Via Inductance
L = 0.2 × h × (ln(4h/d) + 1) nH
Quick answer
This calculator solves L = 0.2 × h × (ln(4h/d) + 1) nH for L. With Via Height (mm) 10 mm, Via Diameter (mm) 22 mm, the result is 3.196 nH.
Calculator
Formula
Description
Every via in a PCB has parasitic inductance due to its length and cylindrical geometry. This inductance creates impedance discontinuities in high-speed signal paths and adds parasitic inductance to power delivery networks. A typical through-hole via in a standard 1.6mm board has about 0.5-1.5 nH of inductance. At GHz frequencies, even 1 nH presents significant reactance (6.3Ω at 1 GHz). Minimizing via inductance is critical for high-speed designs, which is why shorter vias (blind, buried, or microvias) are preferred.
Variables
- L — Via inductance (nH)
- h — Via height (length through the board) (mm)
- d — Via drill diameter (mm)
Practical Notes
The result is in nanohenries. Wider diameter reduces inductance slightly, but the logarithmic dependence means doubling the diameter only reduces inductance by about 15%. Multiple vias in parallel reduce effective inductance: two vias ≈ L/2 if well-separated. Return path vias (ground stitching vias near signal vias) are essential to minimize loop inductance and control impedance at layer transitions.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| h | Via Height (mm) | mm | mm |
| d | Via Diameter (mm) | mm | mm |
Step by step
- 1. What you know: Via Height (mm) 10 mm, Via Diameter (mm) 22 mm
- 2. The relation: L = 0.2 × h × (ln(4h/d) + 1) nH
- 3. Substitute: h = 10 mm, d = 22 mm
- 4. Result: L = 3.196 nH
Worked examples
Minimum range
Given: Via Height (mm) 0.1 mm, Via Diameter (mm) 0.22 mm
Result: L = 0.03196 nH
Low range
Given: Via Height (mm) 1 mm, Via Diameter (mm) 2.2 mm
Result: L = 0.3196 nH
Typical
Given: Via Height (mm) 10 mm, Via Diameter (mm) 22 mm
Result: L = 3.196 nH
High range
Given: Via Height (mm) 100 mm, Via Diameter (mm) 220 mm
Result: L = 31.96 nH
Maximum range
Given: Via Height (mm) 1000 mm, Via Diameter (mm) 2200 mm
Result: L = 319.6 nH
How L changes with Via Height (mm)
| Via Height (mm) (input) | L (result) |
|---|---|
| 1 mm | -0.1409 nH |
| 2.5 mm | 0.1058 nH |
| 5 mm | 0.9047 nH |
| 7.5 mm | 1.965 nH |
| 10 mm | 3.196 nH |
| 15 mm | 6.01 nH |
| 20 mm | 9.164 nH |
| 40 mm | 23.87 nH |
| 70 mm | 49.61 nH |
| 100 mm | 78.01 nH |
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<p><a href="https://vbatpower.com/formulas/via-inductance/">Via Inductance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Via Inductance?
Use L = 0.2 × h × (ln(4h/d) + 1) nH. With Via Height (mm) 10 mm, Via Diameter (mm) 22 mm, L works out to 3.196 nH.
What is the formula for Via Inductance?
The formula is L = 0.2 × h × (ln(4h/d) + 1) nH. Every via in a PCB has parasitic inductance due to its length and cylindrical geometry.
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