# Poynting Vector Calculator Energy-flow density S = E × H = (1/μ₀) E × B with unit selectors, H = B/μ₀, both energy densities, and the plane-wave check where S = c·u. > Canonical page: https://elysiatools.com/en/tools/poynting-vector - **Category:** Science & Education - **Keywords:** poynting vector, energy flux density, electromagnetic wave intensity, plane wave, e cross b, radiation energy flow ## Overview The Poynting Vector Calculator computes the directional energy flux density (S = E × H = (1/μ₀) E × B) of electromagnetic waves. By providing the electric and magnetic field amplitudes, corresponding measurement units, and the angle between them, you can determine total radiation intensity (W/m²), auxiliary magnetic field (H), electric energy density (u_E), magnetic energy density (u_B), and verify plane-wave energy balance. ## Inputs - **Electric field E** (number): e.g. 613.8 - **E field unit** (select) - **Magnetic field B** (number): e.g. 2.047 - **B field unit** (select) - **Angle θ between E and B (degrees)** (number): e.g. 90 ## When to use - Analyzing the radiation intensity and power flow per unit area of electromagnetic waves. - Verifying equipartition of energy between electric and magnetic fields in plane-wave propagation. - Solving physics and electromagnetism problems involving cross-product energy transport in vacuum or air. ## How it works - Enter the electric field magnitude (E) and select its unit (V/m, kV/m, or MV/m). - Enter the magnetic field magnitude (B), select the appropriate unit (T, µT, or nT), and set the angle θ between E and B. - The tool converts fields into base SI units, computes the auxiliary field H = B/μ₀, and evaluates S = E · H · sin(θ). - The tool computes the respective energy densities (u_E = ½ε₀E² and u_B = B²/(2μ₀)) and total energy density (u = u_E + u_B). ## Use cases - Solar irradiance modeling: Calculating solar energy flux on surfaces using measured peak E and B fields. - Antenna and RF radiation analysis: Evaluating power density at given distances from transmitting sources. - Physics coursework and problem sets: Verifying electromagnetic wave theory, field energy densities, and impedance relations. ## Frequently asked questions ### What is the physical meaning of the Poynting vector? The Poynting vector S represents the directional energy flux density of an electromagnetic field, measured in watts per square metre (W/m²). ### How is the auxiliary field H calculated? In free space or non-magnetic media, the auxiliary magnetic field is calculated as H = B/μ₀, where μ₀ is the vacuum permeability. ### What is the plane-wave condition checked by this tool? In a vacuum plane wave, electric and magnetic energy densities are equal (u_E = u_B), and the energy flux satisfies S = c · u. ### Why is the angle θ between E and B needed? Because the Poynting vector is defined by the cross product E × H, its magnitude depends on sin(θ), which equals 1 when fields are perpendicular (90°). ### Which units can be selected for E and B fields? Electric field supports V/m, kV/m, and MV/m. 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