Free Fall Calculator
Calculate fall time, final velocity, distance fallen, or required initial velocity for ideal free fall motion under gravity.
Calculator is for informational purposes only. Terms and Conditions
Choose what to solve for
Select the unknown, motion type, and gravity setting before entering known values.
Enter the known values
Only the values needed for the selected solve mode are active.
Visual Check
See the height, gravity direction, and calculated impact result.
Solution
Live result, quick checks, warnings, and full solution steps.
Quick checks
- Impact speed—
Show solution steps See the equation, substitutions, assumptions, and result path
- Enter values to see the full solution steps and checks.
Source, Standards, and Assumptions
Calculation basis, constants, assumptions, and limitations.
This calculator uses standard constant-acceleration kinematics for ideal free fall.
- Assumptions will appear after a valid calculation.
On this page
Calculator Guide
How to Use the Free Fall Calculator
The Free Fall Calculator above helps you calculate fall time, final velocity, distance fallen, or required initial velocity for an object moving under gravity. It uses standard constant-acceleration kinematics and assumes ideal free fall, which means gravity is the only force included in the calculation.
Use the tool for physics homework, quick motion checks, drop-height problems, and comparing Earth, Moon, Mars, or custom gravity conditions. For real objects with major air resistance, use the result as an ideal baseline rather than a field prediction.
Quick Answer
For an object dropped from rest, use \(t=\sqrt{2s/g}\) to calculate fall time and \(v=\sqrt{2gs}\) to calculate final velocity. If the object is thrown upward or downward, use the more general formula \(s=v_0t+\frac{1}{2}gt^2\) so the initial velocity is included.
When not to rely on the simplified result
This calculator ignores drag, wind, buoyancy, object shape, and terminal velocity. Do not use ideal free fall alone for skydiving, falling leaves, high-altitude drops, sports balls, safety planning, equipment selection, or impact-risk decisions where air resistance or field conditions matter.
Inputs and Outputs Used by the Free Fall Calculator
The calculator uses vertical motion inputs such as height, time, initial speed, and gravity. The required fields change based on whether you are solving for fall time, final velocity, distance fallen, or initial velocity.
| Type | Value | What It Means | Common Units |
|---|---|---|---|
| Input | Distance or height, \(s\) | Vertical distance from the release point to the impact point. | m, ft, cm, in |
| Input | Time, \(t\) | Elapsed time during the free fall motion. | s, min |
| Input | Initial velocity, \(v_0\) | Starting vertical velocity. Downward is positive in the calculator model. | m/s, ft/s, mph, km/h |
| Input | Gravity, \(g\) | Acceleration due to gravity for Earth, another planet, or a custom value. | m/s², ft/s² |
| Output | Calculated result | Fall time, final velocity, distance fallen, or required initial velocity. | Depends on solve mode |
Free Fall Formula
The main free fall equation is the constant-acceleration displacement formula. It works when gravity is treated as constant and air resistance is negligible.
Main Free Fall Formula
Use this form when initial velocity is part of the problem, such as an object thrown downward or thrown upward.
Dropped From Rest
These shortcuts apply when the object starts from rest, so \(v_0=0\).
Velocity Relationship
Use these to connect final velocity, initial velocity, gravity, time, and distance.
Which Formula Should You Use?
Choose the formula based on the values you already know. This is the fastest way to select the correct solve mode in the calculator.
| Known Values | Solve For | Use This Formula |
|---|---|---|
| Height and gravity | Fall time | \(t=\sqrt{2s/g}\) |
| Height and gravity | Final velocity | \(v=\sqrt{2gs}\) |
| Time and gravity | Distance fallen | \(s=\frac{1}{2}gt^2\) |
| Distance, time, and gravity | Initial velocity | \(v_0=\frac{s-\frac{1}{2}gt^2}{t}\) |
| Height and initial velocity | Fall time | \(s=v_0t+\frac{1}{2}gt^2\), then solve the quadratic |
What the Variables Mean
Free fall variables describe one-dimensional vertical motion. This calculator uses downward as the positive direction, so a thrown-down object has positive initial velocity and a thrown-up object has negative initial velocity internally.
\(s\) — distance or displacement
The vertical distance between the release point and the impact point. Use a positive value for a point below the release height.
\(v_0\) — initial velocity
The starting vertical velocity. A dropped object has \(v_0=0\), a thrown-down object has \(v_0>0\), and a thrown-up object is treated as \(v_0<0\).
\(v\) — final velocity
The vertical velocity at the end of the fall. The calculator also reports impact speed as a positive magnitude.
\(g\) — gravity
The acceleration due to gravity. Standard gravity is \(9.80665 \text{ m/s}^2\), or about \(32.174 \text{ ft/s}^2\).
