Poynting Vector Calculator

Poynting Vector Calculator | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Science & Education
Input types: number, select
Output type: text
Sample coverage: 4
API ready: Yes

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.

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

1Enter the electric field magnitude (E) and select its unit (V/m, kV/m, or MV/m).
2Enter the magnetic field magnitude (B), select the appropriate unit (T, µT, or nT), and set the angle θ between E and B.
3The tool converts fields into base SI units, computes the auxiliary field H = B/μ₀, and evaluates S = E · H · sin(θ).
4The 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.

Examples

1. Solar Radiation Intensity Calculation

Physics Student

Background

Studying terrestrial solar power density at sea level during clear noon conditions.

Problem

Determine the Poynting flux and check whether electric and magnetic energy densities are balanced for peak sunlight fields.

How to use

Input 613.8 with unit V/m for the electric field, 2.047 with unit µT for the magnetic field, and set the angle to 90 degrees.

E: 613.8 V/m, B: 2.047 µT, Angle: 90°

Outcome

Yields an energy flux density S ≈ 999.85 W/m² with matching electric and magnetic energy densities u_E ≈ u_B ≈ 1.67 µJ/m³.

2. Light Bulb Field Flux Analysis

Optical Engineering Lab Assistant

Background

Measuring electromagnetic radiation parameters 1 metre away from a 100 W isotropic light bulb.

Problem

Calculate the radiant flux density from weak ambient field measurements.

How to use

Set the electric field to 54.75 V/m, the magnetic field to 182.6 nT, and the angle between them to 90 degrees.

FAQ

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. Magnetic field supports T (Tesla), µT (microtesla), and nT (nanotesla).

E: 54.75 V/m, B: 182.6 nT, Angle: 90°

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Solar Radiation Intensity Calculation

2. Light Bulb Field Flux Analysis

FAQ

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