Convert Magnetic Flux Quanta to Lines
Magnetic Flux Quantum (Φ₀) to Line (ln) magnetic flux conversion — enter any value below to get an instant result, or use the table for common values.
Results from this calculator are estimates provided for general informational purposes only, based on formulas, rates, and standards commonly accepted as of 2026. Figures may differ slightly from other calculators or professional sources due to rounding methods, differing assumptions, or regional regulations, and rules may change over time. Always consult a qualified professional — such as a financial advisor, healthcare provider, or other relevant specialist — before making decisions based on these results.
Result
1 Φ₀ = 2.06783E-07 ln
1 Magnetic Flux Quantum = 2.06783E-07 Lines
1 Line = 4835976.7 Magnetic Flux Quanta
1 Φ₀ in every supported unit
Conversion chart: Magnetic Flux Quantum to Lines
Conversion table
| Magnetic Flux Quantum (Φ₀) | Line (ln) |
|---|---|
| 0.01 Φ₀ | 2.06783E-09 ln |
| 0.1 Φ₀ | 2.06783E-08 ln |
| 1 Φ₀ | 2.06783E-07 ln |
| 2 Φ₀ | 4.13567E-07 ln |
| 3 Φ₀ | 6.2035E-07 ln |
| 5 Φ₀ | 1.03392E-06 ln |
| 10 Φ₀ | 2.06783E-06 ln |
| 20 Φ₀ | 4.13567E-06 ln |
| 50 Φ₀ | 1.03392E-05 ln |
| 100 Φ₀ | 2.06783E-05 ln |
| 1000 Φ₀ | 0.00020678346 ln |
Magnetic Flux Quantum (Φ₀)
Definition: A fundamental physical constant equal to h/2e (Planck's constant divided by twice the elementary charge), representing the smallest discrete unit in which magnetic flux can thread a superconducting loop — approximately 2.0678×10⁻¹⁵ weber.
History: Predicted theoretically from BCS superconductivity theory and confirmed experimentally in the early 1960s, it reflects the quantum-mechanical fact that the Cooper pairs carrying supercurrent have charge 2e, not e, making flux quantization occur in units of h/2e rather than h/e.
Current use: Central to superconducting electronics — SQUID magnetometers (among the most sensitive magnetic field detectors ever built) and superconducting flux qubits both operate by counting or manipulating magnetic flux in exact multiples of this quantum.
Line (ln)
Definition: A CGS unit of magnetic flux numerically identical to the maxwell — one "line of force," equal to 10⁻⁸ weber — from the historical convention of visualizing magnetic flux as a bundle of discrete field lines that could be counted.
History: It predates the formal maxwell unit, coming from Michael Faraday's own visualization of magnetic fields as lines of force threading through space, a picture that 19th-century engineers turned into a literal countable unit of flux.
Current use: Mostly of historical interest today, though "lines per square inch" and related line-based flux density figures still occasionally appear in older American electrical machine literature.
Supported Units
| Unit | Symbol | In Weber |
|---|---|---|
| Weber | Wb | 1 Wb |
| Milliweber | mWb | 0.001 Wb |
| Microweber | µWb | 1E-06 Wb |
| Volt Second | V·s | 1 Wb |
| Unit Pole | up | 1.25664E-07 Wb |
| Megaline | Mline | 0.01 Wb |
| Kiloline | kline | 1E-05 Wb |
| Line | ln | 1E-08 Wb |
| Maxwell | Mx | 1E-08 Wb |
| Tesla Square Meter | T·m² | 1 Wb |
| Tesla Square Centimeter | T·cm² | 0.0001 Wb |
| Gauss Square Centimeter | G·cm² | 1E-08 Wb |
| Magnetic Flux Quantum | Φ₀ | 2.06783E-15 Wb |
About These Parameters
- Value
- The amount of magnetic flux you want to convert, expressed in the "From" unit. Accepts decimals, and can represent anything from a superconducting loop's quantized flux to a large transformer core's weber rating.
