Free Fall Calculator

Solve free-fall problems from rest. Compute time of fall, distance (height), or final velocity with unit conversions.

Configuration

Choose which variable you want to solve for and your preferred output units.

Inputs

Results

Practical Guide

Free Fall Calculator

This guide shows how to use the Free Fall Calculator correctly and how to interpret the outputs. You’ll learn the core free-fall equations, when they apply, what assumptions they hide, and how to sanity-check your results for real engineering and physics problems.

6–8 min read Kinematics Updated 2025

Quick Start

The calculator assumes an object starts from rest and falls vertically under constant gravity. Use these steps to avoid the most common mistakes.

  1. 1Choose a Solve For target: time \(t\), height/distance \(h\), or final velocity \(v\).
  2. 2Enter only the given variables. The calculator hides irrelevant rows for your selection so you don’t accidentally over-constrain the problem.
  3. 3Set units for each input (m/ft, s/ms/min, m/s or ft/s). Make sure your units match the physical situation.
  4. 4Leave gravity blank for standard Earth gravity, or enter a custom \(g\) for another location or test setup.
  5. 5Check the dynamic equation banner to confirm the calculator is using the form you expect (e.g., \(t=\sqrt{2h/g}\)).
  6. 6Read the main result, then scan Quick Stats for the other two variables and average velocity.
  7. 7Open Show Steps to see the substituted math you can copy into homework, reports, or design notes.

Tip: If you know both time and height, you don’t need velocity. If you know time, the final velocity is fully determined by \(v=gt\).

Assumption check: These equations neglect air resistance and assume the object is dropped from rest. For long falls or light objects, drag can dominate.

Choosing Your Method

Free-fall problems are typically solved with constant-acceleration kinematics, but other approaches can be useful depending on what you know and the level of accuracy you need.

Method A — Constant-Acceleration Kinematics (Calculator Default)

This is the standard physics/engineering approach for objects falling from rest with negligible drag. It uses the constant-acceleration relations:

\[ h = \tfrac{1}{2}gt^2,\quad v = gt,\quad v^2 = 2gh \]
  • Closed-form solutions with minimal inputs.
  • Accurate for short drops, dense objects, or vacuum conditions.
  • Fast for hand checks and reporting.
  • Ignores drag, buoyancy, and wind.
  • Assumes release from rest and vertical motion.

Method B — Energy Approach

When you care about speed vs. height but not time, energy is convenient:

\[ mgh=\tfrac{1}{2}mv^2\ \Rightarrow\ v=\sqrt{2gh} \]
  • Very clean when solving for \(v\) from \(h\).
  • Highlights the physical conversion of potential \(\to\) kinetic energy.
  • Doesn’t give time without returning to kinematics.
  • Still assumes no non-conservative losses.

Method C — Drag-Aware / Numerical Fall

For skydivers, feathers, or high-altitude drops, drag makes acceleration non-constant. You may need a numerical model using quadratic drag \(F_d=\tfrac{1}{2}\rho C_d A v^2\). The calculator is not intended for that regime.

  • Captures terminal velocity and time-to-speed behavior.
  • Necessary for long falls in air or fluids.
  • Requires \(C_d\), area, density, and integration.
  • No simple closed-form for most cases.

What Moves the Number the Most

Free fall is a simple model, so a few variables dominate the outputs. The chips below are the levers you can pull.

Gravity \(g\)

Time scales as \(t \propto 1/\sqrt{g}\) and velocity scales as \(v \propto g\). A 10% lower \(g\) increases fall time by about 5%.

Height \(h\)

Time grows with \(\sqrt{h}\), while impact velocity grows with \(\sqrt{h}\). Doubling height increases \(t\) by \(\sqrt{2}\).

Time \(t\)

Height grows with \(t^2\). Small timing errors translate into large distance errors, which matters in experiments.

Initial velocity assumption

The calculator assumes \(v_0=0\). If the object is thrown down or up, use full kinematics: \(h=v_0 t+\tfrac{1}{2}gt^2\).

Air resistance & shape

Drag reduces acceleration and caps speed at terminal velocity. Effects are strongest for low mass, large area, or long falls.

Unit selection

Mixed SI/Imperial inputs are the #1 practical error. Always confirm the unit badges beside each input.

Worked Examples

Example 1 — Solve for Time from Height (Typical Drop Test)

  • Given height: \(h = 50 \text{ m}\)
  • Gravity: Earth standard \(g = 9.80665 \text{ m/s}^2\)
  • Unknown: time of fall \(t\)
1
Use the free-fall distance equation: \[ h=\tfrac{1}{2}gt^2 \]
2
Rearrange for time: \[ t=\sqrt{\tfrac{2h}{g}} \]
3
Substitute values: \[ t=\sqrt{\tfrac{2(50)}{9.80665}} =\sqrt{10.197}\approx 3.19\ \text{s} \]
4
Compute impact velocity for a sanity check: \[ v=gt=9.80665(3.19)\approx 31.3\ \text{m/s} \]

In the calculator, choose Solve For → Time, enter 50 m for height, and leave gravity blank. The calculator hides the velocity row because it is not an independent input for this solve path.

