Stefan Boltzmann Law Formula and Problems

Stefan Boltzmann Law Calculator :

This Stefan Boltzmann law calculator describes the Area in meter square(m²), Temperature in °C, Radiated power in watts(W), and you get the calculator check it.

Stefan Boltzmann Law Calculator

Stefan Boltzmann Law Formula :

Stefan  Boltzmann law formula is the net power of radiation P(ev) in electro volts is equal to the emissivity e(w/m) in watt per meter and multiply the Stefan’s constant σ(wm-2 k4) in watts per meter kelvin4 and multiply the area of radiation A(s/m) in square per meter and multiply the radiator temperature Tr(k) in Kelvin and multiply the surrounding temperature Tc(k) in Kelvin. Hence the Stefan  Boltzmann law  formula can be written as

P(ev)=e(w/m)* σ(wm-2 k4) *A(s/m)(Tr(k)-Tc(k))4


P→ net power of radiation in electro volts

A→ area of radiation in square meter2

Tr→ radiator temperature in kelvin

Tc→ surrounding temperature in kelvin

e→ emissivity in w/m

σ→ Stefan’s constant(σ=5.67*10-8 Wm-2 K-4)

u/A= σ *T4

where σ → Stefan’s constant =5.67*10-8 W/m2 K4

u=e * σ*AT4

Δu=u-u0= e * σ*A[T4-T04]

dp/d λ =1/A=2 π hc2/ λ5(ehc/ λkT-1)

Problem :1

Calculate the initial value of net power emitted by the body? In a body of emissivity (e=0.75), the surface area of 400cm2 and temperature 3230 c are kept in a room at temperature 470c and Stefan’s Boltzmann law.


P=e* σ*A (T4-T04)

=(0.75)(5.67*10-8 W/m2-K4)(400*10-4 m2)*[(500K)4-(300K)4]



Calculate the value of energy radiated in Jm-2 S-1? In ahot black body emits the energy at the rate of 15 j m-2 s-1 and its most intense radiation corresponds to 40,000 A0.When the temperature of this body is further increased and its most intense radiation corresponds to 30,000 A0,


Wein’s displacement law is λm *T=b

T∝[1/ λm]

Here λm becomes half, the Temperature doubles

Now from Stefan Boltzmann Law e=ST4


= e2 =(T1/T2)4


=16.15 J m-2 S-1

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