How to Use the Calculator
Use the calculator by selecting the unknown value first, then entering the known values in matching units. The solve mode determines which inputs are required.
Select the solve mode
Choose fall time, final velocity, distance fallen, or initial velocity. If you only know height and gravity, fall time is usually the most common choice.
Choose the motion type
Select dropped from rest, thrown downward, or thrown upward. This is important because initial velocity changes the fall time and impact speed.
Set gravity and units
Use Earth gravity for standard problems, or choose another gravity preset for Moon, Mars, Venus, Jupiter, or custom acceleration.
Review the sanity checks
Check impact speed, distance used, gravity used, and the solution steps. If the number looks unrealistic, verify height, units, and whether air resistance matters.
How to Interpret Free Fall Results
A free fall result is an ideal motion estimate. It tells you what would happen if gravity were the only important force, not necessarily what a real object will do in air.
What to do with the result
Use fall time to estimate duration, final velocity to estimate impact speed, and distance fallen to check vertical displacement after a known time.
What changes the result most?
Height has a major effect because fall time grows with \(\sqrt{s}\), while final speed grows with \(\sqrt{s}\). Doubling height does not double time, but it does increase both time and impact speed.
Sanity check
Near Earth, a dropped object falls about \(4.9\text{ m}\) in the first second and reaches about \(9.8\text{ m/s}\) after one second, ignoring drag.
Impact speed vs. final velocity
Velocity includes direction. Impact speed is the positive magnitude of that velocity. The calculator may use sign internally, but the speed shown in mph or km/h is usually easier to interpret.
Input Checklist Before You Trust the Answer
Most wrong free fall results come from unit mistakes, wrong motion type, or treating a real drag-heavy fall as ideal free fall.
- Confirm the height is vertical distance, not sloped path length.
- Use the correct motion type: dropped, thrown downward, or thrown upward.
- Check whether initial speed is entered as a magnitude and direction is handled by the motion type.
- Use consistent gravity units, such as \(9.80665\text{ m/s}^2\) or \(32.174\text{ ft/s}^2\).
- Remember that ideal free fall does not include air resistance or terminal velocity.
Worked Example: Object Dropped From 100 Meters
This example matches the most common free fall calculator use case: finding fall time and impact velocity from a known height.
Formula
Substitution
Impact velocity check
Reverse check
Substituting \(t=4.52\text{ s}\) back into \(s=\frac{1}{2}gt^2\) gives approximately \(100\text{ m}\), so the result is internally consistent.
Mini example: 100 ft drop
For a 100 ft drop from rest using \(g=32.174\text{ ft/s}^2\), the fall time is:
This is a useful U.S. customary check because it uses feet with \(32.174\text{ ft/s}^2\), not meters with \(9.80665\text{ m/s}^2\).
Mini example: thrown upward
If an object is thrown upward, the calculator treats the starting velocity as negative in a downward-positive setup. For example, a ball thrown upward at \(10\text{ m/s}\) from a height of \(50\text{ m}\) uses:
The calculator solves the quadratic and keeps the positive time root. This captures the ball slowing down, reaching a peak, and then falling downward.
How to Visualize the Free Fall Calculation
Free fall is easiest to understand as vertical motion with constant downward acceleration. Distance grows with time squared, while velocity changes linearly with time.
The height \(s\) sets the distance available for gravity \(g\) to accelerate the object before impact. The visual uses plain SVG text with no label background boxes, so the labels stay readable and do not create dark or overlapping blocks.
Reference Checks and Gravity Values
For most near-surface Earth problems, use standard gravity \(g=9.80665\text{ m/s}^2\), which is approximately \(32.174\text{ ft/s}^2\). These values are useful for quick checks, but the calculator also allows custom gravity for non-Earth or special acceleration cases.
Source note
For authoritative background, see NASA Glenn’s explanation of free-falling objects and OpenStax’s discussion of free fall and constant-acceleration kinematics.
Design Notes and Practical Ranges
Free fall calculations are useful for education and preliminary estimates, but they are not a complete impact, safety, or drop-test analysis. Real impact behavior depends on object shape, drag, orientation, contact surface, deformation, and energy absorption.
Use as a baseline
The result is the no-drag baseline. It often overestimates impact speed for light, flat, or drag-sensitive objects.
Check energy separately
Impact severity is related to kinetic energy. If you know mass and impact speed, use the Kinetic Energy Calculator to estimate motion energy.
Units and Conversions
Free fall calculations require consistent distance, time, velocity, and acceleration units. The calculator can convert common metric and U.S. units, but the physics still depends on using a consistent base system internally.
