The free fall calculator above does something most free-fall tools do not: it lets you include air resistance instead of silently pretending the atmosphere is not there. Ignoring drag is the single most common error in this class of calculator, and it is not a small one — for a human-sized object falling more than a few tens of metres the vacuum answer is meaningfully too fast, and for a long fall it is wrong by a factor of several.
Arb Digital builds free calculators that name their assumptions in the interface rather than in the small print. Here the model selector is the first control on the page, so you always know which physics produced your number. This page explains both models, when the vacuum answer is genuinely adequate, and where terminal velocity takes over entirely.
What This Free Fall Calculator Does
In vacuum mode it applies the standard constant-acceleration equations to an object released from rest. Enter a drop height and it returns the fall time and impact speed; enter a fall time and it returns the distance fallen and the speed reached. Gravity is adjustable, so the same tool works for the Moon, Mars or any other body once you have a surface gravity figure.
In drag mode it uses the quadratic drag model, where resisting force is proportional to the square of speed. That model has an exact closed-form solution for a body falling from rest, involving hyperbolic functions rather than the simple quadratic of the vacuum case. The tool solves it directly rather than by numerical stepping, so results are precise rather than approximate.
The result grid reports fall time, impact speed in kilometres per hour for a more intuitive sense of scale, kinetic energy at impact from the mass you entered, and terminal velocity. In vacuum mode the last item shows the average speed over the fall instead, because terminal velocity does not exist without drag — nothing limits the speed, and an object falling indefinitely in a vacuum simply keeps accelerating.
How to Use It
- Choose the model before anything else. Vacuum for textbook problems and short drops; drag for anything falling for more than a second or two through air.
- Say whether you know the height or the time. The tool solves for the other one, and the hero label names the quantity being reported.
- Adjust gravity if you are not on Earth. The default is standard gravity. The escape velocity calculator reports surface gravity for any planet if you need a figure.
- Fill in mass, area and drag coefficient for the drag model. A skydiver falling flat has a drag coefficient around 1 and a frontal area near 0.7 m²; a compact object is far smaller in both.
- Compare the two models on the same drop. Switching modes with everything else unchanged is the quickest way to see how much the atmosphere actually matters for your case.
The Formula: How Free Fall Is Calculated
In a vacuum, an object released from rest falls a distance h = ½gt2 and reaches a speed v = gt, which combine to give v = √(2gh) and t = √(2h ÷ g). OpenStax University Physics Volume 1, section 3.5 on free fall, is explicit that an object falling without air resistance or friction is what defines free fall, and notes the average value of g as 9.81 m/s2.
The default gravity here is 9.806 65 m/s2, the standard acceleration of gravity, which NIST lists as an exact defined value. Work the default drop: from 45 m, t = √(90 ÷ 9.80665) = 3.029 s and v = 9.80665 × 3.029 = 29.71 m/s, which is 107.0 km/h.
With quadratic drag the resisting force is ½ρCdAv2, the standard drag equation given by NASA Glenn Research Center. Terminal velocity is the speed at which that force equals weight: vt = √(2mg ÷ ρCdA). Speed then follows v = vt tanh(gt ÷ vt) and distance follows h = (vt2 ÷ g) ln cosh(gt ÷ vt), which the tool inverts exactly when you supply a height.
How Much Difference Air Resistance Actually Makes
Run the same 45 m drop through both models with the default 80 kg object, a drag coefficient of 1 and a frontal area of 0.7 m². Terminal velocity for that body works out at about 42.8 m/s. The vacuum model predicts an impact speed of 29.71 m/s after 3.029 s. The drag model predicts about 26.5 m/s after about 3.15 s — roughly 11 per cent slower, arriving a tenth of a second later.
Eleven per cent may sound tolerable until you remember that kinetic energy scales with speed squared, so the energy at impact is about 20 per cent lower. And the gap widens rapidly with height. Over 200 m the vacuum model still predicts unlimited acceleration while the real object is already close to terminal velocity, and beyond that point the vacuum answer diverges without limit while the true speed does not change at all.
The rule of thumb is that drag is negligible while speed is small compared with terminal velocity, and dominant once it is comparable. For a dense compact object with a high terminal velocity — a steel ball, a dropped tool — the vacuum model stays accurate for a surprisingly long way. For anything light, large or flat, it stops being accurate almost immediately.
Terminal Velocity and Why It Exists
Terminal velocity is not a speed limit imposed from outside. It is simply the speed at which drag force has grown to equal weight, leaving zero net force and therefore zero acceleration. Below it the object speeds up; at it the object stops speeding up; it can never be exceeded in a fall from rest.
Because it depends on mass divided by the product of drag coefficient and area, terminal velocity is really a statement about how dense and how streamlined something is. A skydiver spread flat falls at roughly 50 m/s; the same person in a head-down dive, with a fraction of the frontal area, falls much faster. A sheet of paper falls at walking pace; crumpled into a ball, the same paper falls many times faster with no change in mass at all.
