Dropped object from 10 m
From rest on Earth, t = sqrt(2h/g) gives about 1.43 s, and impact speed is about 14.0 m/s or 31 mph.
Free Fall Calculator
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Leave the selected target value blank; known values can stay filled in.
This models ideal vacuum free fall with constant g. Real skydiving, feathers, leaves, and high-speed falls can differ because drag and terminal velocity are not included.
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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 can solve for time, distance/height, final speed, initial velocity, or gravity, then converts the result into practical metric and US customary units.
Review note: Last reviewed June 24, 2026 by Starlight Tools. The calculator uses the ideal
constant-gravity kinematics model, standard Earth gravity of 9.80665 m/s², and rounded Moon, Mars, and Jupiter
surface-gravity presets. Source notes: standard gravity follows the conventional 9.80665 m/s² value used in SI
references; planetary presets are rounded educational values commonly listed by NASA planetary fact sheets.
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.
Solving other unknowns
The same equations rearrange cleanly. If time is known, height is h = ½gt² − v0t. If height and time are known, initial velocity is v0 = (½gt² − h) / t. If height and time are known but gravity is the unknown, use g = 2(h + v0t) / t². The expandable steps below the result substitute your own values into the active formula.
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: Choose the unit beside each input. The calculator converts internally to meters, seconds, kilograms, and m/s² before solving.
- 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.
Practical Free Fall Examples
Fall for 5 seconds
From rest on Earth, h = 0.5gt² gives about 123 m or 402 ft, with a speed near 49.0 m/s or 110 mph.
Thrown downward
Use a negative initial velocity for a downward throw. From 50 m with v0 = -5 m/s, impact happens sooner than a simple drop.
Moon versus Earth
A 10 m drop takes about 3.51 s on the Moon instead of 1.43 s on Earth because lunar gravity is much weaker.
Free Fall FAQ
How do you calculate free fall time from height?
For a drop from rest with no air resistance, use t = sqrt(2h/g), where h is height and g is gravitational acceleration. For example, 10 m on Earth gives t = sqrt(20 / 9.80665) = 1.43 s.
How far do you fall in 3 seconds?
From rest on Earth, distance is h = 0.5gt^2 = 0.5 x 9.80665 x 3^2 = 44.1 m, or about 145 ft, before air resistance is considered.
What is free fall speed after t seconds?
Starting from rest, speed is v = gt. After 3 seconds on Earth, v = 9.80665 x 3 = 29.4 m/s, about 65.8 mph downward.
Does mass affect free fall?
In the ideal vacuum model, mass does not change fall time or impact speed. Mass only changes kinetic energy because KE = 0.5mv^2.
Why does air resistance change the answer?
Drag pushes opposite the motion and grows with speed, so real objects often fall longer and hit slower than this calculator predicts. Shape, size, air density, and terminal velocity matter.
What is the difference between free fall and weightlessness?
Free fall is motion under gravity alone. Weightlessness is the sensation of having no support force; an orbiting spacecraft and its occupants are in continuous free fall.
What value of g should I use?
Use 9.80665 m/s^2 for standard Earth gravity unless your problem gives another value. Use 9.81 m/s^2 for quick classroom work, or select Moon, Mars, Jupiter, or custom gravity for other settings.