Terminal Velocity Calculator
Find the maximum speed a falling object reaches when aerodynamic drag exactly balances its weight.
kg
m²
kg/m³
m/s²
Speed where drag balances weight
- 1
Numerator 2·m·g
2 × 80 × 9.81 = 1,569.6 - 2
Denominator ρ·A·Cd
1.225 × 0.7 × 1 = 0.8575 - 3
2·m·g ÷ (ρ·A·Cd)
1,569.6 ÷ 0.8575 = 1,830.4373 - 4
Terminal velocity √(ratio)
√(1,830.4373) = 42.78
How does this calculator work?
Terminal velocity is v = √(2·m·g / (ρ·A·Cd)), the speed where aerodynamic drag equals weight so the object stops accelerating. Enter mass, frontal area, drag coefficient, air density, and gravity; heavier or denser objects fall faster while larger area, higher drag, or denser air lower the limit speed.
Formula
How this is calculated
Terminal velocity is the constant speed an object reaches in free fall once the upward drag force grows to equal the downward gravitational force, giving zero net force and zero acceleration. Setting the quadratic drag force ½·ρ·A·Cd·v² equal to the weight m·g and solving for v yields v = √(2·m·g / (ρ·A·Cd)).
The inputs are the mass m (kg), the cross-sectional area A (m²) the body presents to the airflow, the dimensionless drag coefficient Cd that captures shape (about 1.0 for a belly-down skydiver, 0.47 for a sphere), the fluid density ρ (kg/m³, default 1.225 for air at sea level), and gravitational acceleration g (default 9.81 m/s²). Heavier or denser objects fall faster, while larger area, higher drag coefficient, or denser air slow the limit speed.
The approach curve uses the analytic solution for quadratic drag, v(t) = v·tanh(g·t/v), which rises steeply then flattens as it nears the terminal value. We report the time to reach 99% of terminal velocity. The model assumes constant density and drag coefficient and ignores buoyancy and compressibility, so it is most accurate over moderate altitude ranges.
Frequently asked questions
More mass means more weight pulling it down, so drag must build up to a larger value to balance it — which requires a higher speed. Terminal velocity scales with the square root of mass for the same shape and area.
Use roughly 1.0 for a spread-out human skydiver, 0.47 for a smooth sphere, 1.05 for a cube, and as low as 0.04 for a streamlined teardrop. The value is dimensionless and depends mainly on shape.
Yes. Denser air produces more drag, lowering terminal velocity. High-altitude jumps start in thin air (lower ρ) and reach much higher speeds before the air thickens nearer the ground.
Also known as
TG we-Calculate Editorial Team. (2026). Terminal Velocity Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/terminal-velocity-calculator
TG we-Calculate Editorial Team. "Terminal Velocity Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/terminal-velocity-calculator.
TG we-Calculate Editorial Team, "Terminal Velocity Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/terminal-velocity-calculator
@misc{wecalculate_terminal_velocity_calculator, title = {Terminal Velocity Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/terminal-velocity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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