In everyday language, the terms energy and power are often used interchangeably. This confusion can lead to misunderstandings (equipment selection, reading electricity bills, battery use, effort evaluation, etc.). The key to distinguishing these two fundamental concepts lies in an essential but often underestimated parameter: time.
The mathematical relationship that links them is both simple and profound: Power (P, in Watts) is equal to Energy (E, in Joules) divided by Time (t, in seconds). With the formula \( P = \frac{E}{t} \) (or its equivalent \( E = P \times t \)), it becomes easy to switch from one quantity to the other, for calculation, sizing, or comparison.
To understand the difference between energy and power, we can use a very illustrative hydraulic analogy.
Energy (E) is the total amount of "work" stored, transferred, or consumed. In our analogy, it is the total volume of water contained in a tank, expressed in liters (L). Its unit in the International System is the Joule (J). However, for measuring electrical consumption, a practical unit has been established: the kilowatt-hour (kWh). The choice of this unit is not random: as it combines power (kW) and time (h) via the relation \( E = P \times t \), it allows us to quantify and directly bill the energy consumed by our appliances. It is the kilowatt-hour, not the instantaneous power, that appears on our electricity bills.
Power (P) is the rate at which this energy is used, produced, or transferred. Back to the tank: power is the flow rate of the pipe that empties it, expressed in liters per second (L/s). It measures how quickly energy changes form or is consumed. Its unit is the Watt (W), which is equivalent to one Joule per second (1 W = 1 J/s).
Thus, \( E = P \times t \), which is more intuitive, means that the energy consumed is the power multiplied by the duration of use.
Consider an electric heater with a power of 1000 W. This means it consumes 1000 J of energy per second. If this heater operates for 1 hour (3600 seconds), the total energy consumed is:
E = P × t = 1000 W × 3600 s = 3,600,000 J (or 1 kWh)
Consider a smartphone battery with a capacity of 5,000 mAh (5 Ah) at a nominal voltage of 3.7 V. The total energy it can store is:
E = Capacity × Voltage = 5.0 Ah × 3.7 V = 18.5 Wh (or about 66,600 J).
A standard 10 W charger will transfer this energy in:
t = E / P = 18.5 Wh / 10 W ≈ 1.85 h (≈ 1h50).
With a fast 30 W charger:
t = 18.5 Wh / 30 W ≈ 0.62 h (≈ 37 min).
This example shows how energy, power, and time are intrinsically linked: for the same energy to be transferred, a higher power drastically reduces the time required.
The Kaya Identity: The Equation Complicating Our Decarbonization 
The Unsurpassable Speed in the Universe: When Energy Becomes Infinite 
Electromagnetic Runaway: The Secret of the Speed of Light 
Understanding the Photoelectric Effect: Light and Electrons 
How far is the horizon? 
How Do Solar Panels Inject Electricity into the Grid? 
Dynamics of Momentum to explain the propulsion of rockets or jellyfish 
How Electron Energy Dictates Chemical Properties 
The Key Role of Quantum Uncertainty: No Particle Can Be at Rest 
Energy and Power: Don't Confuse Them, Time Makes All the Difference 
Why is there a limit to cold, but not to heat? 
Galileo's Law of Falling Bodies 
The Ideal Gas Law: One Equation, Thousands of Applications 
Schrödinger Equation and Atomic Structure 
Noether's Theorem: conservation of energy follows from symmetries 
Relationship between gravitational mass and inertial mass and the equivalence principle 
Third Equation of Physics: Momentum to Understand Collisions 
The second essential equation in physics: The intuition of a conserved quantity 
The First Equation of Physics: How to Mathematize Force 
The electromagnetic force or Lorentz force 
The solar energy received depends on
the angle of incidence 
Why is marble colder
than wood? 
Why does a photon, which has no mass, have energy?
Bayes Formula and Artificial
Intelligence 
The seven fundamental constants of physics 
What temperature does it feel like in interstellar space? 
Black body radiation curves: Planck's law 
The equivalence principle, gravitational effects are indistinguishable from acceleration 
E=mc2: The four fundamental concepts of the universe revisited 
How to weigh the sun? 
Equation of the free fall of bodies (1604) 
Coulomb's equation (1785) 
Boltzmann's equationon entropy (1877) 
Special relativity equations (1905) 
The equation of general relativity (1915) 
Planetary Rotation Equations: Between Angular Momentum and Gravitational Balance 
Equation of the orbital velocity of a planet 
Planck's equation 
Schrödinger's equation 
How Newton's Three Laws Describe All of Classical Mechanics 
Maxwell's equations 
Paul Dirac's equation 
Conservation of energy 
Equation of electromagnetic induction 
Why do elementary particles have no mass? 
Difference between heat and temperature