Ohm's Law Calculator
Calculate voltage, current, resistance, and power with Ohm's Law. Includes energy cost estimation, AWG wire gauge recommendation, complete formula reference table, and collapsible wire sizing chart.
EM Energy Density Calculator
Calculate energy density of electric and magnetic fields using u_E = ½ε₀E² and u_B = B²/(2μ₀). Includes Poynting vector, EM wave analysis, and field comparison tables.
Enter 0 if only magnetic field is present
V/m
Enter 0 if only electric field is present
T
For total energy calculation
m³
Electric Energy Density (u_E)⧉
0.000003 J/m³
u_E = ½ε₀E² — energy stored per unit volume in the electric field
Magnetic Energy Density (u_B)⧉
0.000003 J/m³
u_B = B²/(2μ₀) — energy stored per unit volume in the magnetic field
Total EM Energy Density⧉
0.000007 J/m³
u = u_E + u_B — total electromagnetic energy density
Total Energy in Volume⧉
0.000007 J
Energy in 1 m³ of field
Poynting Vector Magnitude⧉
1,996.2168 W/m²
S = EB/μ₀ — power flow per unit area for EM wave
u_E / u_B Ratio⧉
1.0037
For EM waves in vacuum, this ratio equals 1
Energy Density Breakdown
Electric: 50.1%
Magnetic: 49.9%
EM Wave Equivalence
| Quantity | Value | Notes |
|---|---|---|
| E from B (EM wave) | 866.4220 V/m | E = cB for plane wave in vacuum |
| B from E (EM wave) | 0.00000290 T | B = E/c for plane wave in vacuum |
| ε₀ | 8.854 × 10⁻¹² F/m | Permittivity of free space |
| μ₀ | 4π × 10⁻⁷ H/m | Permeability of free space |
| c = 1/√(ε₀μ₀) | 2.998 × 10⁸ m/s | Speed of light in vacuum |
Field Strength vs Energy Density
| E (V/m) | u_E (J/m³) | B (T) | u_B (J/m³) |
|---|---|---|---|
| 1 V/m | 0.000000 | 0.0 μT | 0.000000 |
| 100 V/m | 0.000000 | 1.0 μT | 0.000000 |
| 1 kV/m | 0.000004 | 10.0 μT | 0.000040 |
| 10 kV/m | 0.000443 | 100.0 μT | 0.003979 |
| 100 kV/m | 0.044270 | 1.0 mT | 0.397887 |
| 1 MV/m | 4.427000 | 10.0 mT | 39.788736 |
| 3 MV/m | 39.843000 | 100.0 mT | 3,978.873577 |
| 100 MV/m | 44,270.000000 | 1 T | 397,887.357730 |
Planning notes, formulas, and examples
About the EM Energy Density Calculator
Electric and magnetic fields store energy. The energy density (energy per unit volume) of an electric field is u_E = ½ε₀E², while for a magnetic field it is u_B = B²/(2μ₀). These fundamental expressions connect field strengths to the energy they contain, underpinning everything from capacitor and inductor design to understanding electromagnetic wave propagation.
For electromagnetic waves in vacuum, the electric and magnetic energy densities are always equal (u_E = u_B), and the total energy density relates directly to the wave's intensity through the Poynting vector. Sunlight at Earth's surface, for example, carries about 1360 W/m² — the corresponding electric field is about 720 V/m and the magnetic field about 2.4 μT.
This calculator computes both electric and magnetic energy densities, their ratio, the total EM energy in a given volume, and the Poynting vector magnitude. It includes comparison tables showing how energy density scales with field strength across many orders of magnitude.
When This Page Helps
Working with ε₀ (8.854 × 10⁻¹² F/m) and μ₀ (4π × 10⁻⁷ H/m) in scientific notation is tedious and error-prone by hand. This calculator handles the tiny constants and large field values correctly, provides the Poynting vector for wave analysis, and gives context through comparison tables spanning from atmospheric electric fields to MRI magnets.
How to Use the Inputs
- Enter the electric field strength E in V/m (enter 0 if not applicable).
- Enter the magnetic field strength B in Tesla (enter 0 if not applicable).
- Optionally enter a volume to calculate total stored energy.
- Read the individual and total energy densities, Poynting vector, and u_E/u_B ratio.
- For EM waves, check the wave equivalence table showing E↔B relationships.
- Use preset buttons for common scenarios from sunlight to MRI machines.
