Enter the mass, velocity, and height of an object into the calculator to determine the total mechanical energy.

Mechanical Energy Formula

The following formula is used to calculate the total mechanical energy.

ME = \tfrac{1}{2} m v^{2} + m g h
  • ME is the mechanical energy (J)
  • m is the mass (kg)
  • v is the velocity (m/s)
  • h is the height of the object (m)
  • g is the acceleration due to gravity (9.8 m/s2)

To calculate mechanical energy, multiply one half of the mass by the velocity squared, then add the product of the mass, gravity, and height.

5 Essential Questions About Mechanical Energy

Mechanical energy is the sum of energies possessed by a system and can be described as the ability of a system to do work.

In an ideally isolated or static system, mechanical energy remains constant. In moving systems, forces such as friction can change the distribution of energy.

What Is Mechanical Energy and What Are Its Types?

An ideal system in physics has two types of mechanical energy:

  • Potential energy
  • Kinetic energy

Potential Energy

Potential energy is the energy a system has due to its position. When a system is at rest at an elevated position, it can have large potential energy.

Kinetic Energy

Kinetic energy is the energy a system has due to motion. As velocity increases, kinetic energy increases.

Conservation of Mechanical Energy

As a system moves, potential and kinetic energy trade off. In the absence of non-conservative forces, their sum (mechanical energy) remains constant.

Ideal and Real Systems

In real systems, friction, drag, and other forces convert some mechanical energy into other forms (e.g., heat), so total mechanical energy of the system alone may not be conserved.

Is Thermal Energy Part of Mechanical Energy?

Motion with friction generates heat—thermal energy transferred between systems. Friction converts some mechanical energy into thermal energy.

In this sense, thermal energy can be part of a larger energy analysis of the system and its surroundings.

Can Mechanical Energy Be Converted?

Mechanical energy can be converted into other energy forms, and conversions are rarely 100% efficient.

  • Compressing gases stores energy in chemical form.
  • Rotating a magnet inside a coil converts mechanical to electrical energy.
  • Playing a string instrument converts mechanical to sound energy.
  • Friction converts mechanical energy into heat.

What Does Mechanical Energy Depend On?

We use the formula ME = (1/2) m v2 + m g h. Here, m is mass, v is velocity, g is gravitational acceleration, and h is height. Thus, mechanical energy depends on an object’s mass, position, and motion.

Can Mechanical Energy Be Negative?

Mechanical energy is a sum. While kinetic energy is non-negative, potential energy can be negative depending on the chosen reference level, so the total can be negative in some reference frames.

Example: With your hands as the zero-height reference when throwing a ball, the ball has zero potential energy at release, positive when above your hands, and negative when below.