Poynting Vector Calculator
Enter electric field amplitude to compute the average/peak intensity, magnetic field amplitude and total energy density of an EM wave.
Input Data
Results
At a glance:The Poynting vector S = E×B/μ₀ points in the propagation direction and its magnitude is the power per unit area (intensity) carried by an electromagnetic wave. For a sinusoidal plane wave with electric amplitude E₀, the peak intensity is S_peak = E₀²/(μ₀c) and the time-averaged intensity is ⟨S⟩ = E₀²/(2μ₀c) = ½·E₀·B₀/μ₀ (with B₀ = E₀/c). The total energy density u = ε₀E₀² = B₀²/μ₀, and ⟨S⟩ = c·u (averaged, ⟨S⟩ = c·⟨u⟩). This tool returns average/peak intensity, B₀ (T and nT) and energy density from the electric amplitude E₀.
Formula
S = E×B/μ₀
⟨S⟩ = E₀²/(2μ₀c)
B₀ = E₀/c
u = ε₀E₀²
$$\mathbf{S} = \mathbf{E} \times \mathbf{H} = \frac{\mathbf{E} \times \mathbf{B}}{\mu_0}, \quad \langle S \rangle = \frac{E_0^2}{2\mu_0 c}, \quad B_0 = \frac{E_0}{c}$$How to Use
- Enter the electric field amplitude E₀ (V/m).
- The calculator returns average/peak intensity, B₀ and energy density.
Case Studies
Radio wave
E₀ = 1 V/m.
⟨S⟩ = 1/(2×4πe-7×3e8) ≈ 0.00133 W/m².
B₀ = 1/3e8 ≈ 3.33 nT.
FAQ
What does the Poynting vector represent?
It is the directional energy flux (W/m²) of an EM field — the rate and direction of electromagnetic energy flow.
Why average intensity has a ½?
For a sinusoidal wave the time-average of E² is ½E₀², so ⟨S⟩ = ½·E₀²/(μ₀c). Peak uses E₀² directly.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.