Free Fall Calculator (with Air Resistance)
How long a fall takes and how fast it ends — with or without air resistance.
Speed while falling
Distance and speed over time
How it was worked out
Results are estimates from the formulas shown, not a professional design or certification. Have a qualified engineer verify anything safety-critical (structures, electrical installations, gas or pressure systems).
About the Free Fall Calculator (with Air Resistance)
Find how long a fall takes, how fast the object is going when it lands and how far it has fallen — from the height, the fall time or the impact speed — on Earth, the Moon, the other planets or with your own g. It can start from rest or be thrown downwards or upwards.
Without air, the calculator uses the standard free-fall equations. With air resistance switched on, it adds quadratic drag and the object’s terminal velocity v_t = √(2mg ÷ ρCdA): from rest it uses the exact solution of the drag equation; with a starting velocity it integrates the motion numerically. Either way you see the no-air result alongside, a speed–time graph and a table of distance and speed.
The optional impact estimate gives the kinetic energy at impact and the average deceleration and force over a stopping distance you choose. It is an estimate for learning — real impacts peak far above the average — and must not be used for fall-protection or any other safety design.
How to use it
- Choose what you know: the height, the fall time or the impact speed, and type it with its unit.
- Leave the initial velocity at 0 for a drop, or enter a speed — positive downwards, negative upwards (use ± on a phone).
- Pick the gravity: Earth’s standard 9.80665 m/s², the textbook 9.81 or 9.8, the Moon, a planet or a custom value.
- For a realistic fall in air, open Air resistance, tick the box and enter the mass, drag coefficient, cross-section and air density (the defaults are a skydiver).
- To estimate the impact, open Impact energy and force and type the mass and how far it travels while stopping. Copy the results or download the table as CSV.
Examples
h = 50 m, Earth (9.80665 m/s²)
Falls for 3.193 s and hits the ground at 31.32 m/s (112.7 km/h)
t = 3 s from rest, g = 9.8 m/s²
44.1 m fallen, falling at 29.4 m/s
5 m/s downwards from 20 m, g = 9.81 m/s²
Lands at 20.43 m/s after 1.573 s
85 kg, Cd 1.0, area 0.70 m², sea-level air (1.225 kg/m³)
25.80 s, reaching 44.09 m/s (158.7 km/h) — terminal velocity 44.09 m/s. Without air: 14.28 s and 140.0 m/s
h = 10 m, g = 1.62 m/s²
3.514 s, landing at 5.692 m/s
a 1 kg tool dropped 20 m, stopping in 1 cm
196.1 J at impact; an average of 2,000 g and about 19.6 kN while stopping (estimate only)
Common uses
- Physics homework on free fall and terminal velocity, with the working.
- Estimating how long something takes to hit the ground from a building, bridge or cliff.
- Seeing how much air resistance changes a fall, and how quickly terminal velocity is reached.
- Showing why dropped objects are dangerous: the energy and average force involved.
Formulas without air resistance
Taking down as positive, with initial velocity v₀ and gravitational acceleration g:
- Impact speed from a height:
v = √(v₀² + 2 g h)— from restv = √(2 g h) - Fall time:
t = (v − v₀) ÷ g— from restt = √(2 h ÷ g) - Distance fallen in a time:
d = v₀ t + ½ g t², andv = v₀ + g t
These are the free-fall equations of OpenStax University Physics Volume 1 §3.5 with the sign convention down = positive. Near Earth’s surface g varies from about 9.78 to 9.83 m/s²; the standard value is 9.80665 m/s².
Air resistance and terminal velocity
Air pushes back with a drag force F_D = ½ ρ C_d A v² (NASA Glenn; OpenStax §6.4), so a falling object speeds up less and less until drag equals its weight. That speed is the terminal velocity, v_t = √(2 m g ÷ (ρ C_d A)). OpenStax’s 85 kg spread-eagle skydiver (C_d 1.0, A 0.70 m², ρ 1.21 kg/m³) has v_t ≈ 44 m/s; head-down it is far faster.
The equation of motion dv/dt = g − (g ÷ v_t²) v² has an exact solution from rest: v = v_t tanh(g t ÷ v_t) and d = (v_t² ÷ g) ln cosh(g t ÷ v_t), so the time to fall h is t = (v_t ÷ g) arcosh(e^(g h ÷ v_t²)). With a starting velocity the calculator integrates the equation with fourth-order Runge–Kutta instead. Typical drag coefficients (OpenStax Table 6.2): sphere 0.45, skydiver feet first 0.70, spread-eagle 1.0.
The impact estimate — and its limits
If the object stops over a distance s with a constant deceleration, a = v² ÷ 2s and the average force from the surface is F = m (a + g) (from work and energy: F·s = ½mv² + mgs). Halving the stopping distance doubles the average force, which is why soft surfaces and crumple zones help.
Real impacts are not uniform: the peak force can be several times the average, and what an object or body can withstand depends on far more than these numbers. Use the estimate to compare and to learn, never to choose or design fall-arrest equipment, guardrails, helmets, packaging or anything else people rely on for safety — that needs the relevant standards and a qualified engineer.
Sources
- OpenStax, University Physics Volume 1: §3.5 Free Fall (Eqs. 3.15–3.17; g from 9.78 to 9.83 m/s²) and §6.4 Drag Force and Terminal Speed (Eq. 6.5, Table 6.2, Example 6.17).
- NASA Glenn Research Center: Terminal Velocity and The Drag Equation.
- Gravity of other bodies: NASA JPL Planetary Physical Parameters; sea-level air density 1.225 kg/m³ from the U.S. Standard Atmosphere, 1976 (NASA-TM-X-74335).
Limitations
- Gravity is taken as constant, so heights are limited to 100 km.
- The drag model uses one constant drag coefficient and air density; real air gets thinner with height and the coefficient changes with posture and speed.
- Air density presets are for Earth. The Moon has almost no atmosphere, so leave drag off there.
- The impact estimate assumes a uniform deceleration and gives averages only. It is not a safety calculation.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
How long does it take to fall a given height?
Without air resistance, t = √(2h ÷ g). From 50 m on Earth that is √(100 ÷ 9.807) = 3.19 s. With air resistance it takes longer, and much longer for light or large objects.
How fast does an object hit the ground?
Without air, v = √(2gh): from 50 m it is √(2 × 9.807 × 50) = 31.3 m/s, about 113 km/h. In air, the speed can never exceed the terminal velocity — about 44 m/s for a spread-eagle skydiver.
Do heavier objects fall faster?
Not in a vacuum: everything falls with the same acceleration g. In air, a heavier object of the same size and shape has a higher terminal velocity (v_t grows with √m), so it does fall faster once drag matters.
What is terminal velocity?
The steady speed at which air drag balances weight, so the object stops accelerating: v_t = √(2mg ÷ ρCdA). Starting from rest, an object reaches 99% of it after (v_t ÷ g) × 2.65 seconds — about 12 s and 390 m for the default skydiver.
How is the impact force estimated?
From the stopping distance: the average deceleration is v² ÷ 2s and the average force is m(a + g). A 1 kg tool dropped 20 m that stops in 1 cm averages about 2,000 g and 19.6 kN. Peak forces are higher, so this is only an estimate — not for safety design.
What value of g should I use?
Use the value your course or problem gives: 9.81 or 9.8 m/s² are common, and 9.80665 m/s² is the standard value. For the Moon use 1.62 m/s² and for Mars 3.71 m/s².