Case 1
- Number of turns
- 100
- Coil radius
- 1cm
- Coil length
- 5cm
78.9568µH
Open with these valuesCoil Inductance Calculator
78.9568µH
Result: 78.9568 µHInductance grows with the square of the turns and with the cross-section, and falls as the coil gets longer: 100 turns on a 1 cm radius over 5 cm gives about 79 µH. This is the long-solenoid formula, so it overstates short, fat coils.
Worked examples
Case 2
- Number of turns
- 200
- Coil radius
- 1.5cm
- Coil length
- 10cm
355.3058µH
Open with these valuesCase 3
- Number of turns
- 50
- Coil radius
- 2cm
- Coil length
- 8cm
49.3480µH
Open with these valuesHow it's calculated
L = µ0 × N² × π × r² ÷ l
- StepCount the turns of wire on the former.
- StepMeasure the radius to the middle of the winding, in centimetres.
- StepMeasure the length of the winding, not of the former.
- ResultRead the inductance in microhenries; divide by 1000 for mH.
Reference table
| Turns, radius, length | Shape of the coil | Inductance |
|---|---|---|
| 50, 2, 8 | Short and wide — expect an overstatement | 49.3480 |
| 100, 1, 5 | Five times as long as it is wide | 78.9568 |
| 500, 0.5, 20 | Long and thin, closest to the model | 123.3701 |
| 200, 1.5, 10 | Length just over three diameters | 355.3058 |
| 1000, 2, 30 | A large former, densely wound | 5263.7890 |
Questions
How is coil inductance calculated?
Multiply the magnetic constant by the square of the turns and by the cross-sectional area, then divide by the winding length. Doubling the turns quadruples the inductance; doubling the length halves it.
How accurate is this for a real coil?
It assumes a long solenoid whose field is uniform inside and zero outside. A coil as long as it is wide comes out roughly a third too high; one five times longer than wide is within a few per cent.
Which radius do I measure?
From the axis to the middle of the wire, not to the outside of the winding. The area term is squared, so a small error here is doubled in the answer.
Does a ferrite core change the result?
Yes, considerably. This calculator assumes an air core; a magnetic core multiplies the inductance by its relative permeability, which is often in the hundreds.
What if my coil is wound in several layers?
The formula does not apply. It describes a single layer of turns along a cylinder, and a multi-layer winding needs a different treatment entirely.
Sources and last check
Information, not professional advice.