Free Fall Time Calculator

Enter a drop height, optional initial velocity, and gravitational acceleration to find free fall time, impact velocity, and average velocity using t = (-v₀ + √(v₀² + 2gh)) / g.

Quick Facts

Time from rest
t = √(2h / g)
Time to fall a height h starting from zero velocity.
Time with initial velocity
t = (-v₀ + √(v₀² + 2gh)) / g
General kinematic case when the object already has downward speed v₀.
Standard gravity
g ≈ 9.80665 m/s²
Earth's standard gravitational acceleration at sea level (often rounded to 9.81 m/s² or 32.2 ft/s²).

Your Results

Calculated
Fall Time
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t = (-v₀ + √(v₀² + 2gh)) / g
Impact Velocity
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v = v₀ + g × t
Impact Velocity (km/h)
-
Converted for intuition
Average Velocity
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Drop height ÷ fall time

Ready

Enter a drop height, initial velocity, and gravity, then press Calculate.

Formula and Method for Free Fall Time

Free fall is motion under gravity alone, with no other forces (like air resistance) considered. For an object that drops a height h, starting with a downward velocity v₀ (zero if simply released), the position follows the standard kinematic equation h = v₀t + ½gt². Rearranging this as a quadratic in t and solving with the quadratic formula gives the general free-fall time: t = (-v₀ + √(v₀² + 2gh)) / g. When the object is simply dropped (v₀ = 0), this simplifies to the well-known t = √(2h / g).

How the calculation works

Enter the drop height and its unit, an initial downward velocity (use 0 if the object starts at rest), and the gravitational acceleration in m/s² (9.81 m/s² for Earth by default). The calculator converts the height and initial velocity to meters and meters per second, solves the quadratic h = v₀t + ½gt² for the positive root to get the fall time t, then finds the impact velocity from v = v₀ + gt (equivalent to v = √(v₀² + 2gh) by energy conservation). The average velocity over the fall is simply the height divided by the fall time, h / t.

Common mistakes

  • Ignoring air resistance: this calculator uses the ideal vacuum equations. Real objects with significant drag (a feather, a sheet of paper, a parachute) fall slower than predicted and eventually reach a terminal velocity where acceleration stops entirely.
  • Mixing units: the drop height can be entered in meters, feet, centimeters, or inches, but gravitational acceleration must stay in m/s² — convert ft/s² to m/s² (divide by 3.281) before entering it.
  • Wrong sign for initial velocity: a positive initial velocity means the object is already moving downward when timing starts. If it was instead tossed upward first, this simple formula does not separate the "rise" and "fall" phases — treat v₀ as negative only if you want the time to reach a point h below the release point, not the total time up and back down.

Real-world applications

  • Drop testing packaging and electronics to estimate impact speed and impact energy before a product ships.
  • Construction and industrial safety calculations, such as estimating fall-arrest system requirements.
  • Introductory physics labs, where timing a dropped object is a classic way to measure g experimentally.
  • Estimating splashdown or landing speed for objects dropped from a known height, such as a diving platform or a drone.

Frequently Asked Questions

What is the formula for free fall time?
Time to fall a height h from rest is t = √(2h / g). If the object already has a downward initial velocity v₀, use the general form t = (-v₀ + √(v₀² + 2gh)) / g, which reduces to the rest case when v₀ = 0.
What value should I use for gravitational acceleration?
Earth's standard gravity is 9.80665 m/s², commonly rounded to 9.81 m/s² (32.2 ft/s²). Use about 1.62 m/s² for the Moon, 3.71 m/s² for Mars, or 24.79 m/s² for Jupiter if you are modeling a different world.
Does this calculator account for air resistance?
No. It uses the ideal free-fall equations for motion in a vacuum. Real objects experience air drag and eventually reach terminal velocity, so light or large-surface-area objects such as feathers, paper, or parachutes fall slower than this calculator predicts, especially over longer distances.
How is impact velocity calculated?
Impact velocity is v = v₀ + g × t, or equivalently v = √(v₀² + 2gh) from energy conservation. Both give the same speed at the moment the object reaches the ground.

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