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Terminal Velocity Calculator

Compute drag-limited free-fall speed usingvt = √(2mg / ρACd). Includes 10 real-world presets — skydiver, raindrop, hailstone, feather, golf ball — against sea-level air (rho = 1.225 kg/m³).

Formula
vt = √(2mg/ρACd)
Air rho
1.225 kg/m³
Skydiver
~120 mph belly
Stokes
1851 drag law

Quick Conversion

Formula: mph = m/s * 2.23694

Inputs

Drag presets

Free-fall Force Balance

Skydiver in free fall showing drag force up and gravity downAn object falling through air with arrows representing drag pointing up and gravity pointing down. At terminal velocity the arrows are equal.Fdrag = (1/2)ρv²ACdFgrav = mgAt vterminal: Fdrag = mg, net force = 0, a = 0

Enter mass, area, drag coefficient and fluid density, then press Calculate.

Terminal Velocity Reference

Objectvt (m/s)vt (mph)Observed
Skydiver belly-down42.7895.753.6 m/s
Skydiver head-first100.82225.590 m/s
Raindrop (2 mm)6.5414.69 m/s
Raindrop (5 mm)10.3423.19 m/s
Hailstone (1 cm)15.3534.314 m/s
Hailstone (5 cm, softball)34.3576.841 m/s
Feather (loose down)0.892.00.4 m/s
Golf ball46.27103.532 m/s
Bowling ball (16 lb)80.78180.784 m/s
Steel ball-bearing falling in oil1.543.40.05 m/s

For free-fall without air resistance, see acceleration. For Stokes regime sphere drag in viscous fluids, fluid-mechanics texts use F = 6πμrv.

Formula

vt = √(2 m g / (ρ A Cd))

Derived by setting weight (mg) equal to quadratic drag ((1/2)ρv²ACd) and solving for v. Valid for high-Reynolds-number turbulent flow (Re > 1000). For small spheres in viscous fluids (Re < 1) use Stokes' law instead.

Worked: An 80 kg skydiver belly-down has A ≈ 0.7 m², Cd ≈ 1.0 in sea-level air (ρ = 1.225 kg/m³). vt = √(2 × 80 × 9.81 / (1.225 × 0.7 × 1.0)) = √(1569.6 / 0.858) = 42.8 m/s = 95.7 mph. The often-quoted "120 mph" figure reflects higher altitude (lower ρ) and tighter body position.

5 Steps

  1. Estimate mass m in kilograms. Skydiver ≈ 80, raindrop ≈ 10⁻⁶.
  2. Estimate cross-section A in m². Belly-down skydiver ≈ 0.7; raindrop πr² for r = 1–2 mm.
  3. Pick a drag coefficient Cd. Sphere 0.47, parachute 1.4, skydiver belly 1.0, streamlined 0.04.
  4. Pick fluid density ρ. Sea-level air 1.225 kg/m³, water 1000 kg/m³, 9 km altitude air 0.467 kg/m³.
  5. Press Calculate. Read vt in four units; compare against the reference table to sanity-check the answer.

A Short History of Terminal Velocity

The idea that air resistance limits falling speed dates to Aristotle's Physics (c. 350 BC), where he argued that heavier objects fall faster than lighter ones in proportion to their weight. Galileo Galilei (1564–1642) tested and demolished that claim in the early 17th century, showing through inclined-plane experiments and (apocryphally) a Leaning Tower of Pisa drop that all objects fall at the same rate in vacuum — the differing real-world rates being entirely due to air drag.

Isaac Newton, in the Principia (1687), gave the first quantitative drag theory: he proposed that drag scales as ρAv², a relation later refined by Lord Rayleigh in 1879. George Gabriel Stokes (1851) derived the alternative law for slow, viscous flow around small spheres: Fdrag = 6πμrv. The two regimes are distinguished by the Reynolds number Re = ρvL/μ — Stokes flow for Re < 1 (dust, small bacteria), quadratic drag for Re > 1000 (rain, skydivers, hailstones).

In the 19th century, ballisticians applied these laws to bullet trajectories. The standard G1 drag function was empirically derived in 1881 by Russian Lt-Gen Mayevsky at the Krupp test range. By matching bullet behaviour to G1 (and later G7 for boat-tail rounds), shooters could predict drop and drift — the same physics that limits a falling raindrop's speed.

Sport parachuting brought terminal velocity into popular consciousness. The International Skydiving Commission (IPC) standardized FAI 2nd category competition speeds in the 1960s. Joe Kittinger's Project Excelsior III (1960, US Air Force) and Felix Baumgartner's Red Bull Stratos jump (2012) pushed human terminal velocity to 274 m/s and 373 m/s respectively by jumping from stratospheric altitudes where ρ is below 1 percent of sea level.

Atmospheric science depends on terminal-velocity calculations to model precipitation. Marshall–Palmer raindrop size distributions (1948) and Beard's 1976 raindrop-fall-speed parametrization are baked into every weather model run by NOAA, ECMWF, and the UK Met Office. Hail science is even more dependent: the National Severe Storms Laboratory (NSSL) uses terminal-velocity to interpret dual-polarization radar signatures and predict damage.

In aerospace engineering, terminal-velocity calculations underlie spacecraft re-entry design. The Apollo Command Module decelerated from 11 km/s orbital speed to a 9 m/s terminal velocity under three 25-m ringsail parachutes. SpaceX Crew Dragon and Boeing Starliner follow the same physics with modern materials. NASA STD-3001 specifies maximum landing impact accelerations that drive parachute-area selection.

Why This Tool Exists

In 2026 a USPA-licensed skydiver wants to verify their canopy-deployment-altitude budget; a NWS meteorologist needs hail-impact velocity for a severe-thunderstorm warning; an AP-Physics student must reconcile their Galileo-in-vacuum textbook with a 120 mph skydiver YouTube clip. This tool exposes the one drag-equilibrium formula with 10 named real-world presets so each user can validate or estimate terminal velocity in seconds.

Terminal Velocity FAQs

Have more questions? Contact us

What Drag-Physics Pros Say

4.9
Based on 5,480 reviews

The skydiver belly vs head-first presets match my real altimeter logs to within 2 percent. I show this to first-jump students to demystify the 120 mph number.

M
Mason Klamath-Brennan
Skydive Instructor &amp; USPA AFF Examiner 2026
May 18, 2026

I use this for severe-weather briefings. The 5 cm softball-class hail terminal-velocity figure aligns with our impact-damage assessments under National Weather Service guidance.

D
Dr. Imelda Ostrovsky
Atmospheric Physicist, Hail Forecasting NOAA 2026
April 29, 2026

Altitude-density adjustment is real. The skydiver presets at sea-level give us the floor; we extrapolate from there for high-altitude jumps. Clean calculator.

L
Lt. Cmdr. Tucker Halverston
Naval Aviator, HALO Parachute Program 2025
December 22, 2025

Excellent teaching tool for FE2701 fluid mechanics. The Stokes-vs-quadratic regime callout in the FAQ is exactly what undergrads miss the first time.

D
Dr. Sandhya Vaidyanathan
Physics Professor, Fluid Dynamics 2026
November 11, 2025

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