Free Fall with Air Resistance Calculator

Free Fall with Air Resistance Calculator gives fall time and impact velocity from a height, or fall distance from a time. It adds terminal velocity, drag force and a no-air result.

Free Fall with Air Resistance Calculator Setup

The Free Fall with Air Resistance Calculator starts from a fall height or a fall time. It then needs the object, because air affects every object differently. The presets load a skydiver falling flat, a skydiver falling head first or a 4 mm raindrop, and Custom Object accepts any mass.

Drag Details holds the three things that set the air resistance, which are the drag coefficient, the frontal area and the air density. A problem that already gives an air resistance coefficient k can skip them. Switch Drag Entered As to Coefficient k and type the value in kg/m.

The headline is the fall time for a known height, or the fall distance for a known time. Four cards follow with the terminal velocity, the impact velocity, the drag force at impact and the same fall with no air. A speed-time graph shows the curve bending toward the terminal velocity line.

Gravity, an initial velocity and US units sit in the last section. A negative initial velocity means the object is thrown upward first, and the tool follows it up to the peak and back down. The Free Fall Calculator covers the no-air case on its own, including other planets.

Free Fall with Air Resistance Formula

For an object moving fast through air, OpenStax University Physics gives a drag force proportional to the square of the speed. The constants are collected into one air resistance coefficient k, built from the air density ρ, the drag coefficient C and the frontal area A.

$$F = k v^2$$

$$k = \frac{1}{2} \rho C A$$

The flat skydiver preset uses C = 1.0, A = 0.70 m² and sea level air at 1.225 kg/m³, so k = 0.4288 kg/m. Terminal velocity is the speed where this drag equals the weight mg. For the 85 kg skydiver that is 44.09 m/s, or 158.7 km/h.

$$v_T = \sqrt{\frac{m g}{k}}$$

Newton’s second law with this drag force can be solved exactly for a drop from rest. The speed after a time t follows a tanh curve, and the distance fallen follows the logarithm of a cosh. These two lines are what the Free Fall with Air Resistance Calculator evaluates when the known value is the fall time.

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

$$y(t) = \frac{v_T^2}{g} \ln\left(\cosh\left(\frac{g t}{v_T}\right)\right)$$

When the known value is the height h, the same solution is turned around. It gives the impact velocity first and then the fall time. This is the route to calculate the velocity of a falling object from height with drag included.

$$v = v_T \sqrt{1 – e^{-2 g h / v_T^2}}$$

$$t = \frac{v_T}{g} \cosh^{-1}\left(e^{g h / v_T^2}\right)$$

The default 100 m drop returns 35.15 m/s after 4.9 s, against 44.29 m/s and 4.52 s with no air. A second check uses k directly. A 75 kg skydiver with k = 0.24 kg/m falling 2,000 m takes 40 s and reaches the terminal velocity of 55.4 m/s, where the drag force is 735.5 N.

Impact Velocity From Height With Drag

The table runs the flat skydiver through the Free Fall with Air Resistance Calculator from six heights at sea level. Low drops stay close to the ideal figures. From 500 m upward the speed is pinned near 44 m/s, and extra height only adds time.

The second card reports when the object gets within 1% of terminal velocity. The flat skydiver needs 11.9 s and 388 m of fall to get there. Head first, with C = 0.70 and A = 0.18 m², the terminal velocity rises to 97.62 m/s and the same point takes 26.3 s and 1,903 m.

Air density changes the answer for high drops. At 4,000 m the standard atmosphere is down to 0.8194 kg/m³, and the flat skydiver’s terminal velocity rises from 44.09 to 53.91 m/s. The density menu lists the values for each 1,000 m from the U.S. Standard Atmosphere, 1976.

How Far a Skydiver Falls by Time

For questions about seconds of freefall, set the known value in the Free Fall with Air Resistance Calculator to Fall Time. The table compares the no-air distance with both skydiver positions at sea level. The last column is the flat skydiver’s speed at that moment.

