Solenoid fields, solved

Every combination of 14 winding diameters and 15 winding lengths — 210 air-core coils, each with its centre field per amp-turn, the span over which that field holds to 1%, the field at the coil mouth, and the turn count below which the closed-form answer stops being true.

Trace field lines →Embed a result

What the whole set says

Three readings taken over all 210 coils on this build, not quoted from a note.

The µ0·n·I shortcut

0.0% – 1403.3%

too high, from a 8×300 mm coil to a 150×10 mm one

Coils sharing a centre field

273 pairs

agree within 1% because the closed form sees only sqrt(L² + D²) — and none of them agree on the profile

Turns before the formula holds

up to 78

measured against a Biot–Savart sum over the individual turns, coil by coil

Centre field by coil

Rows are winding diameter, columns are winding length. Every cell is the centre field per amp-turn, so a row reads as "what does making it longer cost me".

Ø \ length	10 mm	15 mm	20 mm	25 mm	30 mm	40 mm	50 mm	60 mm	75 mm	100 mm	125 mm	150 mm	200 mm	250 mm	300 mm
8 mm	98.13	73.92	58.34	47.87	40.47	30.81	24.82	20.76	16.66	12.53	10.03	8.37	6.28	5.02	4.19
10 mm	88.86	69.71	56.20	46.67	39.74	30.48	24.64	20.66	16.61	12.50	10.02	8.36	6.28	5.02	4.19
12 mm	80.45	65.42	53.88	45.32	38.89	30.09	24.44	20.54	16.54	12.48	10.01	8.35	6.27	5.02	4.19
16 mm	66.60	57.30	49.06	42.34	36.96	29.17	23.94	20.24	16.39	12.41	9.97	8.33	6.26	5.02	4.18
20 mm	56.20	50.27	44.43	39.25	34.85	28.10	23.34	19.87	16.19	12.32	9.93	8.30	6.25	5.01	4.18
25 mm	46.67	43.10	39.25	35.54	32.18	26.64	22.48	19.33	15.90	12.19	9.86	8.26	6.23	5.00	4.17
30 mm	39.74	37.47	34.85	32.18	29.62	25.13	21.55	18.73	15.56	12.04	9.78	8.21	6.21	4.99	4.17
40 mm	30.48	29.42	28.10	26.64	25.13	22.21	19.63	17.43	14.78	11.67	9.57	8.09	6.16	4.96	4.15
50 mm	24.64	24.07	23.34	22.48	21.55	19.63	17.77	16.09	13.94	11.24	9.33	7.95	6.10	4.93	4.13
60 mm	20.66	20.32	19.87	19.33	18.73	17.43	16.09	14.81	13.08	10.78	9.06	7.78	6.02	4.89	4.11
75 mm	16.61	16.43	16.19	15.90	15.56	14.78	13.94	13.08	11.85	10.05	8.62	7.49	5.88	4.81	4.06
100 mm	12.50	12.43	12.32	12.19	12.04	11.67	11.24	10.78	10.05	8.89	7.85	6.97	5.62	4.67	3.97
125 mm	10.02	9.98	9.93	9.86	9.78	9.57	9.33	9.06	8.62	7.85	7.11	6.44	5.33	4.50	3.87
150 mm	8.36	8.34	8.30	8.26	8.21	8.09	7.95	7.78	7.49	6.97	6.44	5.92	5.03	4.31	3.75

Values are µT per amp-turn. Multiply by turns × amperes for the field you will actually get.

What this table is, and is not

Solved, not sampled

Every figure comes from the current-sheet solenoid evaluated at each coil's two dimensions, with the turn-count floor cross-checked against a Biot–Savart sum over the individual turns. Nothing is fetched, interpolated or recalled, so there is nothing here that can go out of date.

A field is not a coil design

These figures are air-core and on-axis only. A ferromagnetic core multiplies the field by an effective permeability that depends on the core's own shape; wire gauge, winding resistance, the heat a given current makes and the number of layers that physically fit are all real constraints and none of them are here.

The mouth of a long solenoid holds exactly half its centre field, and a short one holds much more — this set spans 0.500 to 0.993. That end ratio, not the centre field, is what decides whether a coil is usable as a field source over a real object.

Getting the field data out, and checking it against a real coil

Every coil here is already an API call

curl "https://makerportal.ai/api/v1/solenoid-field?diameter=25&length=100&turns=200&current=1"returns this lane's solve as JSON — the identical function that renders the page. No key, no account, CORS open. You get the centre field, the on-axis profile out to three half-lengths, the span that holds to 1% and 5%, the mouth ratio, how far µ₀·n·I overstates the answer, and the turn-count floor. Any diameter and length are accepted, not only the 210 published ones, andan embeddable cardof the same answer sits behind the same query.

A solved field is not a measured one

Everything here is an ideal air-core current sheet, on axis. A coil you actually wind has a core, layers, resistance and heat, and the only way to know what it really does is to put a sensor on the axis and log it. BLExAR — BLE Arduino control — HM-10, nRF52, CSV export — is the studio's side of that: BLE Control · Arduino Bridge · CSV Logging, iOS (iPhone + iPad). Log a Hall sensor off the microcontroller, export the CSV, and put it beside the profile above.

BLExAR ↗App Store · $3.99 All studio apps

Paid app, stated up front. Nothing on this page or in the API is behind it.

App Store prices are as Apple reported them on 18 September 2026 and are indicative only — the price shown on the App Store at the time of purchase applies.