1Which of these has the same dimensions as energy?
Energy and kinetic energy both have the dimensions [M L² T⁻²].
MechanicsClass 11, Work, Energy and Power
Dimensional formula of Energy
[M L2 T-2]
The capacity to do work. Every form of energy, heat included, has the dimension of work.
How to get the dimensional formula of energy
- Start from the definition: energy = mass × velocity2.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- Put in the dimension of each part: [M] × [L T-1]2.
- Add the powers of each base quantity: [M L2 T-2].
Quantities with the dimensions [M L² T⁻²]
- Work
- Kinetic energy
- Potential energy
- Torque
- Torsional constant
- Gravitational potential energy
- Strain energy
- Heat
- Internal energy
- Electric potential energy
- Work function
- Photon energy
- Binding energy
Equal dimensions do not make them the same quantity. Compare energy with the others in the full grid.
Three questions on energy
2What is the SI unit of energy?
The SI unit of energy is the joule (J).
3Which one has different dimensions from the others?
Angular acceleration is [T⁻²]. The other three are all [M L² T⁻²].
An equation that uses energy
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
E = m c2E[M L2 T-2]=mc2[M L2 T-2]Dimensionally consistentEvery term is [M L2 T-2]
Energy: quick answers
What is the dimensional formula of energy?
The dimensional formula of energy is [M L² T⁻²]. It comes from energy = mass × velocity².
What is the SI unit of energy?
The SI unit of energy is the joule (J).
Which quantities have the same dimensions as energy?
Energy shares [M L² T⁻²] with work, kinetic energy, potential energy, torque, torsional constant, gravitational potential energy, strain energy, heat. Equal dimensions do not make them the same quantity.