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Free Fall Calculator (h = ½gt²)

Compute distance, time, or final velocity for free fall from rest, given any one plus gravity

Details

What this tool helps you do

Free fall is motion under gravity alone, starting from rest (v₀ = 0).

Equations (given one of h, t, v — plus g — the other two follow):

Distance: h = ½ · g · t²
Time: t = √(2h/g) = v/g
Velocity: v = g · t = √(2gh)

Assumes no air resistance, uniform gravity. g defaults to 9.80665 m/s².

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Tool usage guide

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Key facts

Category: Math & Numbers
Input types: select, number
Output type: html
Sample coverage: 4
API ready: Yes

Overview

The Free Fall Calculator computes the distance, time, or final velocity of an object falling from rest under the influence of gravity. By inputting any one of these parameters along with the acceleration due to gravity, you can instantly solve for the remaining variables using standard kinematic equations, assuming no air resistance.

When to use

When solving physics homework problems involving objects dropped from rest.

When estimating the height of a structure by timing how long a dropped object takes to hit the ground.

When calculating the impact velocity of a falling object on Earth or other celestial bodies with different gravity values.

How it works

1Select the variable you want to solve for: Distance (h), Time (t), or Final Velocity (v).
2Enter the known value for one of the other parameters (distance in meters, time in seconds, or velocity in meters per second).
3Adjust the gravity constant if you are calculating for a body other than Earth (defaults to 9.80665 m/s²).
4Click calculate to compute the remaining values using the equations h = ½gt², t = √(2h/g), and v = gt.

Use cases

Physics students verifying kinematic homework solutions for dropped objects.
Educators creating lesson plans and answer keys for introductory mechanics classes.
Hobbyists estimating heights or drop times during outdoor activities like rock climbing.

Examples

1. Calculating Drop Distance from Time

Physics Student

Background

A student is conducting a lab experiment where a ball is dropped from a high window, and they measure a fall time of 3 seconds.

Problem

Determine how far the ball fell and its final velocity before impact.

How to use

Select 'Distance (h)' in the 'Solve For' dropdown, enter '3' in the Time field, and leave gravity at the default 9.80665 m/s².

Outcome

The calculator determines the distance fallen is approximately 44.13 meters and the final velocity is 29.42 m/s.

2. Finding Fall Time for a Specific Height

Science Teacher

Background

A teacher is preparing a demonstration where a weight is dropped from a 20-meter high ceiling.

Problem

Calculate how long the weight will take to hit the ground.

How to use

Select 'Time (t)' in the 'Solve For' dropdown, enter '20' in the Distance field, and keep the gravity at 9.80665 m/s².

Outcome

The calculator outputs a fall time of approximately 2.02 seconds.

FAQ

Does this calculator account for air resistance?

No, it assumes a pure vacuum where the only force acting on the object is gravity.

Can I calculate free fall on the Moon or Mars?

Yes, you can change the gravity input field to 1.62 m/s² for the Moon or 3.71 m/s² for Mars.

What is the default value used for gravity?

The calculator defaults to Earth's standard gravity, which is 9.80665 m/s².

Can I input an initial velocity other than zero?

No, this calculator is designed specifically for free fall starting from rest where the initial velocity is zero.

What units should I use for the inputs?

Use meters (m) for distance, seconds (s) for time, and meters per second (m/s) for velocity.

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Free Fall Calculator (h = ½gt²)

What this tool helps you do

Run this tool

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Inputs

Result

Prepared example runs

Inputs

Result

Examples that match this tool

Continue with connected tools and hubs

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Calculating Drop Distance from Time

2. Finding Fall Time for a Specific Height

FAQ

Web Image Processing Python Samples

Android Image Processing Java Samples

Android Image Processing Kotlin Samples

macOS Image Processing Objective-C Samples

Buoyancy Calculator (Archimedes, F = ρ·V·g)

Density Calculator (ρ = m/V)

Potential Energy Calculator (PE = mgh)

Image Palette to Design Tokens

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