Free Fall Calculator
Compute free fall speed, distance, and height over time using gravity, initial velocity, and drop height, with clear steps shown.
Equation Preview
Helping Notes
- Downward is positive. Use \(v=v_0+gt\) and \(s=v_0t+\tfrac12gt^2\) (distance fallen).
- Height remaining after time \(t\): \(h_{\text{remain}}=h-s\). Impact when \(s=h\).
- Impact time (if \(h\) known): \(t_{\text{hit}}=\dfrac{-v_0+\sqrt{v_0^2+2gh}}{g}\) (take nonnegative root).
- Earth \(g\approx9.80665\text{ m/s}^2\). Neglects air resistance (like textbook free fall).
Results
At time t
Impact (from height h)
Error
Steps
What is Free Fall Calculator?
A Free Fall Calculator evaluates motion under constant gravitational acceleration with no air resistance. It answers questions like: How long does a dropped object take to hit the ground? What is the speed just before impact? From what height was it released? By modeling gravity as a constant \(g\) near a planet’s surface, the calculator applies the standard kinematics relations to connect position, velocity, time, and acceleration. You can choose the sign convention (typically up is positive), work in meters–seconds or feet–seconds, and set \(g\) (e.g., \(9.81\,\text{m/s}^2\) on Earth, \(1.62\,\text{m/s}^2\) on the Moon). These equations also describe the vertical part of projectile motion when horizontal motion is present; the vertical and horizontal components evolve independently in the idealized vacuum model.
About the Free Fall Calculator
The tool accepts any two or more known quantities (e.g., \(y_0\), \(y\), \(t\), \(v_0\), \(v\), \(g\)) and solves for the remaining variables, showing algebraic steps and numerical evaluations. It handles three common scenarios: (1) drop from rest (\(v_0=0\)), (2) throw upward or downward with initial velocity, and (3) compute required height or time given an impact speed limit. You can switch units and planetary gravity, and the calculator warns about physically impossible inputs (like negative time or contradictory signs). Formulas are presented in responsive blocks so they remain readable on phones and desktops alike.
How to Use this Free Fall Calculator
- Select a scenario: drop, throw upward, or throw downward, and choose your units.
- Enter known values (e.g., \(y_0\), ground level \(y=0\), \(v_0\), or \(t\)) and set \(g\).
- Click calculate to solve the kinematics equations and display steps and results.
- Review signs: with “up positive,” a downward \(v_0\) is negative, and \(g>0\) subtracts from \(v_0\) over time.
- Copy the final values and formulas for homework, labs, or engineering checks.
Examples
Example 1: Drop from rest, \(y_0=h\)
Earth gravity \(g=9.81\,\text{m/s}^2\), height \(h=20\,\text{m}\), \(v_0=0\).
Example 2: Thrown upward from \(1.5\,\text{m}\) with \(v_0=10\,\text{m/s}\)
Solve \(y(t)=0\) for landing time with up positive.
Example 3: Same drop on the Moon
\(h=10\,\text{m},\; g=1.62\,\text{m/s}^2\).
FAQs
What is the difference between free fall and projectile motion?
Free fall describes the vertical motion under gravity alone; projectile motion combines the same vertical dynamics with independent horizontal motion.
Why do we ignore air resistance?
It simplifies to constant acceleration. Real objects experience drag; results are best for dense, compact shapes over short distances.
Which sign convention should I use?
Commonly, take “up” positive so \(v_0\) upward is positive and gravity enters as a minus in \(v(t)=v_0-gt\).
Can I change gravity for other planets?
Yes. Set \(g\) to values like 1.62 (Moon) or 3.71 (Mars) in \(\text{m/s}^2\) to model those environments.
What units does the calculator support?
Use any consistent length–time units (e.g., m–s or ft–s). The equations are unit‑agnostic if inputs are consistent.