Free Fall Calculator
Calculate free fall distance, time, and velocity. Solve for any variable with optional initial velocity, planetary gravity comparison, and distance-time tables.
Free Fall with Air Resistance Calculator
Simulate free fall with drag using numerical integration. Calculate terminal velocity, real vs ideal fall distance, time-velocity tables, and compare drag profiles for different objects.
kg
m²
m
m/s
s
Terminal Velocity⧉
42.78 m/s
154.0 km/h — maximum speed when drag = gravity
Final Velocity⧉
41.85 m/s
97.8% of terminal velocity
Distance Fallen (with drag)⧉
508.56 m
Actual distance accounting for air resistance
Distance (no drag)⧉
1,103.25 m
Drag reduced distance by 53.9%
Air Density⧉
1.2250 kg/m³
ISA model density at the starting altitude
Velocity (no drag)⧉
147.1 m/s
530 km/h — unrealistic without drag
Velocity Approach to Terminal
97.8%
Approaching terminal velocity — drag nearly balances gravity
Time-Velocity-Distance Table (with drag)
| Time (s) | Velocity (m/s) | Velocity (km/h) | Distance (m) | Accel (m/s²) |
|---|---|---|---|---|
| 0.0 | 0.00 | 0.0 | 0.0 | 9.81 |
| 0.5 | 4.88 | 17.6 | 1.2 | 9.68 |
| 1.0 | 9.64 | 34.7 | 4.9 | 9.31 |
| 2.0 | 18.35 | 66.1 | 19.1 | 8.00 |
| 3.0 | 25.52 | 91.9 | 41.2 | 6.30 |
| 5.0 | 34.89 | 125.6 | 102.7 | 3.22 |
| 7.0 | 39.30 | 141.5 | 177.5 | 1.39 |
| 10.0 | 41.51 | 149.4 | 299.5 | 0.30 |
| 15.0 | 41.85 | 150.7 | 508.6 | -0.05 |
Terminal Velocity Comparison
| Object | Mass (kg) | Cd | Area (m²) | Terminal V (m/s) | Terminal V (km/h) |
|---|---|---|---|---|---|
| Skydiver (belly-down) | 80.000 | 1 | 0.7 | 42.8 | 154 |
| Skydiver (head-down) | 80.000 | 0.4 | 0.15 | 146.1 | 526 |
| Baseball | 0.145 | 0.3 | 0.00426 | 42.6 | 153 |
| Soccer ball | 0.430 | 0.25 | 0.038 | 26.9 | 97 |
| Bowling ball | 6.350 | 0.5 | 0.0346 | 76.7 | 276 |
| Feather | 0.003 | 1.2 | 0.003 | 3.7 | 13 |
| Parachute (open) | 80.000 | 1.5 | 30 | 5.3 | 19 |
Planning notes, formulas, and examples
About the Free Fall with Air Resistance Calculator
Real-world free fall differs from the idealized vacuum case because of air resistance (drag). A skydiver in belly-down position reaches terminal velocity of about 55 m/s (200 km/h) after roughly 12 seconds, while a feather reaches its terminal velocity of only 0.5 m/s very quickly.
The drag force on a falling object is F_d = ½ρv²C_dA, where ρ is air density, v is velocity, C_d is the drag coefficient, and A is the cross-sectional area. As the object accelerates, drag increases with v² until it equals the gravitational force mg. At that point, terminal velocity is reached and the object falls at constant speed.
This calculator uses numerical integration to simulate the fall second by second, with optional altitude-dependent air density and comparison tables for different object profiles. That makes it easier to compare a real fall against the ideal vacuum case.
When This Page Helps
Free fall with drag is one of those problems where the physics is simple but the exact motion is not. Numerical simulation lets you see how velocity, distance, and terminal speed evolve together instead of relying on a rough hand estimate.
How to Use the Inputs
- Enter the object mass, drag coefficient, and cross-sectional area — or pick a preset profile.
- Set the starting altitude (affects air density via ISA atmosphere model).
- Enter initial downward velocity (0 to start from rest).
- Set the total simulation time.
- Review terminal velocity and final state after the simulation.
- Compare the distance fallen with and without drag.
- Study the time-velocity table to see how quickly the object approaches terminal velocity.
