What is mechanical energy?

Mechanical energy is the sum of an object's kinetic energy (energy of motion) and its gravitational potential energy (energy due to height). The formula is E = KE + PE = ½mv² + mgh. In a closed system with no friction, mechanical energy is conserved — it may convert between KE and PE but the total stays constant.

What is the formula for kinetic energy?

Kinetic energy is KE = ½mv², where m is the object's mass in kilograms and v is its speed in meters per second. The result is in joules (J). Because velocity is squared, doubling the speed quadruples the kinetic energy.

What is the formula for gravitational potential energy?

Gravitational potential energy is PE = mgh, where m is mass (kg), g is gravitational acceleration (9.81 m/s² on Earth), and h is height (m) above the chosen reference level. It is a linear function of both mass and height.

Why can I change the gravitational acceleration?

Gravity differs by location. Earth's surface averages 9.81 m/s², but it varies slightly by altitude and latitude. Other bodies have different values: Moon ≈ 1.62 m/s², Mars ≈ 3.72 m/s², Jupiter ≈ 24.79 m/s². Changing g lets you explore energy on other planets or in non-standard scenarios.

What does conservation of mechanical energy mean?

If only gravity (a conservative force) does work on an object — no friction, air resistance, or external forces — then total mechanical energy E = KE + PE remains constant throughout the motion. For example, a ball thrown upward loses KE as it gains PE, and vice versa when it falls, with the total E unchanged.

Is mechanical energy always conserved?

No. Mechanical energy is conserved only when no non-conservative forces (friction, drag, applied forces) do work. When friction acts, some mechanical energy converts to thermal energy and is lost. This tool calculates the instantaneous total mechanical energy at a given state, not whether it is conserved over a path.

Mechanical Energy Calculator

Name: Mechanical Energy Calculator
Availability: InStock
Author: Nham Vu

Enter mass, velocity, and height to calculate kinetic energy, gravitational potential energy, and total mechanical energy.

Inputs

Mass (m)

Velocity (v)

Height (h)

Gravity (g, m/s²)

E = ½mv² + mgh

Enter mass, velocity, and height on the left to compute mechanical energy.

E = ½mv² + mgh

Copied!

Summary

Enter mass, velocity, and height to calculate kinetic energy, gravitational potential energy, and total mechanical energy.

How it works

Enter the object's mass and select the unit (kg, g, or lb).
Enter the velocity and select its unit (m/s, km/h, or mph).
Enter the height above the reference point and select the unit (m or ft).
Optionally adjust the gravitational acceleration (default 9.81 m/s² for Earth).
Click Calculate to instantly see KE, PE, and total mechanical energy E = KE + PE.
Click any result card to copy the value to your clipboard.

Use cases

Solve physics homework involving conservation of mechanical energy.
Calculate the total energy of a projectile at a given height and speed.
Analyze a roller coaster car's energy at any point on the track.
Determine how much energy a falling object has just before impact.
Compare mechanical energy on different planets by changing gravity.
Verify conservation of energy in textbook problems.
Estimate the energy of a swinging pendulum at any position.
Study the trade-off between kinetic and potential energy in motion.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu