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Drop Test Calculator

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Unit system:
Inputs
Aerodynamic Drag
Shape preset
Compare Runs

Run a calculation first, then save it to compare scenarios.

Results

Enter values and click Calculate.

How the calculator works

This tool computes the motion of a falling object under gravity, starting from a given height or targeting a required impact velocity. An optional aerodynamic drag model adds realism for objects where air resistance is significant.

Height → Velocity mode

Given a drop height, the impact velocity is calculated from energy conservation. Without air resistance:

v = √(v₀² + 2·g·h)

Time of flight and impact kinetic energy follow directly:

t = (v − v₀) / g
E = ½ · m · v²
  • v₀ — initial velocity (positive = downward)
  • h — drop height
  • m — mass
  • g — gravitational acceleration (editable, default 9.80665 m/s²)

Velocity → Height mode

When the required impact velocity is known instead, the calculator inverts the problem. Without drag this is solved analytically:

h = (v² − v₀²) / (2·g)

With drag enabled, a binary search converges on the drop height that produces the target velocity, accurate to within 0.01%.

Aerodynamic drag

Air resistance opposes motion. Net downward force and acceleration:

F = m·g − ½·ρ·Cd·A·v²

Solved numerically with RK4. Terminal velocity — where drag equals gravity:

v_t = √(2·m·g / (ρ·Cd·A))

Typical drag coefficient values

  • Sphere — Cd ≈ 0.47
  • Cube — Cd ≈ 1.05
  • Long cylinder — Cd ≈ 0.82 (axis perpendicular to flow)
  • Flat plate — Cd ≈ 1.28 (perpendicular to flow)
  • Streamlined body — Cd ≈ 0.04