Free Fall Calculator
Fall time, impact speed and distance for an object dropped from rest, with no air resistance or with quadratic drag and its terminal velocity.
Result…
How it's calculated
No drag: t = √(2h ÷ g), v = g t, h = ½ g t² Terminal velocity v_t = √(2 m g ÷ (ρ C_d A)) With drag: v(t) = v_t tanh(g t ÷ v_t), h(t) = (v_t² ÷ g) ln cosh(g t ÷ v_t) Impact speed from height: v = v_t √(1 − e^(−2 g h ÷ v_t²))
Without air, a dropped object gains g metres per second of speed every second, so distance grows with the square of time. With air, drag pushes back with ½ ρ C_d A v², which grows with speed until it equals the weight m g: that speed is the terminal velocity. Solving m dv/dt = m g − ½ ρ C_d A v² from rest gives the tanh and ln cosh formulas used here exactly, with no step-by-step simulation. Imperial inputs are converted with 1 ft = 0.3048 m and 1 lb = 0.45359237 kg.
Your numbers, step by step
About the Free Fall calculator
This free fall calculator finds how long an object dropped from rest takes to fall, how fast it hits the ground and how far it falls. Start from the height, the fall time or the impact speed. With air resistance ignored it uses the textbook formulas with g = 9.80665 m/s², which you can change for another place or planet. Switch on drag and enter the object's mass, frontal area, drag coefficient and the air density, and it works out the terminal velocity √(2 m g ÷ (ρ C_d A)) and the fall with quadratic drag from the exact tanh solution, so no rough step-by-step simulation is involved. Metric and imperial units both work, with feet and pounds converted exactly. The working is shown at each step, and with drag on it also gives the no-drag fall time to compare.
How to use it
- Choose whether to ignore or include “Air resistance”, and pick metric or imperial “Units”.
- Under “I know the”, choose height, fall time or impact speed and enter that value.
- Leave “Gravitational acceleration” at 9.80665 m/s² or enter the value for your location.
- With drag, enter the “Mass of the object”, “Frontal area”, “Drag coefficient” and “Air density” for your object and conditions.
- Read the fall time or distance, the impact speed and, with drag, the terminal velocity.
Worked example
A stone dropped 45 m with no air resistance falls for √(2 × 45 ÷ 9.80665) = 3.03 s and lands at 9.80665 × 3.03 = 29.7 m/s, about 107 km/h. With drag, an 80 kg body with a 0.7 m² frontal area, a drag coefficient of 1 and air at 1.225 kg/m³ has a terminal velocity of √(2 × 80 × 9.80665 ÷ (1.225 × 1 × 0.7)) = 42.8 m/s. Falling 1000 m takes 26.4 s instead of 14.3 s in a vacuum.
Updated
Questions people ask
How do I calculate how long something takes to fall?
With no air resistance, time t = √(2h ÷ g). For a 20 m drop that is √(2 × 20 ÷ 9.80665) = 2.02 s. Air slows light or wide objects, so include drag when that matters.
What is the formula for terminal velocity?
Terminal velocity is √(2 m g ÷ (ρ C_d A)), where m is mass, ρ the air density, C_d the drag coefficient and A the frontal area. At that speed the drag force equals the weight and the object stops speeding up.
Do heavier objects fall faster?
In a vacuum, no: every object falls with the same acceleration g. In air, a heavier object of the same shape and size has a higher terminal velocity, so it falls faster once drag becomes important.
Where do I get a drag coefficient and frontal area?
They depend on the object's shape and how it is oriented as it falls, so use a measured or published value for your object. A common mistake is using the total surface area instead of the area facing the airflow.
Can I use this for something thrown sideways or upwards?
No, it assumes the object starts from rest and falls straight down. For a launch at an angle, use the projectile motion calculator.
How accurate is the free fall calculator with drag?
The formulas are exact for drag proportional to speed squared with a fixed drag coefficient, area, air density and g. Real objects tumble, and the air thins with height, so treat very long falls as estimates.