Free Fall Calculator
Time to fall, impact velocity and distance fallen — for Earth, Moon, Mars or any custom gravity.
Formulas
Fall time (with initial velocity u): t = (−u + √(u² + 2gh)) / g
Impact velocity: v = √(u² + 2gh)
Velocity after time t: v(t) = u + g·t
Distance fallen after time t: s(t) = u·t + ½·g·t²
How to use
- Enter the drop height above the landing surface.
- Enter an initial downward velocity (0 for a pure drop from rest).
- Optionally, enter a query time to get velocity and distance fallen at that instant.
- Pick gravity and press Calculate.
Physics behind free fall
In an ideal (vacuum) free fall, the only force on the object is gravity, giving a constant downward acceleration g. Because acceleration is constant, the standard kinematics (SUVAT) equations apply: v = u + gt, s = ut + ½gt², v² = u² + 2gh. Mass does not appear anywhere — the result is independent of mass.
In real life, air resistance adds a drag force that grows with speed. At "terminal velocity" the drag equals gravity and the object stops accelerating. For heavy, small objects falling short distances (a rock from a building), air resistance is negligible and the ideal formulas are very accurate.
Worked example
h = 10 m, u = 0, g = 9.80665 m/s²
t = √(2·10/9.80665) ≈ 1.428 s v = √(2·9.80665·10) ≈ 14.007 m/s
Common mistakes
- Using the wrong sign for u. Downward is positive in this tool.
- Forgetting that a falling body keeps accelerating — v keeps growing until impact.
- Using g = 10 when more precision is required.
Related tools
FAQs
What is free fall?
Free fall is motion under gravity alone with no air resistance or other forces.
Does a heavier object fall faster?
In vacuum, no — all objects fall with the same acceleration.
Does this calculator include air resistance?
No. Use the Projectile with Drag simulator for that.