Free Fall Calculator

Free Fall Calculator turns a fall time, a drop height or an impact speed into the other two. It then repeats the same fall with air resistance, terminal velocity and impact energy.

Free Fall Calculator for Time, Height and Speed

The Free Fall Calculator needs one known value. Enter a fall time, a fall height or an impact velocity, and it returns the other two for an object falling straight down. The headline result is the ideal case, with gravity as the only force.

Gravity defaults to Earth’s standard 9.80665 m/s². The preset menu also holds the Moon, Mars, Venus and Jupiter, with values from the NASA Planetary Fact Sheet, and any other value can be typed in.

With Result Units set to US, the gravity field switches to ft/s² and Earth reads 32.174. A textbook value such as 32.2 ft/s² can then be entered as it is. An initial downward velocity covers objects that are thrown down instead of dropped.

Four result cards follow the headline. They give the final velocity in three units, the distance covered in the final second, the kinetic energy and momentum at impact, and the terminal velocity with the same fall worked out in air.

A fall table and a distance-time graph sit below the cards, with the ideal curve drawn against the air-drag curve. An object thrown upward first is a different problem, and the Displacement Calculator handles that turnaround with a negative acceleration.

Free Fall Formula

Free fall is motion with constant acceleration g, so the kinematic equations apply with g in place of a. OpenStax University Physics sets them out for falling objects. With down taken as positive, the free fall formula for distance after a time t is the first line below, and the velocity is the second.

$$h = v_0 t + \frac{1}{2} g t^2$$

$$v = v_0 + g t$$

Here h is the distance fallen, v₀ is the initial downward velocity, g is the acceleration of gravity and t is the fall time. For an object dropped from rest, v₀ is zero and the distance is simply half of g times the time squared.

Fall time from height

When the height is known, the same equation is solved for time. From rest it reduces to the square root of 2h ÷ g. A 100 m drop takes 4.52 s, and a 100 ft drop takes 2.49 s, both without air.

$$t = \frac{\sqrt{v_0^2 + 2 g h} – v_0}{g}$$

Free fall formula for height

When the impact velocity is known, the height it must have fallen from comes from the velocities alone. An object that lands at 25 m/s from rest fell 31.87 m in 2.55 s. The impact velocity for a known height is the same relation turned around.

$$h = \frac{v^2 – v_0^2}{2 g}$$

$$v = \sqrt{v_0^2 + 2 g h}$$

The OpenStax chapter works one example that makes a good check. A ball is thrown down at 4.9 m/s from a 98 m building, with g taken as 9.8 m/s². The textbook gives 4.0 s and 44.1 m/s, and the Free Fall Calculator returns the same pair with those inputs.

Free Fall Distance by Time

Used as a free fall distance calculator, the tool gives the figures in this table for a drop from rest on Earth. The ideal columns ignore air. The last two columns use the free fall calculator with air resistance for an 85 kg skydiver falling flat, the default object in the tool.

A 4 second free fall covers 78.45 m, or about 257 ft, and ends at 39.23 m/s. In feet, a 2 second fall is 64.35 ft and a 3 second fall is 144.78 ft. Doubling the time gives four times the distance, because distance grows with the square of the time.

The longer rows show why air matters. A 12 second fall is 706 m deep on paper, and a 30 second fall is 4,413 m. A real skydiver covers only 394 m and 1,192 m in those times, because the speed stops rising near 44 m/s.

The fall is never even from second to second. In a 4 s drop the object covers 4.9 m in the first second and 34.32 m in the final second. The second result card in the Free Fall Calculator shows that split for any fall time, and falls shorter than two seconds are split into halves.

