📋

Walk-through

How to Use This Calculator

3 steps

1

Enter mass, area, drag coefficient, and air density

Fill in the falling object's mass (kg), the cross-sectional area it presents to the airflow (m²), its drag coefficient, and the air density (kg/m³ — 1.225 at sea level). The calculator updates instantly as you type.

2

Read the terminal velocity

The result card shows the terminal velocity in meters per second, with the miles-per-hour equivalent right below it. This is the constant speed the object reaches once drag force exactly balances its weight.

3

Compare body positions or solve for an unknown

Switch to the Skydiver Preset tab to compare belly-to-earth, head-down, and parachute-open speeds side by side, or use the Solve tab to work backward from a target velocity to the mass, area, or drag coefficient that would produce it.

⚡

Reference

Formula & Methodology

1 formula

Terminal velocity

v = √(2mg / (ρ·A·Cd))

Terminal velocity is reached when drag force (½·ρ·v²·Cd·A) equals the object's weight (m·g), so the object stops accelerating. m is mass in kg, g is standard gravity (9.80665 m/s²), ρ (rho) is air density in kg/m³, A is the cross-sectional area facing the airflow in m², and Cd is the dimensionless drag coefficient.

📖

Glossary

Key Terms Explained

7 terms

Terminal velocity The maximum constant speed a falling object reaches when drag force equals gravitational force, so net acceleration is zero.

Drag force The resistive force air exerts on a moving object, opposing its motion. It grows with the square of velocity, which is why terminal velocity exists at all — drag eventually catches up to weight.

Drag coefficient (Cd) A dimensionless number describing how streamlined an object's shape is. Lower values (like 0.04 for a teardrop) mean less drag; higher values (near 1.0-1.3) mean more, as with a flat plate or an open parachute.

Cross-sectional area The area of the object as seen face-on by the oncoming air — the 'silhouette' the airflow has to push against, measured in square meters.

Air density The mass of air per unit volume, about 1.225 kg/m³ at sea level and 15°C. Air density drops with altitude and rises in colder, drier conditions, which changes terminal velocity.

Free fall Motion under gravity alone with no other forces acting. In true free fall (a vacuum, or ignoring air resistance), an object keeps accelerating and never reaches a terminal velocity.

Equilibrium The state where the net force on an object is zero. At terminal velocity, the upward drag force and downward weight are in equilibrium, so velocity stays constant.

👥

Scenarios

Real-World Examples

3 worked examples

🧍

Skydiver, belly-to-earth

A 75 kg skydiver in the standard spread-eagle, belly-to-earth position (area ≈ 0.84 m², drag coefficient ≈ 0.5) falling through sea-level air (1.225 kg/m³).

Mass 75 kg Area 0.84 m² Drag coefficient 0.5 Air density 1.225 kg/m³

Terminal velocity works out to about 53.5 m/s — roughly 120 mph, matching the commonly cited belly-to-earth skydiving speed. This is the free-fall speed before the parachute opens.

⚖️

Heavier vs. lighter jumper

Two skydivers in the exact same belly-to-earth position and area, but one weighs 100 kg and the other 75 kg.

Mass (heavier) 100 kg Mass (lighter) 75 kg

The heavier jumper reaches about 61.7 m/s versus 53.5 m/s for the lighter one — heavier objects fall faster at terminal velocity when shape and area are equal, because more weight needs more drag force (and thus more speed) to balance it.

🪂

Parachute open

The same 75 kg jumper after deploying a parachute, which increases both the area (≈ 25 m²) and the drag coefficient (≈ 1.5) dramatically.

Mass 75 kg Area 25 m² Drag coefficient 1.5

Terminal velocity drops to about 5.7 m/s (roughly 13 mph) — a safe landing speed. Increasing area and drag coefficient is precisely how a parachute converts a lethal free-fall speed into a survivable descent rate.