Formula used
Drag Force: F_d = ½ρv²C_dA
Net acceleration: a = g − F_d/m = g − (ρv²C_dA)/(2m)
Terminal Velocity: v_t = √(2mg / (ρC_dA))
ISA Air Density: ρ(h) = 1.225 × (T(h)/288.15)^4.256
where T(h) = 288.15 − 0.0065h
Numerical integration (Euler): v(t+dt) = v(t) + a·dt, d(t+dt) = d(t) + v·dtExample Calculation
Result: Terminal velocity = 47.8 m/s (172 km/h), distance = 614 m in 15 s
An 80 kg skydiver (belly-down, Cd=1.0, A=0.7 m²) at sea level: v_t = √(2×80×9.81/(1.225×1.0×0.7)) = 47.8 m/s. After 15 s with drag, falls 614 m vs 1,103 m without drag — a 44% reduction.
Tips & Best Practices
- Terminal velocity scales as √(m/A) — doubling mass increases terminal velocity by √2 ≈ 41%.
- Objects reach 63% of terminal velocity in one "time constant" τ = v_t/g.
- A parachute reduces terminal velocity from ~55 m/s to ~5 m/s by increasing area from 0.7 to 30 m².
- At 10 km altitude, air density is only 1/3 of sea level — terminal velocity is √3 ≈ 1.73× higher.
- The drag force at terminal velocity equals the object's weight: F_d = mg.
- For very small objects (dust), Stokes drag (F ∝ v) replaces the v² quadratic drag law.
Terminal Velocity: When Falling Becomes Steady
Terminal velocity represents the fundamental limit that air resistance places on falling speed. The balance between gravity (constant) and drag (increasing with v²) means that every falling object eventually reaches a maximum speed. For a human skydiver, this takes about 12 seconds and approximately 450 meters of altitude.
The equation v_t = √(2mg/(ρCdA)) reveals which factors matter: increasing mass or decreasing drag coefficient or area raises terminal velocity. This is why streamlined shapes fall faster and why heavier skydivers fall faster than lighter ones at the same body position.
Real-World Complexity
This calculator uses the International Standard Atmosphere (ISA) model for air density, which decreases exponentially with altitude. During a high-altitude jump, the falling speed initially exceeds the sea-level terminal velocity because the thin air produces less drag. As the jumper descends into denser air, they decelerate even while aerodynamic forces increase.
Applications Beyond Skydiving
Understanding drag-limited free fall is essential in many fields: ballistics (bullet trajectory), aerospace (re-entry heating), meteorology (raindrop size distribution), and industrial processes (spray drying, particle separation). The same physics governs sediment settling in water, where the fluid density is much higher.
Sources & Methodology
Last updated:
Frequently Asked Questions
Terminal velocity is the constant speed reached when the drag force equals gravitational force (mg). At this point, net acceleration is zero and the object falls at constant velocity. It depends on mass, shape, and air density.
The differential equation ma = mg − ½ρv²CdA has an analytical solution for velocity vs time (hyperbolic tangent), but distance vs time requires numerical methods. The Euler method steps through time in small increments for valid inputs.
Air density decreases with altitude (about 1.225 kg/m³ at sea level, 0.41 kg/m³ at 10 km). Lower density means less drag and higher terminal velocity — this is why Felix Baumgartner exceeded Mach 1 falling from 39 km.
By changing body position, a skydiver changes both Cd and A. Belly-down (Cd≈1.0, A≈0.7 m²) gives ~55 m/s. Head-down (Cd≈0.4, A≈0.15 m²) gives ~90 m/s. The ratio is roughly √(CdA) between positions.
With dt = 0.01 s, the Euler method gives accuracy within 0.1% for typical free fall scenarios. More sophisticated methods (Runge-Kutta) are rarely needed for 1D falling problems.
For dense objects like humans, buoyancy in air is negligible (less than 0.1% of weight). For very light objects like balloons, buoyancy matters significantly but this calculator focuses on drag-dominated falling.
More in this topic
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Calculate aerodynamic and hydrodynamic drag force using the drag equation F_d = ½ρv²C_dA. Includes fluid presets, shape coefficients, velocity-drag tables, and power analysis.
Free Fall Velocity Calculator
Calculate the velocity of a falling object from time or distance. Speed context chart, velocity build-up tables, Mach number, kinetic energy, and momentum analysis.