Common unit trap
Do not use \(9.81\) with feet unless you convert gravity to \(32.174\text{ ft/s}^2\). Likewise, do not use \(32.174\) with meters. Unit mismatch is one of the fastest ways to get a wrong fall time or impact speed.
Length
\(1\text{ ft}=0.3048\text{ m}\), \(1\text{ in}=0.0254\text{ m}\), and \(1\text{ cm}=0.01\text{ m}\).
Velocity
\(1\text{ mph}=0.44704\text{ m/s}\), and \(1\text{ km/h}=0.27778\text{ m/s}\).
Free Fall vs. Terminal Velocity vs. Projectile Motion
Free fall, terminal velocity, and projectile motion are related, but they answer different questions. For drag-limited falling motion, use the Terminal Velocity Calculator. For launched objects with horizontal motion, use the Projectile Motion Calculator.
Free fall
Use when vertical motion is controlled by gravity and drag is ignored. Best for short classroom-style problems and ideal estimates.
Terminal velocity
Use when drag force matters and the object approaches a steady falling speed. This is better for long falls or drag-sensitive objects.
Projectile motion
Use when horizontal and vertical components both matter, such as launched objects, thrown balls, and trajectory problems.
Common Free Fall Mistakes
Free fall formulas are simple, but the setup can be easy to misread. The most common mistakes involve sign convention, air resistance, and unit consistency.
Do
- Use \(v_0=0\) only when the object is dropped from rest.
- Use the thrown-up or thrown-down mode when initial velocity matters.
- Check whether the result is an ideal estimate or a real-world prediction.
- Verify the output using a quick formula check.
Don’t
- Do not assume mass changes ideal free fall acceleration.
- Do not mix meters with \(32.174\text{ ft/s}^2\).
- Do not ignore drag for skydivers, feathers, leaves, or high-speed drops.
- Do not use horizontal distance as the drop height.
Troubleshooting Unrealistic Results
If the answer looks too high, too low, negative, or impossible, check the inputs before assuming the formula is wrong. A mathematically valid result can still be physically misleading when assumptions are violated.
Fall time looks too high
Check whether the height was entered in feet but treated as meters, or whether a very low gravity setting was selected.
Impact speed looks too high
Confirm the height and remember that the calculator ignores air resistance. A real object may slow down due to drag.
Distance is negative or impossible
For thrown-upward motion, the object may still be above the release point during a short time interval.
Result changes after switching units
Review the numeric values and unit selectors. A unit preset should preserve the physical quantity, but manual unit edits can change the problem.
Assumptions and Limitations
The Free Fall Calculator is best used as an educational and preliminary physics tool. It does not replace a detailed drag, impact, safety, or structural analysis.
Constant gravity
The calculator treats gravity as constant over the fall distance. This is reasonable for many near-surface problems but not for extreme altitude changes.
No air resistance
The model ignores drag, wind, object shape, and terminal velocity. These effects can dominate real falling motion.
Mass excluded
Mass does not appear in ideal free fall because acceleration is independent of mass when air resistance is ignored.
Vertical motion only
This calculator focuses on vertical motion. Use projectile motion methods when horizontal travel also matters.
Key Terms
These terms help connect the calculator inputs, formulas, and results.
Free fall
Motion where gravity is the only force considered. In this calculator, drag and air resistance are ignored.
Initial velocity
The starting vertical velocity. It is zero for a dropped object but not zero for an object thrown upward or downward.
Impact speed
The magnitude of the final velocity at the end of the fall, usually shown as a positive speed.
Gravity
The acceleration that pulls the object downward. Near Earth, standard gravity is \(9.80665\text{ m/s}^2\).
Terminal velocity
The steady falling speed reached when drag balances weight. This is not included in ideal free fall.
FAQ
What does a free fall calculator calculate?
A free fall calculator estimates fall time, final velocity, distance fallen, or initial velocity for an object moving under gravity when air resistance is ignored.
What is the free fall formula?
The main free fall formula is \(s=v_0t+\frac{1}{2}gt^2\), where \(s\) is vertical displacement, \(v_0\) is initial velocity, \(g\) is gravitational acceleration, and \(t\) is time.
Does mass affect free fall?
In ideal free fall, mass does not affect acceleration because the model ignores air resistance. Real objects can fall differently when drag, shape, and surface area matter.
Does this calculator include air resistance?
No. This calculator uses the ideal free fall model and does not include air resistance. Use a drag or terminal velocity calculation when air resistance is important.
How long does it take to fall 100 meters?
Ignoring air resistance and using standard gravity, an object dropped from rest falls \(100\text{ m}\) in about \(4.52\text{ s}\).
Is an object thrown upward still in free fall?
Yes, after release, an object thrown upward can still be in free fall if gravity is the only force considered. It slows down, reaches a peak, then speeds up downward.