Free Fall Height Calculator

Enter a fall time and initial velocity to find the height fallen (h = v₀t + ½gt²), the impact velocity (v = v₀ + gt), and the average velocity during a free fall under constant gravitational acceleration.

Quick Facts

Height fallen
h = v₀t + ½gt²
Distance covered after falling for time t, starting at downward speed v₀ (use v₀ = 0 for a simple drop from rest).
Impact velocity
v = v₀ + gt
Speed at the moment of landing; increases linearly with fall time.
Standard gravity
g ≈ 9.81 m/s² (32.17 ft/s²)
Earth's average gravitational acceleration at sea level; use a smaller value for the Moon (1.62 m/s²) or Mars (3.71 m/s²).
No air resistance
Model assumes a vacuum
Real objects slow their acceleration as drag builds toward a terminal velocity — this model is most accurate for dense objects or short falls.

Your Results

Calculated
Height Fallen
-
h = v₀t + ½gt²
Impact Velocity
-
v = v₀ + gt
Average Velocity
-
v_avg = h / t
Impact Speed
-
Converted to km/h or mph

Ready

Enter a fall time, initial velocity, and gravitational acceleration, then press Calculate.

Formula and Method for Free Fall Height

Free fall is motion under gravity alone, with no air resistance and no other forces acting on the object. Starting from an initial downward velocity v₀ (zero for a simple drop) and falling for time t under constant gravitational acceleration g, the height fallen is h = v₀t + ½gt². This is the standard SUVAT kinematics equation for displacement under constant acceleration — the same relationship Galileo demonstrated: in a vacuum, every object falls at the same rate regardless of its mass.

How the calculation works

Enter how long the object falls (t), its downward speed at the start of the fall (v₀ — use 0 if it is simply dropped), and the gravitational acceleration (g: 9.81 m/s² on Earth, or 32.17 ft/s² if you are working in feet). The calculator plugs these into h = v₀t + ½gt² to get the height fallen, then finds the impact velocity with v = v₀ + gt (the derivative of the height equation with respect to time). Average velocity across the fall is simply h / t, and the impact velocity is also converted to km/h or mph for an easier real-world read.

Common mistakes

  • Forgetting v₀: if the object was thrown downward or already moving when the timer started, leaving v₀ at 0 will understate both the height and the impact velocity.
  • Mixing unit systems: g must match your chosen unit system — 9.81 m/s² for meters, 32.17 ft/s² for feet. Mixing the two produces results that are off by a factor of about 3.28.
  • Ignoring air resistance for light or wide objects: this formula assumes a vacuum. A feather, a sheet of paper, or a skydiver reaches a much lower speed in practice because drag opposes the fall — use a free fall with air resistance model for those cases.

Real-world applications

  • Engineering and safety: estimating impact speed for fall-arrest systems, drop testing, and packaging design.
  • Physics education: verifying Galileo's result that fall time is independent of mass in the absence of air resistance.
  • Construction and demolition: estimating how long debris takes to reach the ground from a given height, and how fast it will be moving on impact.
  • Sports and diving: estimating entry speed for platform diving or short, dense-body falls where air resistance is negligible.

Frequently Asked Questions

What is the formula for free fall height?
The height an object falls in time t is h = v₀t + ½gt², where v₀ is its initial downward velocity (0 if dropped from rest) and g is the gravitational acceleration (9.81 m/s² on Earth). For a simple drop this simplifies to h = ½gt².
How do I find the impact velocity of a falling object?
Impact velocity is v = v₀ + gt. Equivalently, if you know the height instead of the time, v = √(v₀² + 2gh). Dropped from rest, a fall of 20 m produces an impact velocity of about 19.8 m/s (roughly 71 km/h).
Does this calculator account for air resistance?
No — it uses the idealized free fall model (constant acceleration, no drag), which is accurate for dense, compact objects falling short distances. Light or large-surface-area objects reach a terminal velocity where drag balances gravity; for those, use a free fall with air resistance calculator instead.
What gravitational acceleration should I use for other planets or the Moon?
Replace g with the local value: about 1.62 m/s² on the Moon, 3.71 m/s² on Mars, and 24.79 m/s² on Jupiter. Earth's standard value is 9.81 m/s² (32.17 ft/s²) at sea level and decreases very slightly with altitude.

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