Free Fall With Air Resistance

Ideal free fall has no speed limit, but air does. OpenStax gives the drag force on a fast object as proportional to the square of its speed. In the formula, ρ is the air density, C is the drag coefficient and A is the frontal area.

$$F_D = \frac{1}{2} \rho C A v^2$$

Drag grows until it equals the weight, and from then on the speed stays constant. That speed is the terminal velocity. Setting drag equal to mg and solving for speed gives the formula the tool uses as a free fall calculator with terminal velocity.

$$v_T = \sqrt{\frac{2 m g}{\rho C A}}$$

The default object in the Free Fall Calculator is the textbook’s 85 kg skydiver in a flat position, with C = 1.0, A = 0.70 m² and air at 1.21 kg/m³. The tool returns 44.37 m/s, which the textbook rounds to 44 m/s. Switching to 75 kg, C = 0.70 and A = 0.18 m² gives the head-first case, 98 m/s or about 350 km/h.

The speed on the way to terminal velocity follows a tanh curve for an object dropped from rest. The flat skydiver reaches 90% of terminal velocity after 6.7 s and 99% after 12 s. After that, extra fall time adds distance at a steady rate and no more speed.

$$v(t) = v_T \tanh\left(\frac{g t}{v_T}\right)$$

A height can be compared the same way. From 100 m the ideal result is 4.52 s and 44.29 m/s, while the same skydiver in air takes 4.9 s and lands at 35.24 m/s. The message under the results says whether the gap is large enough to matter.

The drag model keeps air density and the drag coefficient constant and leaves out buoyancy. That suits falls of a few kilometers near the ground. Bullets are handled differently, with a measured ballistic coefficient, as in the Ballistic Coefficient Calculator.

Weight, Energy and Momentum at Impact

Mass does not change the ideal fall time or speed. It does set what the object carries into the ground, which is why the tool also works as a free fall calculator with weight. An 85 kg object after a 4 s fall has 65.4 kJ of kinetic energy and 3,334.3 kg·m/s of momentum.

The same card lists the weight, mass times g, which is 833.57 N for 85 kg on Earth. With US result units the three values switch to ft·lbf, lbf·s and lbf. The momentum figure is the starting point for a collision problem in the Conservation of Momentum Calculator.

What is weight in free fall?

The weight of a falling object is still mg, because gravity keeps pulling on it. What disappears is the apparent weight. A scale falling along with the object would read zero, since nothing pushes back against it, and that is the weightless feeling of a drop.

Free Fall on the Moon, Mars and Jupiter

Changing gravity in the Free Fall Calculator rescales every result. The table uses the preset values for a drop from rest. Distance and speed after 4 s rise in step with g, while the time to fall 100 m shrinks with its square root.

NASA lists these as the acceleration at the equator including the planet’s rotation, and Jupiter’s figure is taken at the 1 bar pressure level because it has no solid surface. The air density field should be changed too when the drag card is used for another world.

A car leaving a ramp falls the same way in the vertical direction while it keeps moving forward. The Car Jump Distance Calculator combines that drop with the forward speed, and other motion tools are listed under Kinematics Calculators.

Free Fall Definitions and Fall Rates

How is free fall defined?

Free fall is motion in which gravity is the only force acting on an object. The acceleration is then g, directed downward, whatever the object’s mass. The definition covers objects moving upward as well, so a ball is in free fall from the moment it leaves the hand.

Real falls through air only approximate it. A dense object dropped a few meters comes close, and a skydiver after a few seconds does not. The Free Fall Calculator shows both versions so the size of the difference is visible for each case.

How do you calculate fall time?

For a drop from rest, divide twice the height by g and take the square root. A 20 m drop gives √(40 ÷ 9.80665) = 2.02 s. In the Free Fall Calculator, set Known Value to Fall Height to get the time, the impact velocity and the fall time with drag together.

The fall rate is not one number, because the speed changes all the way down. The rate of change is g, so the speed rises by 9.81 m/s, or 32.17 ft/s, in every second of an ideal fall. The average speed over a drop from rest is half the final speed.

What is a 1:40 fall?

That is a different meaning of the word. In drainage and paving, a fall is a slope, and 1:40 means the surface drops 1 unit for every 40 units of run. That is 25 mm per meter, or a 2.5% gradient.

To calculate fall over distance for a slope, divide the run by the ratio. A 6 m pipe run at 1:40 needs 6,000 ÷ 40 = 150 mm of fall from one end to the other. None of the free fall formulas above apply to it.