1Which of these has the same dimensions as speed of light?
Speed of light and root mean square velocity both have the dimensions [L T⁻¹].
Fundamental constantsClass 12, Electromagnetic Waves
Dimensional formula of Speed of light
[L T-1]
The speed of light in vacuum, 299 792 458 m/s. It has the dimension of velocity.
How to get the dimensional formula of speed of light
- Start from the definition: speed of light = length / time.
- Put in the dimension of each part: [L] / [T].
- Add the powers of each base quantity: [L T-1].
Quantities with the dimensions [L T⁻¹]
Equal dimensions do not make them the same quantity. Compare speed of light with the others in the full grid.
Three questions on speed of light
2What is the SI unit of speed of light?
The SI unit of speed of light is the metre per second (m/s).
3Which one has different dimensions from the others?
Wien's constant is [L K]. The other three are all [L T⁻¹].
An equation that uses speed of light
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]
Speed of light: quick answers
What is the dimensional formula of speed of light?
The dimensional formula of speed of light is [L T⁻¹]. It comes from speed of light = length / time.
What is the SI unit of speed of light?
The SI unit of speed of light is the metre per second (m/s).
Which quantities have the same dimensions as speed of light?
Speed of light shares [L T⁻¹] with velocity, escape velocity, root mean square velocity. Equal dimensions do not make them the same quantity.