Permeability Converter — magnetic H/m and fluid darcy

The permeability converter above handles two entirely different physical quantities that share one unfortunate name. Magnetic permeability describes how readily a material carries magnetic flux and is measured in henries per metre. Fluid permeability describes how readily a porous rock or filter medium lets liquid pass and is measured in darcies or square metres. They are unrelated, and no number converts one to the other.

Arb Digital built this page with two separate modes rather than one long unit list precisely because of that ambiguity. Choose a mode and the dropdowns are filtered to that quantity only, so selecting darcy in one box and H/m in the other is structurally impossible. Most converters that cover permeability quietly mix the two, and a tool that lets you produce a physically meaningless answer is worse than no tool.

The Two Permeabilities, and How to Tell Them Apart

Magnetic permeability, usually written µ, is the ratio of magnetic flux density to magnetising field strength in a material. Its SI unit is the henry per metre, which is dimensionally the same as a newton per ampere squared. Iron, ferrite and mu-metal have high permeability, which is why they concentrate magnetic flux and make effective transformer cores and magnetic shields. Air and copper have permeability close to that of vacuum.

Fluid permeability, usually written k, is a property of a porous medium describing how easily fluid flows through it under a pressure gradient, as set out in Darcy's law. Its SI unit is the square metre, which looks like an area but is not one — it emerges from the dimensional analysis of Darcy's law rather than describing any physical surface. Because the square metre is an absurdly large unit for real rock, the practical unit is the darcy, and most reservoir rock is quoted in millidarcies.

Telling them apart in practice is easy once you know to look. If the document discusses cores, transformers, inductors, shielding, B-H curves or saturation, it means magnetic permeability. If it discusses reservoirs, aquifers, cores in the geological sense, porosity, or filter media, it means fluid permeability. The word "core" appearing in both vocabularies is a genuine trap, and it is the single most common source of confusion between the two.

How to Use It

1. Choose the mode first. Magnetic or fluid — this filters both unit dropdowns to the correct quantity.
2. Enter your permeability value from the datasheet, core report or measurement.
3. Choose the source unit from the filtered list.
4. Choose the target unit you need.
5. Read the result, which updates as you type. The four-item grid also switches to units appropriate to the mode you selected.

The Formula: How Permeability Conversion Is Calculated

Both modes use the same pivot arithmetic, each with its own base unit:

result = value × factor(from) ÷ factor(to)

In magnetic mode the base is the henry per metre. The important entry is relative permeability, µr, which is dimensionless — it is the material's permeability divided by the magnetic constant. Converting µr to H/m therefore means multiplying by the vacuum permeability µ₀. Since the 2019 SI revision µ₀ is no longer exactly 4π × 10⁻⁷ but a measured quantity tied to the fine-structure constant; the CODATA value is 1.25663706127 × 10⁻⁶ H/m, which differs from 4π × 10⁻⁷ only in the tenth significant figure. This tool uses the CODATA value, consistent with the BIPM SI Brochure. Gauss per oersted is included because in the Gaussian system permeability is numerically equal to µr.

In fluid mode the base is the square metre. The darcy is defined through Darcy's law using the standard atmosphere: one darcy is the permeability that passes one cubic centimetre per second of a fluid of one centipoise viscosity through a one square centimetre cross-section under a pressure gradient of one atmosphere per centimetre. Working that through with the standard atmosphere of exactly 101,325 Pa gives 9.869233 × 10⁻¹³ m². A convenient consequence is that one square micrometre equals about 1.0133 darcy. Unit definitions follow NIST Special Publication 811.

Reference Table: Magnetic Permeability Units

Each factor is the number of henries per metre in one of that unit.

• henry per metre (H/m) — 1 (SI base for this quantity)
• millihenry per metre (mH/m) — 1 × 10⁻³ H/m
• microhenry per metre (µH/m) — 1 × 10⁻⁶ H/m
• nanohenry per metre (nH/m) — 1 × 10⁻⁹ H/m
• newton per ampere squared (N/A²) — 1 H/m exactly; the same unit written differently
• relative permeability (µr, dimensionless) — 1.25663706127 × 10⁻⁶ H/m
• vacuum permeability (µ₀ units) — 1.25663706127 × 10⁻⁶ H/m
• gauss per oersted — 1.25663706127 × 10⁻⁶ H/m, numerically equal to µr

Reference Table: Fluid Permeability Units

Each factor is the number of square metres in one of that unit.