Strictly, the approach to terminal velocity is asymptotic — the object gets ever closer without formally arriving. In practice a falling body reaches 99 per cent of terminal velocity within a few multiples of the characteristic time vt divided by g, which for a human is around twelve seconds, or roughly the first 400 metres.
Where Both Models Stop Being Accurate
The quadratic drag model assumes constant air density, a constant drag coefficient, and no lift. All three assumptions weaken in real falls. Air density falls with altitude, so a high-altitude jump begins with a much higher terminal velocity than the sea-level figure this tool reports. The drag coefficient is not fixed either, as it depends on Reynolds number and on the body's orientation, which changes constantly for anything tumbling.
The model also treats the object as falling straight down from rest with no horizontal motion. Any launch velocity, wind, spin or aerodynamic lift takes the problem outside this equation entirely. And for very small or very slow objects — dust, mist, a feather in still air — drag is proportional to speed rather than to speed squared, so a different equation applies from the start. Our drag force calculator covers the drag equation itself in more detail.
Reading Impact Energy Rather Than Impact Speed
Speed is the number people ask for, but energy is usually the number that matters. Kinetic energy at impact is one half of mass times speed squared, and because of that square it grows far faster than the drop height suggests. Doubling the drop height in a vacuum multiplies speed by about 1.41 and energy by exactly two — energy is simply proportional to height, which is the cleanest way to think about a fall.
The grid reports impact energy in joules from the mass you entered. For the default 80 kg object from 45 m the vacuum figure is around 35,300 J, which is comparable to the kinetic energy of a small car at 30 km/h. Expressing a fall that way tends to be more informative than a speed in metres per second, particularly when comparing two very different objects.
What energy alone does not tell you is the force on impact. That depends on stopping distance, which is a property of what is hit rather than of the fall. The same energy absorbed over a centimetre of concrete or a metre of crash mat produces forces differing by a factor of a hundred, and the force calculator shows how directly deceleration and force are tied together.
How This Fits With the Site's Other Physics Tools
The boundary against the converters is simple: a converter rescales a quantity between units, while this calculator derives fall time, speed and energy from formulas. The speed converter will turn an impact speed into miles per hour, and the energy converter will turn the impact energy into calories or foot-pounds, but neither can produce those numbers from a drop height.
Among the calculators, the acceleration calculator handles constant-acceleration problems that are not vertical falls, and the speed distance time calculator covers steady motion. The kinetic energy calculator takes the impact speed from this page and works with it further, and the gravitational force calculator gives the underlying attraction between two masses that makes any of this happen.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using the vacuum model for a long fall — it predicts unlimited acceleration, while a real object stops speeding up once drag balances weight.
- Assuming mass changes the vacuum answer — it does not. In a vacuum a feather and a hammer fall identically; mass only matters once drag is in play.
- Forgetting the object starts from rest — a thrown object has an initial velocity that these equations do not include.
- Using sea-level air density for a high-altitude drop — thinner air means a higher terminal velocity, sometimes far higher.
- Treating terminal velocity as a fixed property of a person or object — it changes with posture, orientation and area, often by a factor of two or more.
Related Free Tools From Arb Digital
Rescale results with the speed converter or the energy converter. For the drag side of the problem use the drag force calculator, and for other motion problems the acceleration calculator and the speed distance time calculator. The kinetic energy calculator takes impact speed further, the gravitational force calculator covers attraction between masses, and the escape velocity calculator gives surface gravity for other worlds. The full free online tools hub lists everything.
Frequently Asked Questions
Only if you choose the vacuum model, which is the default. The model selector at the top of the tool also offers a quadratic air-resistance model that includes terminal velocity, and the page reports which one produced your result.
Not in a vacuum, where mass cancels out of the equations entirely and everything falls identically. With air resistance mass does matter, because terminal velocity increases with mass for a given size and shape, so a denser object does fall faster through air.
The speed at which drag force exactly balances weight, leaving no net force and therefore no further acceleration. It is the square root of twice the weight divided by the product of air density, drag coefficient and frontal area.
While the speed reached is small compared with terminal velocity. For a dense compact object with a high terminal velocity the vacuum model stays close for a long drop; for anything light or with a large area it diverges within the first second or two.
The standard acceleration of gravity, 9.80665 metres per second squared, which NIST lists as an exact defined value. The field is editable, so entering a different figure lets you model a fall on the Moon, Mars or any other body.
No. These equations assume release from rest with no initial velocity and no horizontal motion. A thrown or launched object is a projectile problem, which needs the initial velocity and launch angle as additional inputs.
Because the equation of motion with drag proportional to speed squared has an exact solution in terms of hyperbolic tangent for speed and hyperbolic cosine for distance. Solving it that way is precise, where numerical stepping would only approximate it.
This tool is provided for educational and study use. It models an idealised fall with constant gravity and, where selected, constant air density and drag coefficient, and it is not a safety, rescue or engineering assessment of any real fall.