In feet, a 2 second fall is 64.3 ft with no air and 62.3 ft for the flat skydiver. A 3 second fall is 144.8 ft with no air and 135.2 ft with it. The gap is small this early because drag is still a minor part of the weight.

The gap then grows quickly. After 12 s the no-air formula says 706 m, while the flat skydiver has covered 393 m. After 30 s the textbook figure of 4,413 m is almost four times the 1,185 m that the skydiver actually falls.

Drag Force and Mass

The third card works as a free fall force calculator for the air. It gives the drag force at the end of the fall, its share of the weight and the acceleration that is left. In the default case of the Free Fall with Air Resistance Calculator the drag is 529.61 N against a weight of 833.57 N, so 63.5% of gravity is cancelled and 3.58 m/s² remains.

Heavier objects of the same shape fall faster in air. Drag depends only on shape, area and speed, while weight grows with mass, so a heavier object must go faster before the two balance. Terminal velocity rises with the square root of the mass.

With no air, all five rows would land together. That is why a free fall calculator with weight only matters once drag is switched on. A raindrop shows the other extreme, since its tiny mass gives it a terminal velocity of only a few meters per second.

A 4 mm drop modeled as a rigid sphere with C = 0.45 comes out near 9.7 m/s. Real drops of that size flatten as they fall and land at just under 9 m/s, and the laboratory values of Gunn and Kinzer remain the standard reference for them.

Throws, Limits and Assumptions

An initial velocity changes the starting point on the same curve. Thrown down faster than terminal velocity, an object slows toward it instead of speeding up. Thrown up at 20 m/s, the flat skydiver model rises 18.55 m in 1.91 s, compared with 20.39 m in 2.04 s without air.

The Free Fall with Air Resistance Calculator keeps air density, drag coefficient and frontal area constant for the whole fall, and it leaves out wind and buoyancy. Very high drops pass through thinner air first, so one density value is an average at best. Bullets and other shapes near the speed of sound need a ballistic coefficient, as in the Ballistic Coefficient Calculator.

Air Resistance Questions

Does free fall ignore air resistance?

By the strict definition, yes. Free fall means gravity is the only force acting, so the textbook free fall formula h = ½gt² has no air in it. That is also why true free fall is not possible in air, where drag always acts on a moving object.

In everyday use the phrase covers any unpowered fall, including a skydiver’s. The Free Fall with Air Resistance Calculator handles that second meaning and shows the strict one beside it on the fourth card. Other motion tools are listed under Kinematics Calculators.

How do I calculate air resistance?

Multiply half the air density by the drag coefficient and the frontal area to get k, then multiply k by the speed squared. For the flat skydiver at 35.15 m/s that is 0.42875 × 35.15² = 529.6 N. The force is in newtons, or pounds-force with US units.

The unit of air resistance depends on which quantity is meant. The drag force is in newtons, the coefficient k is in kilograms per meter, and the drag coefficient C has no unit at all. Mixing up k and C is the most common slip in these problems.

When can we ignore air resistance?

When the object stays far below its terminal velocity. Drag as a share of weight equals the speed divided by terminal velocity, squared. At 10% of terminal velocity the drag is only 1% of the weight.

The 10 m row above shows it in practice, where the skydiver loses just 2.5% of the no-air speed. The message under the results calls air resistance minor while that loss stays below 10%. Dense, compact objects on short drops usually qualify.

How do you test air resistance?

Measure a terminal velocity and work backward. Drop a light object from high enough that it settles at a steady speed, then time it over a marked distance near the bottom. The coefficient follows from k = mg ÷ v_T².

A 2 g object that settles at 1.5 m/s has k = 0.002 × 9.80665 ÷ 1.5² = 0.0087 kg/m. Enter that with the Coefficient k option and the Free Fall with Air Resistance Calculator predicts the fall time from any other height, which can then be checked with a stopwatch.