• square metre (m²) — 1 (SI base for this quantity)
• darcy (D) — 9.869233 × 10⁻¹³ m²
• millidarcy (mD) — 9.869233 × 10⁻¹⁶ m²
• microdarcy (µD) — 9.869233 × 10⁻¹⁹ m²
• square micrometre (µm²) — 1 × 10⁻¹² m², about 1.0133 darcy
• square centimetre (cm²) — 1 × 10⁻⁴ m²
• square foot (ft²) — 0.09290304 m² exactly

Relative Permeability and Why It Is Not a Constant

Magnetics datasheets quote relative permeability as a single headline number, and that number is almost always a simplification. Ferromagnetic materials have a permeability that varies with the applied field, with temperature, with frequency and with how the material was previously magnetised. A silicon steel quoted at µr = 4,000 may show several times that at low field and collapse toward the permeability of air once the core saturates.

Because of this, datasheets distinguish between initial permeability, measured at very low field, amplitude permeability at a stated drive level, and incremental permeability under a DC bias. They are different numbers for the same material, and a design that uses an initial-permeability figure at a working flux level will overestimate inductance, sometimes badly. Converting µr to H/m is exact arithmetic; deciding which µr to convert is the engineering judgment. Once you have an inductance figure, the inductance converter handles the henry side, and the magnetic field converter covers tesla and gauss.

Frequency adds another layer. A ferrite that behaves well at a few kilohertz can lose most of its permeability by the time it is driven at a megahertz, because the domain walls that carry the magnetisation cannot follow the field quickly enough. Manufacturers therefore publish permeability as a curve against frequency rather than a single figure, and the useful band is usually bounded at the top by the point where losses rise sharply. If you take the headline permeability from the front page of a datasheet and use it at ten times the intended frequency, the conversion arithmetic will be flawless and the design will still be wrong. Read the curve, pick the value at your operating point, and convert that.

Why Reservoir Rock Is Measured in Millidarcies

The darcy is sized for reasonably permeable material. Clean, well-sorted sandstone might reach a few darcies. Most producible reservoir rock sits between about one and several hundred millidarcies. Tight gas formations and shales run into microdarcies and below, which is why they require hydraulic fracturing to produce at all — the rock's natural ability to transmit fluid is thousands of times below conventional reservoir quality.

Permeability also depends on direction. Sedimentary rock is laid down in layers, so horizontal permeability along the bedding is typically much higher than vertical permeability across it, sometimes by an order of magnitude. A single scalar figure therefore describes a specific direction and a specific measurement method, and core-plug measurements made in a laboratory routinely differ from well-test values that average over a much larger volume of rock. As with magnetic permeability, the unit conversion is exact and the underlying number is conditional.

Permeability Is Not Porosity, and Not Permeance

Two more near-neighbours worth separating. Porosity is the fraction of a rock's volume that is void space, expressed as a dimensionless percentage. Permeability is how well those voids connect to allow flow. A pumice stone can be highly porous and nearly impermeable if its bubbles are isolated, so high porosity does not imply high permeability and the two are measured independently.

On the magnetic side, permeance is the magnetic analogue of electrical conductance for a specific circuit path, measured in henries, while permeability is the material property, measured in henries per metre. The relationship involves the geometry of the magnetic path in the same way that resistance relates to resistivity — see our resistance converter for that parallel. Building-physics literature adds a third homonym, the water-vapour "perm", which is yet another distinct quantity. This converter covers only the two quantities named in its modes, and deliberately excludes the rest.

Common Mistakes to Avoid

• Converting between magnetic and fluid permeability — they are unrelated quantities and any such result is meaningless.
• Treating relative permeability as a fixed material constant — it varies with field, temperature, frequency and history.
• Assuming high porosity means high permeability — isolated pores contribute volume but no flow path.
• Confusing permeability with permeance — one is a material property per metre, the other is a whole-path quantity in henries.
• Reading the square metre as an area in fluid permeability — it is a dimensional artefact of Darcy's law, not a surface.

Related Free Tools From Arb Digital

For the magnetic side, use the magnetic field converter for tesla and gauss and the inductance converter for henries. For the fluid side, the viscosity converter covers the centipoise term in Darcy's law, the pressure converter the driving gradient, and the flow rate converter the resulting volumetric flow. The area converter and the free online tools hub cover everything else.

Frequently Asked Questions