Magnetic Field Calculator (Straight Wire & Solenoid)
By Santaji GadepatilinUpdated November 2, 2026
An electric current creates a magnetic field: it circles a straight wire and becomes strong and uniform inside a coil. This magnetic field calculator gives the flux density around a long straight conductor and inside a solenoid — the same field that pulls the plunger in a solenoid valve and that a Hall-effect sensor measures.
How to use the magnetic field calculator
For a straight wire, enter the current and the distance from the conductor’s centre. For a solenoid, enter the same current, the number of turns, the coil length and the relative permeability of the core. The calculator returns both flux densities in millitesla and the solenoid’s field strength H.
Magnetic field formulas
Straight wire: B = μ0 I ÷ (2π r)
Solenoid: B = μ0 μr N I ÷ L · H = N I ÷ L
μ0 = 1.25663706212 × 10⁻⁶ H/m (≈ 4π × 10⁻⁷).
Example
10 A flowing in a long straight wire, measured 10 mm away; and the same current through a 500-turn, 10 cm air-core solenoid:
- Wire: B = 1.2566 × 10⁻⁶ × 10 ÷ (2π × 0.01) = 0.200 mT (200 µT)
- Solenoid: H = 500 × 10 ÷ 0.1 = 50,000 A/m
- Solenoid: B = 1.2566 × 10⁻⁶ × 500 × 10 ÷ 0.1 = 62.83 mT
Field around a straight wire
| Distance | 1 A | 10 A | 100 A | 1,000 A |
|---|---|---|---|---|
| 1 mm | 200.00 µT | 2,000.0 µT | 20,000 µT | 200,000 µT |
| 5 mm | 40.00 µT | 400.0 µT | 4,000 µT | 40,000 µT |
| 10 mm | 20.00 µT | 200.0 µT | 2,000 µT | 20,000 µT |
| 50 mm | 4.00 µT | 40.0 µT | 400 µT | 4,000 µT |
| 100 mm | 2.00 µT | 20.0 µT | 200 µT | 2,000 µT |
| 500 mm | 0.40 µT | 4.0 µT | 40 µT | 400 µT |
| 1000 mm | 0.20 µT | 2.0 µT | 20 µT | 200 µT |
| 5000 mm | 0.04 µT | 0.4 µT | 4 µT | 40 µT |
For comparison, the Earth’s magnetic field is about 50 µT and a fridge magnet about 5–10 mT.
Notes
- The wire formula assumes a long, straight conductor and a point outside it. Inside a round conductor, B rises linearly from zero at the centre.
- The field of two conductors carrying equal and opposite currents (a cable’s live and neutral) largely cancels, which is why twisted pairs pick up little interference.
- The force on a conductor or a moving charge in this field is given by the Lorentz force calculator.
Frequently asked questions
What is the magnetic field around a straight wire?
B = μ₀ I ÷ (2π r), with μ₀ = 4π × 10⁻⁷ H/m. A 10 A current gives 0.2 mT (200 µT) at 10 mm — about four times the Earth's field.
What is the magnetic field inside a solenoid?
B = μ₀ μr N I ÷ L for a long coil (length much greater than diameter). 500 turns on a 10 cm air-core coil with 10 A give about 62.8 mT.
How do I convert tesla to gauss?
1 T = 10,000 G, so 1 mT = 10 G and 1 µT = 0.01 G. The Earth's field is about 25–65 µT (0.25–0.65 G).
Why is the field at the end of a solenoid weaker?
At each open end of a long solenoid the flux density drops to about half the central value, because the field lines spread out.