Apollo hammer drop
On the Moon with g = 1.62 m/s², David Scott’s hammer and feather hit the dust together after ~3 s—air resistance is the only reason they don’t on Earth.
Vacuum reveal
Free Fall & Gravity Calculator
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Upward is positive; downward is negative.
Tip: Press Ctrl/Cmd + Enter to calculate. The URL updates so you can bookmark or share your inputs.
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Free Fall Explained: Formulas, Assumptions, and Quick Checks
Free fall describes vertical motion under a constant gravitational acceleration g with no air resistance. In this idealized model, the only force acting on the object is gravity, so its vertical position follows a simple quadratic curve in time. This calculator focuses on three classroom staples—time to hit the ground, impact velocity, and kinetic energy—and lets you explore different worlds using presets for Earth, Moon, Mars, and Jupiter.
Core model
We measure height from the ground upward and take upward as the positive direction. With initial height h0 (meters), initial vertical velocity v0 (m/s), and gravity magnitude g (m/s²) acting downward, the height at time t seconds is y(t) = h0 + v0 t − (g/2) t². The time to impact is the non-negative solution of y(t)=0:
thit = ( v0 + √( v02 + 2 g h0 ) ) / g.
The impact velocity (signed, upward positive) is vimpact = v0 − g thit, and the impact speed is |vimpact|. Kinetic energy on impact is KE = ½ m |vimpact|²; if mass is not provided, the calculator reports KE per kilogram (J/kg), which equals ½ |v|².
What changes between planets?
Only g changes. On the Moon (≈1.62 m/s²), falls are slower and impact speeds are lower for the same height. On Mars (≈3.71 m/s²) they are in between Earth (≈9.80665 m/s²) and the Moon. Jupiter’s strong gravity (≈24.79 m/s²) produces much shorter fall times and higher impact speeds. Use the presets to compare how g reshapes the height–time curve and your results.
Common pitfalls (and how to avoid them)
- Sign convention: Enter v0 positive for an upward toss, negative for a downward throw. The tool handles the signs internally.
- Initial height = 0: With h0=0 and v0=0, the time is zero because you are already at the ground. Use a positive height to see a fall.
- Units: All inputs are SI (m, s, kg). Keep everything consistent to avoid conversion errors.
- No air resistance: Real objects experience drag, which typically increases fall time and reduces impact speed compared to this ideal model.
Worked example
Drop (no initial push) from h0=10 m on Earth (g=9.80665). Then thit = √(2h/g) ≈ √(20/9.80665) ≈ 1.43 s. Impact speed is |v| ≈ g·t ≈ 9.80665 × 1.43 ≈ 14.0 m/s. If the mass is 2 kg, the kinetic energy at impact is ½·2·14.0² ≈ 196 J. Changing only g to the Moon stretches the time to ≈3.5 s and lowers the speed to ≈5.7 m/s.
Why the quadratic?
Acceleration due to gravity is (approximately) constant near a planet’s surface. Integrating constant acceleration gives a linear velocity change in time and a quadratic position curve. That’s why the height–time graph is a downward-opening parabola whose curvature increases with larger g.
Tip: Use a small positive v0 to model tossing an object upward before it falls. The calculator automatically includes the up-and-down portion in the total time to impact.
5 Fun Facts about Free Fall
Six-second skyscraper
Drop from 180 m on Earth and you’ll fall for roughly 6 s, reaching ~77 m/s—long enough to recite Newton’s apple story twice.
Urban physics
Jupiter’s unforgiving g
Jupiter’s 24.79 m/s² gravity means a 10 m drop takes only 0.9 s, but impact speed rockets to ~22 m/s—double Earth’s energy per kilogram.
Giant leaps
Up first, then down
Give an object an upward toss (say +5 m/s) and total time grows: it “pauses” at the apex before the calculator’s quadratic brings it back to Earth.
Toss trick
Energy per kilogram
Leaving mass blank shows KE per kg = ½ v² — useful when you just want the punch of the impact without choosing an object.
Impact insight