📄

Deep Dive

Understanding the Terminal Velocity Calculator

3 chapters · 4 min read

This calculator finds the constant speed a falling object eventually reaches once air resistance grows large enough to balance its weight. It's the same physics behind skydiving speeds, raindrop sizes, and why a feather and a bowling ball fall very differently in air (but identically in a vacuum).

How the Terminal Velocity Calculator works

As an object falls, gravity accelerates it downward while air resistance (drag) pushes back, growing stronger the faster it goes — drag force scales with velocity squared. Eventually drag force exactly equals the object's weight, acceleration drops to zero, and the object falls at a constant speed: its terminal velocity. The calculator solves v = √(2mg / (ρ·A·Cd)) directly from Newton's second law at that equilibrium point, using standard gravity g = 9.80665 m/s².

Inputs and what they mean

Mass (kg) is the total weight of the falling object, including any gear. Cross-sectional area (m²) is how much surface the object presents to the oncoming air — a spread-eagle skydiver presents far more area than the same person diving head-down. Drag coefficient is a dimensionless shape factor: streamlined shapes have low values (0.04-0.3), flat or irregular shapes are closer to 1.0-1.3, and a deployed parachute canopy is typically 1.3-1.5. Air density (kg/m³) defaults to 1.225, the sea-level standard, but drops at altitude — thinner air means less drag and a higher terminal velocity for the same object.

Limits and edge cases

This formula assumes a constant drag coefficient and steady, low-turbulence airflow, which is a good approximation for most everyday falling objects but breaks down at very high speeds (transonic and supersonic regimes, where drag behaves differently) or for objects that tumble and change orientation mid-fall. It also assumes the object starts from rest and has enough distance to actually reach terminal velocity — a skydiver typically needs about 12 seconds and 450-460 meters of fall to get there. Air density inputs should reflect the altitude and conditions of the fall, not just sea level, for the most accurate result.

❓

Questions

Frequently Asked Questions

6 questions

What formula does the Terminal Velocity Calculator use?+

It uses v = √(2mg / (ρ·A·Cd)), derived by setting drag force (½·ρ·v²·Cd·A) equal to weight (m·g) and solving for v. Here m is mass, g is standard gravity (9.80665 m/s²), ρ is air density, A is cross-sectional area, and Cd is the drag coefficient.

How fast is a skydiver's terminal velocity?+

A skydiver in the standard belly-to-earth position typically reaches about 120 mph (roughly 53-55 m/s). Diving head-down in a streamlined position reduces the cross-sectional area and can push terminal velocity up to 150-200 mph, while deploying a parachute increases area and drag coefficient enough to slow descent to a safe 10-15 mph.

Why does opening a parachute slow you down so much?+

A parachute dramatically increases both the cross-sectional area (from under 1 m² to 20-30 m² or more) and the drag coefficient. Since terminal velocity depends on the square root of 1/(A·Cd), a large increase in either variable produces a large drop in terminal velocity — turning a ~120 mph free fall into a ~12 mph landing.

When is terminal velocity actually reached?+

Terminal velocity is reached asymptotically — technically it's never hit exactly, but an object gets close enough to be indistinguishable from it after enough fall time and distance. A skydiver, for example, reaches about 99% of terminal velocity after roughly 12 seconds and 450-460 meters of fall.

What units does this calculator use?+

Mass is in kilograms, area in square meters, air density in kilograms per cubic meter, and drag coefficient is dimensionless (no unit). The result is shown in both meters per second and miles per hour so it's readable in either system.

Why do heavier objects fall faster at terminal velocity?+

For objects with the same shape and area, a heavier object needs a larger drag force to reach equilibrium, and drag force only grows by going faster — so heavier objects settle into a higher terminal velocity than lighter ones of identical shape. This is why a bowling ball and a beach ball, dropped from the same height with similar shapes but very different masses, hit very different terminal speeds despite falling in the same air.

Download a one-page PDF of your numbers instantly. Add your email to also get our occasional calculator tips — no spam, unsubscribe anytime. Privacy.

Terminal Velocity Calculator

Inputs