Formula used
Electric Energy Density: u_E = ½ε₀E²
Magnetic Energy Density: u_B = B²/(2μ₀)
Total: u = u_E + u_B
Poynting Vector: S = EB/μ₀ (magnitude)
EM Wave Relations: E = cB, B = E/c
Constants:
ε₀ = 8.854 × 10⁻¹² F/m
μ₀ = 4π × 10⁻⁷ H/m
c = 1/√(ε₀μ₀) = 2.998 × 10⁸ m/sExample Calculation
Result: 6.68 × 10⁻⁶ J/m³
Sunlight at Earth: E = 868 V/m, B = 2.89 μT. u_E = ½(8.854×10⁻¹²)(868²) = 3.34×10⁻⁶ J/m³, u_B = (2.89×10⁻⁶)²/(2×4π×10⁻⁷) = 3.34×10⁻⁶ J/m³. Total = 6.68×10⁻⁶ J/m³. The equal values confirm this is an EM wave.
Tips & Best Practices
- For EM waves, remember E = cB — you only need to know one field to find the other.
- Magnetic energy density is proportional to B², so doubling the field quadruples the stored energy.
- A 1 T magnetic field stores about 400 kJ/m³ — compare to gasoline at about 34 GJ/m³.
- Superconducting magnets can maintain persistent fields with no energy input, making them efficient energy storage systems.
- In dielectric materials, replace ε₀ with ε₀εᵣ and in magnetic materials replace μ₀ with μ₀μᵣ.
- The intensity (W/m²) of an EM wave equals c × u_total = c(u_E + u_B).
Energy in Electromagnetic Fields
The concept that fields themselves contain energy was one of the great insights of 19th-century physics. Before Maxwell, energy was associated only with matter — kinetic energy of moving objects and potential energy of their configurations. Maxwell showed that electromagnetic fields are themselves repositories of energy, with well-defined energy densities.
This realization was crucial for understanding electromagnetic radiation. When a radio antenna emits waves, energy leaves the antenna and travels through space as oscillating electric and magnetic fields. The energy is not "in" the antenna or "in" the receiver — it is in the fields themselves, traveling at the speed of light.
Practical Energy Storage
While electromagnetic energy storage sounds exotic, it is commonplace in everyday electronics. Every capacitor stores energy in an electric field: a 1 μF capacitor charged to 1000 V stores 0.5 J in the electric field between its plates. Every inductor stores energy in a magnetic field: a 1 H inductor carrying 100 A stores 5000 J in its magnetic field.
Superconducting Magnetic Energy Storage (SMES) systems use persistent currents in superconducting coils to store significant amounts of energy in magnetic fields, achieving round-trip efficiencies above 95%. They are used for power quality applications where rapid charge/discharge is needed.
Astrophysical Magnetic Fields
The strongest known magnetic fields exist on magnetars — neutron stars with surface fields of 10⁸ to 10¹¹ Tesla. The energy density in such a field is staggering: at 10¹¹ T, u_B ≈ 4 × 10²⁴ J/m³, comparable to nuclear energy densities. These extreme fields can actually polarize the quantum vacuum and fundamentally alter the properties of matter.
Sources & Methodology
Last updated:
Frequently Asked Questions
In a plane electromagnetic wave in vacuum, E = cB. Substituting into the energy density formulas and using c = 1/√(ε₀μ₀) shows that u_E = u_B exactly. This equality is a fundamental property of EM waves.
The Poynting vector S = E × B/μ₀ describes the direction and magnitude of electromagnetic energy flow. Its magnitude gives the power per unit area (intensity) of an EM wave in W/m².
A 1 Tesla field has u_B = 1/(2 × 4π×10⁻⁷) ≈ 398,000 J/m³. A large MRI magnet (1.5 T) with 1 m³ bore volume stores about 900,000 J — enough energy to be seriously dangerous if released suddenly.
ε₀ (permittivity) characterizes how electric fields interact with the vacuum, while μ₀ (permeability) does the same for magnetic fields. Together they determine the speed of light: c = 1/√(ε₀μ₀).
Capacitors store energy in electric fields (E = ½CV² uses u_E internally). Inductors store energy in magnetic fields (E = ½LI² uses u_B). These are the practical devices that harness EM energy storage.
The strongest sustained magnetic field in a lab is about 45 T (hybrid magnet). Pulsed fields reach over 1000 T briefly. Magnetars (neutron stars) have surface fields of about 10⁸–10¹¹ T.
More in this topic
Energy to Wavelength Calculator
Convert between photon energy and wavelength using E = hc/λ. Supports eV, joules, frequency, and nm inputs. Includes EM spectrum reference and common photon energies.
Electron Speed Calculator
Calculate electron speed from kinetic energy or accelerating voltage. Includes relativistic corrections, de Broglie wavelength, classical vs relativistic comparison.