Can Energy Be Negative: Every Facts You Need to Know

Energy is required to do any sort of work then it is evident that the energy should be positive then how can energy be negative? That we are going to discuss here.

The concept of negative energy is widely used to study the quantum physics of black holes. If we take a glance over the formulas and concepts, then we will come across electrostatic energy, gravitational potential energy, and mechanical energy can actually be negative.

What energy can be negative?

The energy acquired by the objects tells about the efficiency, internal energy, enthalpy, amount of work that it can do, and how it reacts with surroundings and other objects.

The gravitational potential energy between the two objects that binds them together is always negative. It is also true that, if the potential energy possessed by the object is maximum than its kinetic energy, then the total mechanical energy will be negative.

can energy be negative
Gravitational potential energy between Earth and Moon is negative; Image Credit: pixabay

The electric potential energy is a product of the charges carried by the charged particles divided by the square of the distance separating both. The electric potential energy between the two charges will be negative by formula. That is for two unlike charges the electric potential energy is negative.

How energy can be negative?

If we talk about electronic energy then it is negative if the transition of electrons is from a higher level to a lower level.

This is given by the formula indicating negative sign for transition of electrons [latex]E_n=-R_H\left ( \frac{1}{n^2} \right )[/latex]. It implies that the energy possessed by the electron after making the transition is smaller than the actual energy that it holds in its stable state.

Just now we spoke about the negative electric potential energy, but you will think that the unlike charges show the attractive force towards each other, then there is some work done by the charges then how can energy be negative. Is it only because of the charge that they carry?

The negative sign suggests that there is more amount of force required to do this work or more amount of energy used to separate both the particles from attracting each other. Well so is not the result in the case of two like charges as they already repel away from each other by applying the electrostatic force.

When energy can be negative?

The energy can be negative if any work demands more amount of energy than the energy possessed by the object.

The work done against the required work to be done then also the energy used will be negative energy. This is because again double the amount of energy will be required to produce to do the necessary work.

The work has to be done to separate the two attractive magnetic poles and placed them at a distance ‘x’ between each other, but the magnetic flux lines in the field around the magnets are actually doing the work by inducing the magnetic forces attracting them towards each other.

In such a scenario, the work done to place them at a certain distance will become smaller and smaller, and hence more work and therefore more amount of energy will be utilized to do this work.

Where energy can be negative?

If in a vacuum the space is filled by antiparticles, then the energy in the vacuum will be negative.

Any attractive energy is negative whether it is between the two charged particles, two magnets, or two giant bodies. It is because of the force incident on the object from the opposite pair to do the work. This force is inversely proportional to the distance separating both objects.

The potential energy is the integral of the force between the two objects with respect to the distance and hence ends up getting the negative potential energy.

If the force between the two particles is F,


Where k is a constant equal to [latex]k=\frac{1}{4\pi r^2}[/latex]

[latex]q_1[/latex] and [latex]q_2[/latex] are charges of particles, and

r is a distance between the two charges

U is the potential energy required to do the work, then the potential energy to bring the particles together is

[latex]U=\int F.dr[/latex]

Substituting the value,

[latex]U=\int k\frac{q_1q_2}{r^2}.dr[/latex]

After integrating the above equation, we will get


Hence, we get the negative potential energy.

Can ionization energy be negative?

Ionization basically means the formation of ions that has a charge and this is acquired by removing or gaining the electrons from the atom.

The energy required to release out or gain the extra electron in the outmost shell of an atom is called the ionization energy and is negative because the energy has to be supplied in order to do the work.

It is a kind of endothermic process where most of the energy available is utilized to gain or lose the electron and the ion formed is left with a lower state of energy. It is similar to the transition of electrons from a higher energy state to a lower energy level.

What does it imply if the energy is negative?

If the energy is negative then we can gesture that more amount of energy is utilized to do the work.

Since work is large, the amount of energy required to do the work will also be large, but if an object does not possess enough potential energy to do that work, then the energy left with the object after doing the work will be zero.

Can mechanical energy be negative?

The mechanical energy is the sum of the total kinetic energy and the energy possessed by the object.

The kinetic energy is never the negative but the potential energy can be, hence if the potential energy is larger than the kinetic energy and, in negative value then the mechanical energy will be negative.

Why kinetic energy cannot be negative?

The kinetic energy of the object is persist when the object is in motion and moves with a certain velocity.

The kinetic energy of the object is directly proportional to its mass and the square of its velocity. Now mass can’t be negative, it has some positive value; and if the velocity of the object is negative, then also the square of the velocity will get us a positive value.

Is push energy negative?

The push energy is the energy required to push the object away from us.

The push energy is always positive as we apply positive energy to push the object and hence the work done is also positive, but it can be negative if the force is applied and no work is done because the energy used is insufficient to do the work.


The energy is not always positive, it can be negative also depending upon the energy required to do the work. The energy is negative in the case of attractive potential energy. It becomes more negative as the distance between the two particles decreases as the potential energy is inversely related to the distance and the value is negative.


Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess. Connect me on LinkedIn -

Recent Posts