Use this physics calculator to solve common free-fall problems. You can calculate either: (1) time and impact velocity from a known drop height, or (2) displacement and velocity after a known elapsed time.
What this free fall calculator does
This free fall calculator helps you quickly solve motion problems under constant gravitational acceleration. In idealized free fall, the only force acting on an object is gravity. That means no air resistance and no lift or thrust. This simplified model is exactly what introductory physics classes use, and it is extremely useful for quick estimates in engineering, sports science, and education.
Equations used
For one-dimensional vertical motion, with downward direction treated as positive, we use:
Velocity: v = v0 + gt
If you know drop height instead of time, the calculator solves the quadratic equation: 1/2 gt² + v₀t − h = 0, where h is the drop height.
How to use the calculator
Mode 1: From drop height
- Enter the vertical drop height in meters.
- Set initial velocity (0 for simple drop, negative if thrown upward first).
- Set gravity (9.81 m/s² on Earth; smaller on the Moon).
- Click Calculate to get time to ground and impact velocity.
Mode 2: From elapsed time
- Enter the elapsed time in seconds.
- Set initial velocity and gravity.
- Click Calculate to get displacement and current velocity at that time.
Example calculations
Example A: Dropping a ball from 20 m (v₀ = 0)
With Earth gravity at 9.81 m/s², the object reaches the ground in about 2.02 seconds, and impact speed is about 19.8 m/s (around 71.3 km/h).
Example B: Motion after 3 seconds
For v₀ = 0 and g = 9.81 m/s², after 3 s the displacement is approximately 44.1 m downward, and velocity is approximately 29.4 m/s downward.
Common mistakes to avoid
- Mixing units: Keep height in meters and time in seconds.
- Wrong sign convention: This calculator uses downward as positive.
- Using g = 9.81 everywhere: Different planets have different gravity.
- Ignoring air drag in real-world cases: Drag can be significant for light or large objects.
Typical gravity values
- Earth: 9.81 m/s²
- Moon: 1.62 m/s²
- Mars: 3.71 m/s²
- Jupiter: 24.79 m/s²
Quick FAQ
Is this calculator accurate?
It is accurate for ideal free-fall motion with constant gravity and negligible air resistance. For high speeds or large surface-area objects, aerodynamic drag should be included in a more advanced model.
Can I use negative initial velocity?
Yes. Negative initial velocity means the object is launched upward first (using this page’s sign convention). The calculator still solves the motion correctly.
Why can free-fall time differ from real experiments?
Real measurements include air resistance, spin effects, and timing uncertainty. The ideal model is best viewed as a strong baseline estimate rather than a perfect real-world prediction.