Air-Coil Inductance (Wheeler)
L = µ0·N²·π·r² / (l + 0.9·r)
Quick answer
This calculator solves L = µ0 × N² × π × r² / (l + 0.9 × r) for Inductance. With Number of Turns 0.5, Coil Radius 10 mm, Coil Length 2.2 cm, the result is 3.184 nH. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Wheeler’s short-coil approximation gives the inductance of a single-layer air-core solenoid from its turns, radius, and length, correcting the ideal-solenoid formula for the finite length of real coils. It is the standard hand-calculation for winding RF coils, Tesla-coil secondaries, and air-core chokes, accurate to about 1% when the coil length is at least 0.4 times its diameter.
Variables
- L — Inductance (H)
- N — Number of turns
- r — Coil radius (m)
- l — Coil length (m)
Practical Notes
The 0.9·r term accounts for the field spilling out the ends of a short coil; as l ≫ r it reduces to the ideal solenoid µ0N²A/l. Accuracy degrades for very short, fat coils.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| L | Inductance | µH | nH, µH, mH, H |
| N | Number of Turns | — | — |
| r | Coil Radius | mm | mm, cm, m, km |
| l | Coil Length | mm | mm, cm, m, km |
Step by step
- 1. What you know: Number of Turns 0.5, Coil Radius 10 mm, Coil Length 2.2 cm
- 2. The relation: L = µ0 × N² × π × r² / (l + 0.9 × r)
- 3. Substitute: N = 0.5, r = 10 mm, l = 2.2 cm
- 4. Result: Inductance = 3.184 nH
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 3.3 nH | 3.7% |
| E24 | 3.3 nH | 3.7% |
Worked examples
Minimum range
Given: Number of Turns 0.025, Coil Radius 0.1 mm, Coil Length 0.22 mm
Result: Inductance = 7.96 × 10⁻⁵ nH
Low range
Given: Number of Turns 0.25, Coil Radius 1 mm, Coil Length 2.2 mm
Result: Inductance = 0.07959 nH
Typical
Given: Number of Turns 0.5, Coil Radius 10 mm, Coil Length 2.2 cm
Result: Inductance = 3.184 nH
High range
Given: Number of Turns 0.8, Coil Radius 10 cm, Coil Length 22 cm
Result: Inductance = 81.5 nH
Maximum range
Given: Number of Turns 8, Coil Radius 1 m, Coil Length 2.2 m
Result: Inductance = 81.5 µH
Solving for each variable
Solve for Inductance
Number of Turns 0.025, Coil Radius 0.1 mm, Coil Length 0.22 mm → 7.96 × 10⁻⁵ nH
Solve for Number of Turns
Inductance 100 nH, Coil Radius 0.1 mm, Coil Length 0.22 mm → 28.02
Solve for Coil Length
Inductance 100 µH, Number of Turns 25, Coil Radius 10 cm → 15.67 cm
How Inductance changes with Number of Turns
| Number of Turns (input) | Inductance (result) |
|---|---|
| 0.05 | 0.03184 nH |
| 0.125 | 0.199 nH |
| 0.25 | 0.7959 nH |
| 0.375 | 1.791 nH |
| 0.5 | 3.184 nH |
| 0.75 | 7.163 nH |
| 1 | 12.73 nH |
| 2 | 50.94 nH |
| 3.5 | 156 nH |
| 5 | 0.3184 µH |
The same result in other units
| Unit | Value |
|---|---|
| nH | 3.184 |
| µH | 0.003184 |
Embed this calculator
Paste this into any page. It keeps working when this page updates, and credits the source.
<iframe src="https://vbatpower.com/embed/air-coil-inductance-wheeler/" width="100%" height="460" style="border:1px solid #1f2a37;border-radius:12px" loading="lazy" title="Air-Coil Inductance (Wheeler)"></iframe>
<p><a href="https://vbatpower.com/formulas/air-coil-inductance-wheeler/">Air-Coil Inductance (Wheeler)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Air-Coil Inductance (Wheeler)?
Use L = µ0 × N² × π × r² / (l + 0.9 × r). With Number of Turns 0.5, Coil Radius 10 mm, Coil Length 2.2 cm, Inductance works out to 3.184 nH.
How do you calculate wheeler formula single layer air core coil inductance?
Rearrange for Inductance: with Number of Turns 0.25, Coil Radius 1 mm, Coil Length 2.2 mm, Inductance is 0.07959 nH.
What is the formula for Air-Coil Inductance (Wheeler)?
The formula is L = µ0 × N² × π × r² / (l + 0.9 × r). Wheeler’s short-coil approximation gives the inductance of a single-layer air-core solenoid from its turns, radius, and length, correcting the ideal-solenoid formula for the finite length of real coils.
How do you find Number of Turns when you know the other values?
Rearrange for Number of Turns: with Inductance 100 nH, Coil Radius 0.1 mm, Coil Length 0.22 mm, Number of Turns is 28.02.
How do you find Coil Length when you know the other values?
Rearrange for Coil Length: with Inductance 100 µH, Number of Turns 25, Coil Radius 10 cm, Coil Length is 15.67 cm.
What units does Air-Coil Inductance (Wheeler) use?
Inductance is shown in nH, µH. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Inductors formulas →Need more features?
Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.
Try the App