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.

Last updated: December 20, 2025

CreatorFrank Zhao

Traveling Object

Object Mass (m)

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Drop Height (h)

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Gravitational Acceleration (g)

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m/s²

Drag Coefficient (k)

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Cross-section Area (A)

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m²

Drag Coefficient (Cd)

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Medium Density (ρ)

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kg/m³

Time and Velocity

Fall Duration (t)

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sec

Peak Velocity (vmax)

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m/s

Terminal Velocity (vt)

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m/s

Drag Force

At Velocity...

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m/s

Aerodynamic Drag Is...

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Quick Navigation

This Free Fall with Air Resistance Calculator is a more realistic variation of our Free Fall Calculator. It accounts for aerodynamic drag, so you can estimate fall time and speed more accurately — including terminal velocity and the maximum speed actually reached.

→Introduction / overview
→What is free fall?
→Air resistance formula
→Maximum vs. terminal velocity
→How to calculate air resistance (step-by-step)
→Real-world examples
→Common scenarios
→Tips & best practices
→Calculation method / formulas
→Related concepts
→FAQs
→Limitations & sources

Introduction / Overview

What this calculator does

It estimates free-fall motion when air resistance matters — including fall time, terminal velocity, maximum velocity before impact, and drag force at a chosen speed. The goal is not “perfect aerospace simulation”, but fast, practical, and physically consistent estimates.

Who it’s for

Students learning drag, curious skydivers comparing posture assumptions, and anyone who wants a realistic “impact speed” estimate for a drop.

Why it’s more realistic than vacuum fall

Drag grows quickly with speed, so acceleration fades over time. That’s why real falls often top out at a “speed limit” instead of accelerating forever.

Prefer watching rather than reading?

Here’s a quick YouTube search for “free fall with air resistance” — great for building intuition before you start plugging numbers in.

Watch on YouTube

Related Concepts / Background

What is free fall?

In strict physics, “free fall” means gravity is the only force acting — which can describe a falling object or an orbiting body. In everyday use (and in this calculator), we mean “falling toward the ground without external thrust”, while gravity pulls down and air resistance pushes up.

Gravity (weight)

F_g = m g

Drag (air resistance)

F_d = k v^2

Air resistance formula

Aerodynamic drag is a force that opposes motion. In this tool we use a quadratic drag model (common for many real falls):

F_d = k\,v^2

The coefficient $k$ bundles together medium density, the object’s area, and its shape. If you want to compute it from common inputs, a typical relationship is:

k = \frac{\rho\,A\,C_d}{2}

$\rho$ : medium density (air near sea level ≈ $1.225\ \mathrm{kg/m^3}$ )
$A$ : cross‑sectional area
$C_d$ : drag coefficient (shape-dependent)

Maximum vs. terminal velocity

Terminal velocity is the “speed limit” where drag balances weight and acceleration fades to zero. But an object may hit the ground before reaching that limit — that’s why the calculator also reports the maximum speed reached during the fall.

Terminal velocity

Defined by $F_d = F_g$ :

k v_t^2 = m g

v_t = \sqrt{\frac{m g}{k}}

Maximum velocity

$v_{max}$ is the speed at impact for your chosen height. It’s always $\le v_t$ in this model.

For basic unit conversions, use our Velocity Calculator.

If you want to study terminal velocity in isolation, try our Terminal Velocity Calculator.

How to Use / Quick Start

Here’s a practical walkthrough using a classic scenario (a skydiver). You can follow these steps with any object.

Enter mass: $m = 75\ \mathrm{kg}$ .
Enter altitude: $h = 2000\ \mathrm{m}$ .
Keep the default air resistance coefficient: $k = 0.24\ \mathrm{kg/m}$ .
Read results: fall time, terminal velocity $v_t$ , and maximum velocity $v_{max}$ .
(Optional) Copy the max velocity into the drag-force section to compute drag force at that speed.

Worked example: drag force at max speed

With the values above, terminal velocity is very close to $55.4\ \mathrm{m/s}$ , and in this height range the skydiver reaches it. To estimate drag force at that speed:

F_d = k v^2

=

0.24\,(55.4)^2

=

736.6\ \mathrm{N}

Quick intuition check: at terminal velocity, drag force is close to weight $mg$ . For $m=75$ , $mg \approx 736\ \mathrm{N}$ — very close.

Tip: if you mainly want the “vacuum” answer, use the Free Fall Calculator, then compare results side by side.

Real-World Examples / Use Cases

These examples use realistic numbers and show the kind of questions this calculator answers. (Your exact results may vary depending on your choice of $k$ .)

Skydiver from 2000 m

Background: estimate whether terminal velocity is reached.

Inputs:

m=75\ \mathrm{kg}

h=2000\ \mathrm{m}

k=0.24\ \mathrm{kg/m}

v_t

=

\sqrt{mg/k}

\approx

55.4\ \mathrm{m/s}

Result: the fall is long enough that

v_{max} \approx v_t

Application: use this to sanity-check speed expectations (and compare with the vacuum result).

