Height to Velocity Converter

Convert height in meters to velocity in meters per second using the physics formula: v = √(2gh)

Input Parameters

Default value is Earth's gravity (9.81 m/s²)

Calculation Results

Calculation Formula

v = √(2 × g × h)

Where:
v = velocity (m/s)
g = acceleration due to gravity (m/s²)
h = height (meters)

Result

Velocity: 0.00 m/s

Equivalent to: 0.00 km/h

Equivalent to: 0.00 mph

Height to Velocity Converter Calculator Usage Guide

Learn how to use the Height to Velocity Converter calculator and its working principles

How to Use This Calculator

  1. Enter the height in meters from which an object is falling or projected. For example, the height of a diving board could be 3 meters.
  2. You can optionally change the gravity value if you're calculating for a different planet (e.g., Moon's gravity is approximately 1.62 m/s²).
  3. Click the "Calculate" button to compute the resulting velocity.
  4. The calculator displays the velocity in meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph).

Working Principle

This calculator uses the physics formula for converting height to velocity using gravitational potential energy. When an object falls freely under gravity, its potential energy is converted to kinetic energy:

PE = mgh (potential energy)

KE = ½mv² (kinetic energy)

At the point of impact, PE = KE, so:

mgh = ½mv²

Canceling mass (m) from both sides gives:

gh = ½v²

v = √(2gh)

Where:

  • v = velocity (m/s)
  • g = acceleration due to gravity (m/s²)
  • h = height (meters)

Examples

Example 1: A diver jumps from a 10-meter high diving board. What will be their velocity upon hitting the water?

Using g = 9.81 m/s² and h = 10 m:

v = √(2 × 9.81 × 10) = √196.2 = 14.01 m/s

This is equivalent to 50.44 km/h or 31.33 mph.

Example 2: A ball is dropped from a height of 2 meters on the Moon (g = 1.62 m/s²). What will be its velocity?

v = √(2 × 1.62 × 2) = √6.48 = 2.55 m/s

This is equivalent to 9.18 km/h or 5.71 mph.