Free Fall Height
Calculate free fall height from gravitational acceleration, initial velocity, and time using h = v₀t + ½gt². Free online physics calculator with charts for students and engineers.
About This Calculator
The Free Fall Height Calculator computes the maximum height an object travels during free fall given its initial velocity, time of fall, and gravitational acceleration. It is designed for physics students, engineers, and anyone studying kinematics who needs to solve free fall problems quickly and accurately.
The calculator uses the free fall height formula: h = v₀ × t + ½ × g × t², where h is the height in meters, v₀ is the initial velocity in m/s, t is the time in seconds, and g is the gravitational acceleration in m/s². On Earth with no initial velocity, this simplifies to h = 4.903 × t². The calculator also computes the final velocity using v = v₀ + g × t, and generates an interactive Height vs Time chart showing how the fall distance accumulates over the fall duration.
You can select from various celestial bodies — Earth (g = 9.80665 m/s²), Moon (1.62 m/s²), Mars (3.71 m/s²), Jupiter (24.79 m/s²), and more — or enter a custom gravitational acceleration manually. This makes the calculator useful for physics problem-solving across different planetary environments, astrophysics exercises, and engineering scenarios involving falling objects.
Regional Notes
Worldwide (SI Units): The calculator uses standard SI units (meters, seconds, m/s²) which are the international standard for physics and engineering education globally. The gravitational constant used is the standard g = 9.80665 m/s², accepted worldwide by scientific communities including NIST, BIPM, and ISO.
Frequently Asked Questions
What is the free fall height formula?
The free fall height formula is h = v₀t + ½gt², where h is the height, v₀ is the initial velocity, t is the time of fall, and g is the gravitational acceleration (9.80665 m/s² on Earth).
How do you calculate height in free fall?
To calculate height in free fall, multiply the initial velocity by the time of fall, then add half of the gravitational acceleration times the square of the time. On Earth with no initial velocity, this simplifies to h = 4.903325 × t².
What is gravitational acceleration?
Gravitational acceleration is the acceleration an object experiences due to gravity. On Earth it is 9.80665 m/s². On the Moon it is 1.62 m/s², and on Mars it is 3.71 m/s².
What is free fall?
Free fall is the motion of an object under the sole influence of gravity, with no other forces like air resistance acting on it. In free fall, the object accelerates at the gravitational acceleration of the celestial body.
Can I use this calculator for other planets?
Yes, the calculator includes a celestial body selector with presets for Earth, Moon, Sun, Mars, Jupiter, and other planets. You can also manually enter any gravitational acceleration value.
What units are used for free fall height?
The calculator uses meters (m) for height, meters per second (m/s) for velocity, and seconds (s) for time. Gravitational acceleration is in meters per second squared (m/s²).
How does initial velocity affect free fall height?
If an object is thrown downward with an initial velocity, it covers more distance in the same time compared to being dropped from rest. The formula h = v₀t + ½gt² accounts for this initial velocity component.