needed.

  3. Enter the fluid density, defaults to 1.225 kg/m³ for sea-level air; use a different value for other altitudes or fluids.

  4. Enter the cross-sectional area, the object's area facing the direction of fall, in square meters.

  5. Enter the drag coefficient, a unitless value describing how streamlined the object is (see reference values in the FAQ).

  6. Read the terminal velocity result, the highlighted result shows the steady falling speed in m/s and km/h.

Show formula & methodology ↓Show less ↑

Formula & Methodology

Terminal velocity formula:
v = √(2mg ÷ (ρ × A × Cd))

Variable definitions:
- m, mass (kilograms)
- g, gravitational acceleration (meters per second squared)
- ρ, fluid density (kilograms per cubic meter)
- A, cross-sectional area (square meters)
- Cd, drag coefficient (unitless)
- v, terminal velocity (meters per second)

Worked example:

A skydiver weighing 80 kg falls belly-down (A = 0.7 m², Cd = 1.0) through sea-level air (ρ = 1.225 kg/m³) under standard gravity (9.8 m/s²).

v = √(2 × 80 × 9.8 ÷ (1.225 × 0.7 × 1.0)) ≈ 42.6 m/s (about 153 km/h)

Note: This calculator uses the quadratic drag model, most accurate for moderate-to-high-speed falls through air. For very small particles or low-speed fluid motion, linear (Stokes') drag applies instead and produces different results.

Frequently Asked Questions

What is the formula for terminal velocity?
Terminal velocity is calculated as v = √(2mg ÷ (ρ × A × Cd)), where m is mass, g is gravitational acceleration, ρ is the density of the fluid (usually air), A is the cross-sectional area facing the direction of motion, and Cd is the drag coefficient. This calculator applies that formula directly using your inputs.
What is terminal velocity in simple terms?
Terminal velocity is the constant maximum speed a falling object reaches when the upward force of air (or fluid) resistance exactly balances the downward force of gravity, so the object stops accelerating and falls at a steady speed. A skydiver in a belly-down position reaches a terminal velocity of roughly 55 m/s (about 195 km/h).
What are typical default values for skydiving calculations?
The default values in this calculator (80 kg mass, 9.8 m/s² gravity, 1.225 kg/m³ air density at sea level, 0.7 m² cross-sectional area, and a drag coefficient of 1.0) approximate a skydiver in a stable belly-to-earth position, producing a terminal velocity around 53–55 m/s, consistent with real-world skydiving data.
How does body position affect a skydiver's terminal velocity?
A belly-down, spread-eagle position maximizes cross-sectional area and drag, producing a terminal velocity around 195 km/h, while a head-down, streamlined dive position minimizes area and can push terminal velocity above 240–300 km/h. Adjusting the area and drag coefficient inputs lets you model both scenarios.
Why does a heavier object have a higher terminal velocity (all else equal)?
Terminal velocity increases with the square root of mass (v ∝ √m), so a heavier object needs to fall faster before air resistance builds up enough to balance the larger gravitational force pulling it down. This is why a bowling ball reaches a higher terminal velocity than a feather of the same shape.
Why does air density affect terminal velocity?
Denser air creates more drag force at a given speed, so terminal velocity decreases as air density increases, this is why terminal velocity is higher at high altitude (thinner air) than at sea level, and why skydivers accelerate more as they descend into denser lower-altitude air.
What is a drag coefficient and how do I choose one?
The drag coefficient (Cd) is a dimensionless number describing how streamlined an object is relative to a flat reference area, lower values mean less drag for the same area. Typical values are about 0.47 for a sphere, 0.7–1.0 for a spread-eagle human, and as low as 0.05–0.2 for very streamlined shapes like teardrops or race cars.
Does terminal velocity depend on the height an object falls from?
No, terminal velocity itself is a fixed value determined by mass, drag, area, and air density, not the drop height. However, an object needs enough falling distance to actually reach terminal velocity; if dropped from too low a height, it may hit the ground before drag fully balances gravity.
How is terminal velocity used outside of skydiving?
Terminal velocity calculations apply to raindrop and hailstone size prediction in meteorology, parachute and parafoil design, sediment settling rates in fluid dynamics and geology, and the design of falling probes or instruments in atmospheric and oceanic research.
How does this relate to free fall without air resistance?
Without air resistance, an object in free fall would keep accelerating indefinitely at g (9.8 m/s² near Earth's surface) with no upper speed limit. Terminal velocity exists specifically because air resistance grows with speed until it exactly cancels gravity, see the [Free Fall Calculator](/free-fall-calculator/) for the no-drag case.
What units should I use for the inputs?
Use kilograms for mass, meters per second squared for gravity, kilograms per cubic meter for air (or fluid) density, square meters for cross-sectional area, and a unitless value for drag coefficient. The result is returned in meters per second and kilometers per hour.
How accurate is this calculator for real-world falling objects?
This calculator uses the standard quadratic drag equation, which is accurate for objects falling at moderate-to-high speeds through air (like skydivers and larger falling objects), but less accurate for very small or very slow-moving objects where linear (Stokes') drag dominates instead, such as fine dust particles or droplets.
Also known as
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