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Inductance Unit Converter

Convert inductance between henries, millihenries, microhenries, nanohenries, and picohenries.

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Formula

1H=103mH=106muH=109nH=1012pH1 H = 10³ mH = 10⁶ mu H = 10⁹ nH = 10¹² pH

How It Works

This calculator converts between henries, millihenries, microhenries, nanohenries, and picohenries for power electronics engineers, RF designers, and EMC specialists. Per SI Brochure (BIPM), the henry is defined as Wb/A = V·s/A = kg·m^2/(A^2·s^2), representing inductance that produces 1 V EMF when current changes at 1 A/s. Inductance spans 12 orders of magnitude: picohenries for bond wire inductance (~1 pH/mm per IEEE packaging guidelines), nanohenries for RF matching (1-100 nH), microhenries for DC-DC converters (1-1000 uH), and millihenries for AC filters and motor drives (1-100 mH). PCB trace inductance is approximately 1 nH per mm length per IPC-2141, critical for high-speed signal integrity above 100 MHz.

Worked Example

Problem

A 500 kHz buck converter requires 10 uH inductor with 30% ripple current at 3 A DC. Calculate peak current, energy storage, and verify saturation margin.

Solution
  1. Inductance: 10 uH = 0.01 mH = 10,000 nH = 10^-5 H
  2. Ripple current: 30% of 3 A = 0.9 A peak-to-peak
  3. Peak current: I_pk = I_DC + dI/2 = 3 + 0.45 = 3.45 A
  4. Energy stored at peak: E = 0.5 × L × I^2 = 0.5 × 10e-6 × 3.45^2 = 59.5 uJ
  5. V = L × dI/dt, so dI/dt = V/L = (12-5)/(10e-6) = 700,000 A/s during on-time
  6. Saturation margin: select inductor rated for I_sat > 4 A (15% margin above 3.45 A peak)
  7. Core loss: at 500 kHz, ferrite core gives ~100 mW/cm^3 per Steinmetz equation

Practical Tips

  • ✓PCB trace inductance per IPC-2141: ~1 nH/mm for traces over ground plane. A 50 mm power trace adds 50 nH, causing 3 V drop at 100 A/us slew rate (typical for fast logic). Minimize trace length to IC power pins
  • ✓Inductor selection per Coilcraft/Wurth guidelines: DC-DC converters use 1-100 uH with high I_sat; EMI filters use 100 uH - 10 mH common-mode chokes; RF matching uses 1-100 nH with high Q (>50 at frequency)
  • ✓Inductor code marking: 4-digit similar to capacitors, where first 3 digits are value and last is multiplier in nH. Example: 101 = 10 × 10^1 nH = 100 nH; R47 = 0.47 uH (R is decimal point per EIA-198)

Common Mistakes

  • ✗Confusing uH (10^-6 H) with mH (10^-3 H) - they differ by 1000x. A 10 mH inductor has 1000x more inductance than 10 uH. DC-DC converters use uH; line filters use mH
  • ✗Ignoring parasitic lead inductance (~1 nH/mm per IEEE) - at 1 GHz, 10 nH of lead inductance = 63 ohm reactance, potentially dominating a 100 ohm circuit. Use surface-mount components for RF
  • ✗Not accounting for saturation - inductor datasheets specify both L_nominal and I_sat. When I > I_sat, inductance drops 20-50%, causing increased ripple and potential instability. Verify I_sat > I_peak

Frequently Asked Questions

Per Faraday's law: V = L × dI/dt, so 1 H produces 1 V when current changes at 1 A/s. In practice: 10 uH inductor with 1 A/us current slew produces 10 V. This is why fast power delivery (100 A/us for modern CPUs) requires very low inductance (< 1 nH total) between VRM and load.
Per application frequency: nH for RF/microwave (> 100 MHz) where reactance X = 2*pi*f*L matters (10 nH at 1 GHz = 63 ohm). uH for power electronics (10 kHz - 10 MHz DC-DC converters). mH for line-frequency applications (50/60 Hz EMI filters, motor drives). Match inductance to operating frequency.
Per IEEE packaging models: a straight wire has self-inductance L = 0.2 × length_mm × (ln(2 × length/radius) - 0.75) nH, approximately 1 nH/mm for typical bond wire diameters. At 5 GHz, 2 nH = 63 ohm reactance, which is why flip-chip packaging (10x lower inductance) is required for > 1 GHz ICs.
Divide by 1000: 470 nH = 0.47 uH = 0.00047 mH. Multiply by 1000 for reverse: 4.7 uH = 4700 nH. Standard values per IEC 60063 E-series: E24 (5% tolerance) gives 47, 51, 56... in any decade. Typical DC-DC inductors: 1 uH, 2.2 uH, 4.7 uH, 10 uH, 22 uH, 47 uH.

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