The Conservation of Energy

The most reliable rule in physics

If you remember just one idea from all of physics, make it this one: energy is never created or destroyed. It can be moved around, change from one form into another, and spread out — but the grand total never changes. This is called the principle of conservation of energy, and in over two centuries of careful experiments, no exception has ever been found.

That makes it a powerful tool. If you know how much energy a system starts with, you know how much it must have at the end, no matter how complicated the events in between. Engineers, astronomers and chemists all lean on this single accounting rule. Energy itself comes in several forms, which you can review in forms of energy.

Energy stores and transfers

Modern physics describes energy using two ideas: stores and transfers.

An energy store is where energy is held at a given moment. The main stores are:

• Kinetic — energy of a moving object.
• Gravitational potential — energy due to an object's height in a gravitational field.
• Elastic (strain) — energy in a stretched or squashed object, like a spring or drawn bow.
• Thermal (internal) — energy in the random motion of an object's particles; raising it raises temperature.
• Chemical — energy in the bonds of fuels, food and batteries.
• Nuclear — energy locked in the nucleus of atoms.

A transfer is the way energy moves from one store to another. There are four pathways:

• Mechanically — by a force moving (doing work), e.g. pushing a box.
• Electrically — by a current in a circuit, e.g. a kettle element.
• By heating — from a hotter object to a cooler one.
• By radiation (waves) — by light, sound or other waves.

The key phrase to learn is: **energy is transferred from one store to another by a pathway. For example, when you ride a bike, the chemical store in your muscles is transferred mechanically to the kinetic** store of the bike.

Watching energy change form

The clearest way to see conservation in action is with objects that move.

A falling ball. Hold a ball above the floor and it has a full gravitational potential store and no kinetic store (it isn't moving). Let go: as it drops, its height falls (gravitational store empties) and its speed rises (kinetic store fills). Ignoring air resistance, at every instant:

gravitational store lost = kinetic store gained

The two always add up to the same total. The energy didn't appear from nowhere or vanish — it simply moved between stores.

A pendulum. Pull a pendulum to one side and release it. At the top of a swing it pauses (all gravitational, no kinetic). At the bottom it moves fastest (mostly kinetic). It swaps back and forth between the two stores on every swing. A perfect pendulum would swing forever; a real one slowly stops because friction and air resistance transfer energy to the thermal store of the surroundings.

The maths of conservation

Two equations let you put numbers on this.

• Gravitational potential energy: GPE = m × g × h (mass × gravitational field strength × height).
• Kinetic energy: KE = ½ × m × v² (half × mass × speed squared).

On Earth, g ≈ 10 N/kg (more precisely 9.8).

Worked example 1. A 2 kg ball is dropped from a height of 5 m. Ignoring air resistance, how fast is it moving just before it hits the ground?

GPE at the top = m × g × h = 2 × 10 × 5 = 100 J. By conservation, all of this becomes kinetic energy at the bottom: KE = 100 J. So ½ × m × v² = 100 → ½ × 2 × v² = 100 → v² = 100 → v = 10 m/s.

Notice we never needed to know the messy details of the fall — just that the total energy is conserved.

Worked example 2. A 0.5 kg ball is thrown straight up at 8 m/s. How high does it rise?

KE at the start = ½ × 0.5 × 8² = ½ × 0.5 × 64 = 16 J. At the highest point it momentarily stops, so all that KE has become GPE: GPE = 16 J. m × g × h = 16 → 0.5 × 10 × h = 16 → 5h = 16 → h = 3.2 m.

What about "wasted" energy and efficiency?

If energy is always conserved, why does a bouncing ball eventually stop, and why do machines feel like they "lose" energy? Because some energy is transferred to stores we don't want — usually the thermal store of the surroundings, through friction, air resistance or sound. This energy is dissipated: spread out so thinly that it becomes useless. It is not destroyed; it is just no longer available to do a useful job.

This is why no machine is ever 100% efficient. Efficiency measures how much of the input energy ends up in the useful store:

efficiency = (useful energy out ÷ total energy in) × 100%

A typical car engine is only about 30–40% efficient; the rest leaves as heat and sound. A modern LED bulb is far better than an old filament bulb because it wastes far less as heat. You can explore this further in energy efficiency and transfers.

Why the universe obeys this law

Why should energy be conserved at all? The deep answer, discovered by mathematician Emmy Noether in 1918, is profound: conservation of energy is a consequence of the fact that the laws of physics do not change over time. Because an experiment done today gives the same result tomorrow, energy must be conserved. This links a practical accounting rule to a fundamental symmetry of nature — one of the most beautiful results in all of physics.

Try it yourself! 🧪

Demo — the energy-swap pendulum. You need a length of string, a small heavy object (a metal nut or a bag of coins), and a fixed point to hang it from (a door handle works).

1. Tie the object to the string and hang it so it can swing freely.
2. Hold the object out to one side, level with your nose, and note the height. This is its starting gravitational store.
3. Release it (don't push) and watch it swing across and up the other side. Notice it rises to almost the same height — but slightly lower each time.
4. Watch where it moves fastest: at the bottom of the swing, where its store is mostly kinetic. Watch where it pauses: at the top of each swing, where its store is mostly gravitational.

The energy is constantly trading between the gravitational and kinetic stores. The reason it doesn't return to exactly the same height is that a little energy is transferred to the thermal store of the air and the string on every swing. Nothing is destroyed — it has simply moved to a store you can no longer use. That, in a single swing, is the conservation of energy.