Free Fall with Air Resistance Calculator
Compute fall time, terminal velocity, and drag force
Analyze free fall motion considering both gravity and aerodynamic drag. Calculate terminal velocity, maximum speed, and air resistance forces.
Traveling Object
Time and Velocity
Drag Force
Introduction / overview
This calculator estimates falling motion when gravity and aerodynamic drag both matter. Compared with a basic free-fall model, the results are usually more realistic because the falling object doesn’t keep accelerating forever.
✅ Use it when you want a realistic fall time or speed estimate — especially for skydivers, paratroopers, falling objects in the air, and high drops where drag can’t be ignored.
What problems it helps with
- Estimate fall time from a height
- Understand terminal velocity vs peak velocity
- Compute drag force at a chosen speed
Who typically uses it
- Students learning drag & terminal speed
- Engineers doing quick “back-of-the-envelope” checks
- Curious people comparing “with drag” vs “no drag”
Want the idealized version (no drag)? Try our Free Fall Calculator to compare.
What is free fall?
In a strict physics definition, free fall means the only force acting is gravity. In real life, objects moving through air also experience drag — so this calculator uses a practical definition: “an object falling downward under gravity while being slowed by air resistance.”
A quick intuition
- At the start, gravity dominates → speed increases quickly.
- As speed grows, drag grows → acceleration shrinks.
- Eventually, drag balances gravity → speed stops increasing (terminal velocity).
Air resistance formula
This calculator models drag using a common “quadratic drag” relationship where drag force grows with the square of speed.
Drag force model
Where is drag force (), is speed (), and is the air resistance coefficient.
The coefficient bundles together the effects of air density, object size, and shape. If you open the optional section in the calculator, you can estimate it from more “physical” inputs:
Coefficient from geometry & air density
is air density (), is cross-sectional area (), and is the dimensionless drag coefficient.
Tip: If you don’t know or , start with the default and treat it as a calibration knob. Small changes in can noticeably change the predicted fall time.
Maximum vs. terminal velocity
Terminal velocity is the steady speed reached when drag balances weight. But many real falls end before that balance happens — the object hits the ground first.
Terminal velocity ()
The theoretical “speed limit” in this model for a given mass, gravity, and . If the fall is long enough, the speed approaches .
Peak / maximum velocity ()
The highest speed reached during the actual fall before impact. It can be below if the drop is short.
✅ If you enter a peak velocity that’s greater than terminal velocity, the calculator warns you — because in this model you’d need infinite time to reach that speed.
How to use (quick start)
You can use the calculator in a “forward” way (give inputs → get results) or in a “reverse” way (set a result like and solve for time/height). Here’s the fastest workflow.
Enter the object mass and drop height
For example: , .
Choose gravity and drag coefficient ()
Keep Earth gravity by default, then use the default as a starting point.
Read the results (time, , )
With the example above, you should see approximately:
Compute drag force at the peak speed
Use the Use Peak Velocity shortcut button to copy into the drag-force section, then read the force.
Want a comparison baseline? Open our Free Fall Calculator with the same height and see how much faster the “no drag” model becomes.
How to calculate air resistance (hands-on example)
Let’s do a practical example: a skydiver falling from a high altitude. We’ll estimate fall time, terminal velocity, and the drag force near the peak speed.
Example inputs
Object mass
= 75
Drop height
= 2000
Gravitational acceleration
= 9.80665
Drag coefficient
= 0.24
What the calculator will compute
Fall time
40
Terminal velocity
55.4
Peak velocity
55.4
📝 Note
Small differences are normal depending on rounding, units, and whether you adjust . This fall is long enough to essentially reach terminal velocity.
After you have , tap the Use Peak Velocity button in the Drag Force section. It’s the fastest way to estimate drag force at the most relevant speed.
Real-world examples / use cases
Skydiving planning
Try , , to see how close gets to .
Object drop checks
Estimate whether a falling object is closer to “ideal” free fall or heavily drag-limited.
Body position sensitivity
Use the optional section to adjust and to represent “spread-eagle” vs “streamlined” posture.
Tips & best practices
Start with a stable input set
A good “first run” is: mass + height + (and keep default). Then explore what changes when you tweak .
Common mistakes to avoid
- Entering greater than (the calculator will warn you).
- Mixing unit systems without noticing (double-check the unit dropdowns).
- Assuming the default applies to all shapes (it’s a starting point, not a universal constant).
Calculation method & formulas
The calculator uses the quadratic drag model with an analytic solution for velocity and position. A few key relationships are helpful for interpretation.
Terminal velocity
Heavier objects (larger ) tend to have higher . Stronger drag (larger ) lowers .
Variable glossary (what each symbol means)
Mass
Object weight, measured in kilograms ()
Drop height
Distance fallen from starting point, in meters ()
Gravitational acceleration
Strength of gravity, typically on Earth
Air resistance coefficient
Combines effects of density, area, and shape ()
Speed / Velocity
How fast the object is moving, in meters per second ()
Drag force
Air resistance pushing back against motion, in Newtons ()
Related concepts / background
Why density matters ()
Air density changes with altitude, temperature, and humidity. In many everyday scenarios, using sea-level density is “good enough” for quick estimates.