- From Unit
- The unit your input value is currently measured in — a transformer's weber rating, a power-electronics volt-second product, or an older text's maxwell or line figure.
- To Unit
- The unit you want the result converted into. Use the swap button to flip From and To instantly, which is handy when translating a historical CGS maxwell or line figure into the modern SI weber or vice versa.
How Magnetic Flux Conversion Works
The Formula
Every unit here is defined by a fixed multiplier relative to the weber. To convert a value from one unit to another:
result = value × (factor of "From" unit ÷ factor of "To" unit)
For Magnetic Flux Quantum → Line: multiply by 2.06783E-07. For example, 1 Φ₀ × 2.06783E-07 = 2.06783E-07 ln.
Why Weber, Volt-Second, and Tesla-Square-Meter Are All the Same Number
Three of the units on this page are numerically identical to the weber, and it's not a coincidence — each one simply expresses the same physical quantity through a different equation. Faraday's law says a flux changing at one weber per second induces one volt, so "volt second" is just flux written as a time-integral of voltage. Flux density times area equals flux, so "tesla square meter" is just flux written as a density-times-area product. And in the CGS system, the exact same relationship holds one level down in scale: a maxwell is defined as a gauss times a square centimeter, which is why maxwell, line, and gauss-square-centimeter are all numerically identical too, just at 10⁻⁸ of the SI scale.
The Magnetic Flux Quantum and Superconductivity
At the quantum scale, magnetic flux doesn't vary continuously at all. Inside a superconducting loop, flux can only ever take on integer multiples of a fixed quantum, Φ₀ = h/2e (Planck's constant divided by twice the elementary charge, since current in a superconductor is carried by paired electrons called Cooper pairs). This flux quantization, predicted by BCS theory and confirmed experimentally in the early 1960s, is the working principle behind SQUID magnetometers — the most sensitive magnetic-field detectors ever built — and superconducting flux qubits used in quantum computing.
Example
A magnetic flux of 1 Φ₀ equals 2.06783E-07 ln. For scale, a small transformer core might carry a fraction of a milliweber of flux, a large power transformer core can reach several webers, and a single magnetic flux quantum is an almost inconceivably small 2.07×10⁻¹⁵ weber — it would take roughly 483 trillion of them to add up to just one weber.
Frequently Asked Questions
How many Lines are in 1 Magnetic Flux Quantum?
1 Magnetic Flux Quantum (Φ₀) equals exactly 2.06783E-07 Lines (ln).
Why are weber, volt-second, and tesla square meter all equal?
They're not three different quantities that happen to match — they're the same physical flux quantity expressed through three different defining equations. Faraday's law relates flux to an induced voltage over time (volt-second), while the flux-density-times-area relationship relates it to tesla and square meters. Both equations describe the weber, so all three read the same number.
What is a "unit pole" and is it a real magnetic monopole?
No — isolated magnetic monopoles have never been observed in nature. The unit pole is a 19th-century CGS convention that modeled magnetic flux as if it radiated from an idealized point pole, by analogy with how electric charge radiates an electric field. It's a historical calculational tool, not evidence that monopoles exist.
What's the difference between line, kiloline, and megaline?
They're the same "line of force" unit (numerically equal to the maxwell, 10⁻⁸ weber) scaled by the standard metric multiples: a kiloline is 1,000 lines and a megaline is 1,000,000 lines. All three come from the older habit of visualizing and literally counting magnetic field lines, a convention that predates the formal maxwell unit.
Why does flux come in fixed quantum steps inside a superconductor?
Inside a superconducting loop, the current is carried by paired electrons (Cooper pairs) whose collective quantum wavefunction must stay consistent all the way around the loop. That consistency requirement forces the enclosed flux to be an exact integer multiple of Φ₀ = h/2e — no in-between values are physically allowed, which is the phenomenon SQUID magnetometers exploit for extreme sensitivity.