Small object short drop

Background: a short drop often doesn’t get close to terminal velocity.

Inputs:

m=0.20\ \mathrm{kg}

h=5\ \mathrm{m}

k=0.01\ \mathrm{kg/m}

Result:

v_t\approx 14.0\ \mathrm{m/s}

v_{max}\approx 8.8\ \mathrm{m/s}

Meaning: you’re far below the “speed limit”, so drag matters less than in long falls.

High-drag object reaches terminal fast

Background: a light object with high drag hits terminal speed quickly.

Inputs:

m=0.43\ \mathrm{kg}

h=20\ \mathrm{m}

k=0.06\ \mathrm{kg/m}

Result:

v_t\approx 8.4\ \mathrm{m/s}

v_{max}\approx 8.4\ \mathrm{m/s}

Application: explains why some objects never feel “fast” even from decent heights.

Streamlined drop test

Background: lower drag means higher impact speed.

Inputs:

m=2\ \mathrm{kg}

h=100\ \mathrm{m}

k=0.05\ \mathrm{kg/m}

Result:

v_t\approx 19.8\ \mathrm{m/s}

v_{max}\approx 19.7\ \mathrm{m/s}

Meaning: the object can get very close to terminal velocity over 100 m.

Want the easiest “sanity check” speed? Use the vacuum model first, then compare: Free Fall Calculator.

Common Scenarios / When to Use

You suspect drag matters

People, flat objects, or anything that “catches air” tends to have a large effective k.

You want impact speed

Use v_max to estimate how fast the object is moving at the ground.

You want drag force

Plug a speed into the drag-force section to estimate F_d.

You’re comparing models

Run the vacuum version and compare results side by side.

You’re teaching/learning

Quadratic drag is a great example of a non-linear differential equation with a clean solution.

You need a quick intuition check

Adjust k up and down to see sensitivity, then refine if needed.

When it may not apply

Very small particles moving slowly through thick liquids may follow a linear drag model (Stokes’ law) instead. Very high-altitude falls may require changing air density.

Tips & Best Practices

If you don’t know $k$ , start with the default, then try a higher and lower value to see sensitivity.
Use consistent units. The calculator supports unit switching, but mixing assumptions is a common source of errors.
If $v_{max}$ is close to $v_t$ , you’re in a drag-dominated regime.
For quick mental checks, compare $mg$ and $k v^2$ at your speed of interest.

Common mistake

Confusing terminal velocity with maximum velocity. Terminal velocity depends on $m$ , $g$ , and $k$ ; maximum velocity depends on the available height/time before impact.

Calculation Method / Formula Explanation

The model assumes quadratic drag and falling from rest. The net-force equation is:

m\frac{dv}{dt} = mg - k v^2

Terminal velocity

Set $dv/dt = 0$ and solve:

v_t = \sqrt{\frac{mg}{k}}

Velocity over time

v(t) = v_t\,\tanh\left(t\sqrt{\frac{gk}{m}}\right)

Height vs time (used internally)

h(t) = \frac{m}{k}\ln\left(\cosh\left(t\sqrt{\frac{gk}{m}}\right)\right)

If you’re solving “time from height”, the calculator rearranges this relationship.

Drag force at a chosen speed

F_d = k v^2

Variable guide

m

: mass

h

: drop height / altitude

g

: gravitational acceleration

k

: quadratic drag coefficient

v_t

: terminal velocity

v_{max}

: max velocity before impact

Frequently Asked Questions

Does mass affect falling speed?

With drag, yes. Terminal velocity scales like $v_t = \sqrt{mg/k}$ , so a larger $m$ generally increases $v_t$ .

What does the coefficient k represent?

It bundles aerodynamics into one number. A typical relationship is $k = \rho A C_d / 2$ , where $\rho$ is density, $A$ is area, and $C_d$ is shape-dependent.

Can maximum velocity exceed terminal velocity?

Not in this quadratic model. You should always see $v_{max} \le v_t$ .

Why is drag proportional to v^2 here?

For many everyday falls at moderate to high speed, quadratic drag matches measurements well. At low speeds in viscous fluids, a linear model can be better.

Why does the math use tanh and cosh?

The differential equation $m dv/dt = mg - kv^2$ integrates to a hyperbolic form. It’s the standard closed-form solution for quadratic drag.

Does this account for wind or parachutes?

No. It assumes vertical motion with a constant drag coefficient.

Is air density always 1.225 kg/m^3?

That’s a common sea-level reference value. Real density changes with altitude, temperature, and humidity.

How do I sanity-check the drag force result?

Use $F_d = kv^2$ with the same $k$ and $v$ shown in the calculator. Near terminal velocity, compare to $mg$ .

Limitations / Disclaimers

Educational use

This calculator is for learning and estimation. It’s not a substitute for engineering safety analysis, professional skydiving instruction, or equipment certification.

Assumes constant $g$ and constant air density.
Uses a single quadratic drag coefficient $k$ (no posture/shape change mid-fall).
Does not model wind, lift, tumbling, or parachute deployment.

External references

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