Magnetic Pressure Calculator - Calculator Academy

Select magnetic pressure or flux density magnitude as the missing value, then enter the known nonnegative value in Pa, psi, bar, atm, T, G, or mT units.

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Magnetic Pressure Formula

The magnetic pressure calculator uses the magnetic pressure relationship for a magnetic field in free space, using the permeability of free space as a fixed constant.

P = B² / (2 \times μ₀)

B = sqrt(2 \times P \times μ₀)

P = magnetic pressure, in pascals (Pa) in the base calculation
B = magnetic field strength, in tesla (T) in the base calculation
μ₀ = permeability of free space, approximately 1.25663706127 × 10^-6 H/m (2022 CODATA central value)

If you enter magnetic field strength, the calculator finds magnetic pressure using P = B² / (2μ₀). If you enter magnetic pressure, it rearranges the same equation to find magnetic field strength using B = √(2Pμ₀).

The calculator converts your selected units to base SI units before calculating, then converts the result back to the unit selected for the missing value.

Magnetic Pressure Unit Conversions

These are the unit conversions used before and after the main calculation.

Pressure unit	Equivalent in pascals
1 Pa	1 Pa
1 psi	approximately 6,894.757293 Pa
1 bar	100,000 Pa
1 atm	101,325 Pa

Magnetic field unit	Equivalent in tesla
1 T	1 T
1 mT	0.001 T
1 G	0.0001 T

Example Calculations

Example 1: Calculate magnetic pressure from magnetic field strength

Suppose the magnetic field strength is 2 T.

P = B² / (2 \times μ₀)

P = 2² / (2 \times 1.25663706127 \times 10⁻6)

P = 1591549.43 Pa

The magnetic pressure is approximately 1,591,549.43 Pa.

Example 2: Calculate magnetic field strength from magnetic pressure

Suppose the magnetic pressure is 100,000 Pa.

B = sqrt(2 \times P \times μ₀)

B = sqrt(2 \times 100000 \times 1.25663706127 \times 10⁻6)

B = 0.5013 T

The magnetic field strength is approximately 0.5013 T.

FAQ

What does magnetic pressure mean?

Magnetic pressure is the pressure associated with a magnetic field. In vacuum, its numerical value equals the magnetic energy density in joules per cubic meter and is commonly expressed in pascals. Net magnetic force also depends on field direction, geometry and stress on the complete boundary. A stronger magnetic field gives a much larger magnetic pressure because the pressure is proportional to the square of the magnetic field strength.

Why does the calculator use μ₀?

The calculator uses μ₀, the permeability of free space, because the formula shown is for a magnetic field in vacuum or air approximated as free space. If you are working in a material with a different magnetic permeability, the result may not match the real physical pressure in that material.

Why can I only enter one value?

Select the missing variable with Solve for. Enter flux density magnitude to calculate magnetic pressure, or enter magnetic pressure to calculate flux density magnitude. Both zero and positive values are supported.