Why shape matters ()
A streamlined shape can have a much lower than a blunt one. That’s why posture changes can dramatically change terminal velocity.
Frequently asked questions (FAQs)
Why is my peak velocity lower than terminal velocity?
Because the drop may be too short. Terminal velocity is a long-time limit; peak velocity is what you actually reach before impact.
What does the warning “peak velocity cannot exceed terminal velocity” mean?
In this model, speeds above aren’t reachable in finite time. The warning is a physics sanity check, not a software error.
Should I calculate from , , and ?
If you know those values, yes — it makes less “mysterious.” If you don’t, it’s totally fine to treat as an adjustable parameter.
Can I use this for supersonic speeds?
Not reliably. Drag behavior changes near and above the speed of sound, and can vary significantly with speed.
What if I want the idealized “no air” version?
Use our Free Fall Calculator and compare the difference.
Limitations & sources
Limitations
- Assumes quadratic drag with a constant (real drag can vary with speed and posture).
- Assumes constant gravity and constant air density.
- Ignores wind, lift, tumbling, parachute deployment dynamics, and body control.
External References & Sources
Core Physics Principles
Feynman Lectures on Physics: Mechanics & Heat
Richard Feynman, Robert B. Leighton, Matthew Sands (1963)
Classic university-level treatment of classical mechanics including drag forces and motion. ISBN: 978-0201021127
OpenStax Physics: Drag Forces
OpenStax College (2013)
https://openstax.org/books/physicsFree, peer-reviewed textbook covering drag forces, terminal velocity, and numerical solutions.
Terminal Velocity & Case Studies
"The Physics of Skydiving"
Theresa Knott & Tom Waigh, University of Manchester
Practical analysis of skydiver aerodynamics, drag coefficient variation with body position, and realistic calculations for different postures.
"How do small animals escape from a fall?"
Lyd Luc Snik (1945)
Seminal study on terminal velocity and falling mechanics in small creatures (mice, rats), showing how larger creatures can safely fall from heights.
Wikipedia: Terminal Velocity
https://en.wikipedia.org/wiki/Terminal_velocityComprehensive overview with empirical measurements for humans, animals, and objects.
Advanced Modeling
"Modeling High-Altitude Free Fall with Variable Gravity & Air Density"
Advanced physics research
For high-altitude jumps or near-vacuum conditions, gravity and air density are not constant. This guide uses simplified constant assumptions.
"Felix Baumgartner Stratospheric Jump Analysis"
Red Bull Stratos mission data
https://www.redbullstratos.com/Real stratospheric jump data (128 km altitude) demonstrating extreme air density variations and exceeding local speed of sound.
Drag Coefficient & Fluid Mechanics
"Hydrodynamics" (Classical Treatise)
Horace Lamb (1932)
Foundational work on fluid resistance. ISBN: 978-0486602561. Mathematical derivation of drag forces in Newtonian fluids.
NASA Glenn: Drag Equation
https://www.grc.nasa.gov/www/k-12/airplane/drageq.htmlAuthoritative introductory resource on the drag equation, drag coefficient, and reference areas.
Wikipedia: Drag (Physics)
https://en.wikipedia.org/wiki/Drag_(physics)Overview of drag types (quadratic, linear, Stokes), drag coefficients for various shapes, and Reynolds number effects.
Real-World Applications
"Parachute Design & Deployment Dynamics"
Professional skydiving engineering
Our calculator excludes parachute effects. Real skydives use staged descent: free fall, drogue deployment, main parachute deployment.
"Meteorite Impact & Atmospheric Braking"
Planetary science
Drag forces significantly reduce meteorite impact velocity. This calculator models the basic physics used in impact energy estimates.
"Sediment Transport & Settling Velocity"
Geophysics & hydrology research
Terminal velocity calculations are essential for modeling particle settling in rivers, lakes, and oceans (Stokes' law for small particles).
Numerical & Mathematical Methods
"Numerical Recipes: The Art of Scientific Computing"
William H. Press, et al. (3rd ed., 2007)
Standard reference for numerical integration methods (Runge-Kutta, Euler) used to solve differential equations like the free fall model. ISBN: 978-0521880688
"Solving Differential Equations Numerically"
MIT OpenCourseWare
https://ocw.mit.edu/Free online courses covering ODE solvers for physics simulations.
Biological Applications & Scaling
"Allometric Scaling Laws in Biology"
Geoffrey B. West, James H. Brown, Brian J. Enquist (1997)
Scaling of body size to terminal velocity. Larger organisms have higher terminal velocities; small animals experience proportionally higher drag.
"Seed Dispersal by Wind: Terminal Velocity & Trajectory"
Plant ecology research
Seeds, pollen, and spores rely on air drag for dispersal strategies. Terminal velocity determines spread distance.
"Comparative Biomechanics: Life's Physical World"
Steven Vogel (2nd ed., 2003)
Comprehensive treatment of how drag affects animal locomotion, falling, and flight. ISBN: 978-0691112977
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