How this calculator works
The model starts from rest and balances weight against drag proportional to speed squared. Density, drag coefficient, area and gravity stay constant over the entire drop, and buoyancy is omitted. Terminal speed is an asymptotic limit, not a speed reached after a finite fall. The maximum speed attained in this particular drop is the impact speed. Zero drag is handled as ordinary free fall rather than reporting an infinite numeric result.
Formula
m dv/dt = mg-kv^2; k = rho Cd A/2; vt = sqrt(mg/k); v(t)=vt tanh(gt/vt); h(t)=vt^2 ln(cosh(gt/vt))/g.
Worked example
For m = 10 kg, g = 10 m/s2 and k = 1 kg/m, terminal speed is 10 m/s. A drop of 4.337808305 m takes 1 s and reaches 7.61594156 m/s. At 3 m/s, drag is 9 N.
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Frequently asked questions
Does density change with altitude?
No. The entered density is held constant; large atmospheric altitude changes require a different model.
Is k the same as Cd?
No. Cd is dimensionless. Here k includes density and area and has units kg/m.
Can I enter an initial downward speed?
This closed-form tool describes release from rest. It does not model powered motion or a changing parachute configuration.