What it does
A coil wound on an iron or ferrite core drives magnetic flux round the core much as a battery drives current round a circuit. The magnetomotive force N I (ampere-turns) plays the part of voltage, flux Φ plays the part of current, and each part of the core has a reluctance ℜ = l/(μ₀ μr A), like a resistor. An air gap, with μr = 1, has thousands of times the reluctance of the same length of iron, so even a 1 mm gap usually decides how much flux flows.
This solver adds up the reluctances of the segments you list, solves the circuit and gives:
- the total reluctance, the flux and the flux density B and field strength H in every segment;
- the inductance N²/ℜ, the A_L value and the stored energy (and how much of it sits in the gaps);
- the pull across a gap, B²A/2μ₀, as in an electromagnet or relay;
- the current needed for a target flux density in the gap;
- a warning when any core segment goes past the saturation value you set.
It handles a single loop, or a three-leg core (like an E-core or a transformer core) with the coil on the centre leg and two return legs that share the flux.
How to use it
- Pick a starting core or type your own. Each line is one segment:
core length area μrorgap length area, lengths in mm along the middle of the core, areas in mm². - For a three-leg core, put the coil leg (with its gap, if any) in the first box and the two outer legs in the return boxes. Leave the return boxes empty for a single loop.
- Give the turns and current, the saturation value of your core material, and optionally a target B in the gap.
- Tick fringing to let the gap flux spread over a slightly larger area, which lowers the gap reluctance a little.
Worked example
A made-up ring core with a 300 mm mean path, a 20 × 20 mm (400 mm²) section, μr 2000 and a 1 mm gap, wound with 500 turns carrying 2 A. The core’s reluctance is 298 k A-t/Wb and the gap’s 1.99 M A-t/Wb, so the gap uses 87 % of the 1000 ampere-turns. The page shows Φ = 437.1 µWb, B = 1.093 T in the gap, an inductance of 109.3 mH, 218.5 mJ stored (87 % of it in the gap) and a pull of 190 N across the gap. For 0.8 T in the gap you would need 1.464 A. Ticking fringing lowers the gap field to 1.078 T, spread over 441 mm².
Tips
- Gaps are added to inductors on purpose: they store the energy, keep L steady as μr varies and stop the core saturating.
- Because the gap dominates, doubling μr of the core barely changes L once there is a gap.
- In a three-leg core with equal outer legs, each carries half the centre-leg flux, so the outer legs can have half the area.
FAQ
Does it model saturation? No: μr is constant. It warns when a core segment passes the saturation value you give; above that the real flux is lower than shown.
Why is my real inductance a bit higher? Some flux leaks around the coil without following the core, and fringing at gaps widens their effective area. Tick fringing for a better estimate.
Is anything uploaded? No. Everything is worked out in your browser.
Where the numbers come from
- Magnetic circuit analysis (reluctance l/μA, Hopkinson's law, flux division between parallel legs), inductance N²/ℜ, stored energy and the Maxwell-stress pull B²A/2μ₀: standard results, for example Hughes' Electrical and Electronic Technology and Fitzgerald, Kingsley and Umans, Electric Machinery.
- The fringing allowance (√A + g)² is a common first approximation for square poles, not an exact result.
- μ₀ = 1.25663706127 × 10⁻⁶ N/A² (CODATA 2022). The saturation value offered is a rounded example; no material data tables are used.
- Checked against an exact SymPy (rational arithmetic) solution of the same circuits and against Ampère's law and flux conservation, written for the tests. The example cores are made up.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.