Dimensional formula of Stefan-Boltzmann constant

How to get the dimensional formula of Stefan-Boltzmann constant

1. Start from the definition: Stefan-Boltzmann constant = power / (area × temperature⁴).
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
4. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
5. displacement = length, so displacement is [L] = [L].
6. work = force × displacement, so work is [M L T^-2] × [L] = [M L² T^-2].
7. power = work / time, so power is [M L² T^-2] / [T] = [M L² T^-3].
8. Put in the dimension of each part: [M L² T^-3] / ([L²] × [K]⁴).
9. Add the powers of each base quantity: [M T^-3 K^-4].

Three questions on Stefan-Boltzmann constant

Related quantities

• G Gravitational constant [M⁻¹ L³ T⁻²]
• c Speed of light [L T⁻¹]
• h Planck's constant [M L² T⁻¹]
• ħ Reduced Planck's constant (h-bar) [M L² T⁻¹]
• k Boltzmann constant [M L² T⁻² K⁻¹]
• R Universal gas constant [M L² T⁻² K⁻¹ mol⁻¹]