Example 2 — Solve for Height from Final Velocity (Energy/Kinematics Cross-Check)

  • Given impact speed: \(v = 120 \text{ ft/s}\)
  • Gravity: \(g = 32.174 \text{ ft/s}^2\)
  • Unknown: height fallen \(h\)
1
Use the velocity-height relation: \[ v^2 = 2gh \]
2
Rearrange: \[ h=\tfrac{v^2}{2g} \]
3
Substitute: \[ h=\tfrac{(120)^2}{2(32.174)} =\tfrac{14400}{64.348}\approx 224\ \text{ft} \]
4
Back-calculate time: \[ t=\tfrac{v}{g}=\tfrac{120}{32.174}\approx 3.73\ \text{s} \]

In the calculator, choose Solve For → Height, enter final velocity 120 ft/s and gravity in ft/s². The tool will compute both time and height, then show them in Quick Stats.

Common Layouts & Variations

Real problems often deviate from the “drop from rest in still air” idealization. Use the table to decide whether the calculator’s assumptions fit.

Scenario / ConfigurationHow to Use the CalculatorProsCons / Notes
Short lab drop (1–10 m)Solve for \(t\) or \(v\) using Earth \(g\).Drag negligible; high accuracy.Timing uncertainty can dominate results.
Drop tower / QA impact testGiven \(h\), solve for \(v\) to size safety or cushioning.Matches standard kinematic design checks.Include fixture friction or guides separately.
Moon / Mars fallEnter custom \(g\) (Moon \(\approx 1.62\), Mars \(\approx 3.71\) m/s²).Instant comparison across celestial bodies.Atmosphere differences may matter on Mars for light objects.
High-altitude or skydiver fallCalculator gives an upper-bound speed/time.Fast first estimate.Drag limits \(v\) to terminal velocity; real \(t\) is longer.
Object thrown downward/upwardDo not use default equations.—Requires \(v_0\neq 0\): \(h=v_0t+\tfrac{1}{2}gt^2\).
  • Confirm motion is essentially vertical.
  • Check whether air drag is small relative to weight.
  • Use custom \(g\) for centrifuge or non-Earth tests.
  • Back-calculate another variable for a quick sanity check.
  • Report significant figures consistent with measurement accuracy.
  • Round up for safety margins in design loads.

Specs, Logistics & Sanity Checks

Free-fall results often feed into designs for safety, impact, or motion-control systems. Before you lock numbers into drawings or reports, run these checks.

Assumptions to Verify

  • Initial velocity is effectively zero at release.
  • Gravity is constant across the fall distance.
  • Drag and buoyancy are small (or you’re okay with an upper-bound estimate).

Engineering Uses

  • Impact speed for drop tests and packaging design.
  • Fall time for safety clearances and control logic.
  • Height requirements to reach target speed.

Sanity-Check Numbers

  • Earth fall time: ~0.45 s from 1 m, ~3.2 s from 50 m.
  • Impact speed from 10 m: ~14 m/s (~46 ft/s).
  • If your result is far off, recheck units and givens.

Design note: If you are sizing protective systems, use the computed \(v\) to get kinetic energy \(KE=\tfrac{1}{2}mv^2\). Always include an engineering safety factor.

Safety note: Free-fall calculations can describe hazardous outcomes. Treat results as estimates and follow lab/site safety procedures.

Frequently Asked Questions

What equations does the Free Fall Calculator use?
It uses constant-acceleration kinematics from rest: \[ h=\tfrac{1}{2}gt^2,\quad v=gt,\quad v^2=2gh \] The calculator selects the minimal rearranged form depending on your Solve For choice.
Does the calculator include air resistance?
No. It assumes drag is negligible. For long falls in air or for light, high-area objects, real fall times are longer and speeds may approach terminal velocity.
Why is the final velocity input hidden when solving for time?
When the object starts from rest, velocity is not an independent input for time. Once you provide \(h\) and \(g\), time is determined by \[ t=\sqrt{\tfrac{2h}{g}} \] and velocity follows automatically from \(v=gt\).
Can I use this for objects thrown upward or downward?
Not directly. The calculator assumes \(v_0=0\). If the object is thrown, use: \[ h=v_0t+\tfrac{1}{2}gt^2,\quad v=v_0+gt \] and solve with the appropriate initial velocity.
What value of gravity should I use?
Leave it blank for standard Earth gravity \(9.80665\text{ m/s}^2\) (or \(32.174\text{ ft/s}^2\)). Enter a custom value for other planets, centrifuge tests, or local standards.
How accurate are the results for tall structures?
For moderate heights (tens of meters) and dense objects, results are usually very close to reality. For hundreds or thousands of meters, air density changes and drag become important, so treat outputs as upper-bound speeds and lower-bound times.
How do I check my result quickly without redoing all the math?
Use an alternate form: if you solved for \(t\), verify \[ v=gt \] and compare with \[ v=\sqrt{2gh} \] using the calculator’s Quick Stats. The two should match within rounding.
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