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Free Fall Calculator

Calculate time to impact, impact speed, and a height-vs-time mini visual. Toggle air resistance (linear drag) to see terminal velocity and a satisfying speed gauge.

Background

In ideal free fall (no air resistance), acceleration is constant: a = g. With air resistance, the object speeds up quickly at first, then approaches a maximum speed called terminal velocity.

Enter inputs

Internally we solve in SI, then convert outputs back to your unit system.

Standard problems assume Earth: g ≈ 9.80665 m/s².

Positive v₀ means downward. Negative means thrown upward.

Air resistance

Student-friendly model: Fdrag = k·v (downward positive). This produces a clean terminal velocity.

Options

Off by default (quiet classroom-safe).

Display

Chips fill values and solve immediately.

Result:

No results yet — enter inputs and click Calculate.

How to use this calculator

  • Enter h and v₀ (downward positive).
  • Toggle Air resistance to include linear drag and see terminal velocity + gauge.
  • Click Calculate to get impact time, impact speed, and optional steps + mini viz.

How this calculator works

  • No drag: constant acceleration a=g.
  • With drag: m·dv/dt = m·g − k·v (downward positive).
  • Terminal velocity: vt = m·g/k.

Formula & Equation Used

Ideal free fall: h = v₀ t + (1/2)g t², v(t)=v₀+g t

Linear drag model: dv/dt = g − (k/m)v

Velocity: v(t)=vt + (v₀−vt)e^{−t/τ}, τ=m/k

Distance: y(t)= vtt + (v₀−vt)τ(1−e^{−t/τ})