Bonding Strap Impedance Calculator

A bonding strap is meant to hold two pieces of metal at the same potential, and it stops doing that far lower in frequency than anyone expects, because it is an inductor. Its DC resistance, its inductance from the published flat-conductor formula, its impedance against frequency, and the frequency at which it exceeds the milliohm limit your own standard sets at DC.

Last updated 24 Sep 2026

Where the strap stops meeting its own milliohm limit

Geometry + frequency → bond impedance

Strap length (mm)The electrical length of the strap between the two bonded surfaces, including the run out to the fastener and back — not the nominal length of the part. This is the input that dominates everything below.

Strap width (mm)Inductance falls slowly with width and fast with shortness, which is why NASA-STD-4003A requirement EBR 68 asks for a length-to-width ratio below 5 to 1 rather than simply for a wide strap. The page shows both trades below so you can see the difference.

Strap thickness (mm)Barely affects the inductance — it enters through a logarithm alongside the width. It sets the DC resistance, and it decides where skin effect starts: once the skin depth falls below about half the thickness the resistance starts rising with the square root of frequency.

Strap materialThe resistivity sets the DC resistance and the skin depth. Two warnings. A tinned or nickel-plated strap is a copper strap at DC and something worse at RF, because the current runs in the plating once the skin depth is thinner than it. And a magnetic material — anything with a relative permeability above 1 — has a much smaller skin depth than this page computes, so its AC resistance is worse than shown; the calculation here assumes a non-magnetic strap.

Frequency you care about (Hz)10 MHz is inside the conducted emissions band and well above where a strap has stopped behaving as a resistance. The chart shows the whole range; this input picks the frequency the numbers below are quoted at.

Stray capacitance across the joint (pF)The capacitance between the two pieces of metal by every path other than the strap — the overlap of the two flanges, the gap the strap bridges, the bracket beside it. It resonates with the strap’s inductance, and at that resonance the bond presents its highest impedance. A few picofarads for a small gap, tens for a flange overlap, hundreds for two panels almost touching. This is an estimate and the page treats it as one.

Bond resistance limit from your own standard (mΩ)Type in the figure that applies to you. NASA-STD-4003A — a US Government work — sets 2.5 mΩ for Class R radio-frequency and EMI bonds (requirements EBR 20 to 28) and for Class L lightning bonds, 0.1 Ω for Class H shock-hazard bonds and 1 Ω for Class S electrostatic-discharge bonds, with Class C power-return bonds depending on the current. ECSS-E-ST-20-07C Rev.2 has its own electrical bonding requirements in clause 4.2.11; those are copyrighted and are not reproduced here. Whatever figure you use, note that it is a DC figure.

A bond is not a wire. Drawn here as what it actually is: the strap's resistance and inductance in series between two pieces of structure, with the capacitance across the joint — the flange overlap, the gap, the bracket beside it — in parallel with the pair of them. The two rectangles are the two pieces of metal, not conductors in a circuit. Above the resonance of that inductance with that capacitance the current takes the capacitor instead and the strap contributes nothing; the inductor turns amber and red as the bond's impedance at your frequency climbs past ten and a hundred times its own DC resistance.

7.029kHzExample

a 100 × 20 × 0.5 mm copper strap — a 5:1 length-to-width ratio, exactly the NASA-STD-4003A ceiling — bridging a joint with 20 pF of stray capacitance, against a 2.5 mΩ Class R bond resistance limit

A strap is an inductor with a small resistance in it

R_DC = ρ·l ÷ (w·t)
L = (µ₀ ÷ 2π)·l·[ ln(2l ÷ (w + t)) + 0.5 + 0.2235(w + t) ÷ l ]
R_AC = ρ·l ÷ (2δw) · (sinh 2a + sin 2a) ÷ (cosh 2a − cos 2a), a = t ÷ 2δ, δ = √(ρ ÷ πfµ₀)
|Z_bond| = |(R_AC + j2πfL) ∥ 1 ÷ j2πfC_joint|

L: Terman’s flat-conductor formula. It is a geometric-mean-distance approximation and it is good to better than 1% for a strap five times longer than it is wide, and a few per cent low for a strap as wide as it is long
ln(2l/(w+t)): why width buys so little. The length is outside the logarithm and inside it; the width is only inside it. Halving the length beats doubling the width by a wide margin
C joint: the capacitance between the two bonded parts by every route except the strap. It resonates with L, and above that resonance the bond is a capacitor and the strap is irrelevant
δ: skin depth, assuming a non-magnetic strap. A magnetic or plated strap is worse than this page shows

Worked example

a 100 × 20 × 0.5 mm copper strap — a 5:1 length-to-width ratio, exactly the NASA-STD-4003A ceiling — bridging a joint with 20 pF of stray capacitance, against a 2.5 mΩ Class R bond resistance limit
The DC resistance is ρl ÷ wt = 172.4 µΩ, which is 6.90% of the 2.5 mΩ limit. On the test record this strap passes comfortably
Its inductance is 56.47 nH. The reactance of that equals the DC resistance at 485.9 Hz — below the bottom of the audio band. Above a few hundred hertz this is an inductor with a small resistance in it, not a resistance
So it passes 2.5 mΩ only up to 7.029 kHz, three and a half decades below the frequencies a Class R bond exists to control
At 10 MHz the bond presents 3.564 Ω — 20,674 times its own DC resistance. The skin depth there is 20.9 µm, which raises the resistance to 2.062 mΩ, and that is still three orders of magnitude below the 3.548 Ω of reactance
And the strap resonates with the 20 pF of joint capacitance at 149.8 MHz, above which the bond is capacitive. Two ways to improve it, both shown on the chart: halving the length takes the inductance to 21.76 nH, a 61.5% reduction, while doubling the width only reaches 43.75 nH, 22.5%. That asymmetry is the whole reason a length-to-width limit is written as a ratio

Bond classes and their DC resistance requirements in NASA-STD-4003A

Reproduced because NASA-STD-4003A is a US Government work. The standard’s own commentary on the Class R figure is the most useful sentence in it: there is no RF design basis for the historical 2.5 milliohm requirement except to ensure a good metal-to-metal contact. The requirement is a continuity check. Requirement EBR 68 is the one that addresses radio frequency, and it does so geometrically — a length-to-width ratio below 5 to 1, to minimise the inductance — because inductance is what actually decides the answer. ECSS-E-ST-20-07C Rev.2 clause 4.2.11 sets European spacecraft bonding requirements; it is copyrighted and is not reproduced here.
Class	What it is for	Maximum DC resistance	Requirements
C	power current return	depends on the current carried	EBR 7 to 13
H	shock and fault protection	0.1 Ω	EBR 14 to 19
R	radio frequency and EMI	2.5 mΩ	EBR 20 to 28
L	lightning protection	2.5 mΩ	EBR 29 to 40
S	electrostatic discharge	1.0 Ω	EBR 41 to 61

The number on the bonding record is not the number the noise sees

A bond is supposed to hold two pieces of metal at the same potential. The requirement is written as a DC resistance — a few milliohms — and it is verified with a milliohmmeter and a signature. What that verifies is that there is metal touching metal and that the joint is not corroded or painted. It says almost nothing about what happens at the frequencies the bond exists to control, and NASA-STD-4003A says so itself: there is no RF design basis for the historical 2.5 milliohm requirement except to ensure a good metal-to-metal contact.

The strap is an inductor. A 100 mm copper strap 20 mm wide has about 56 nH of inductance and about 0.17 mΩ of resistance, and the reactance of 56 nH equals 0.17 mΩ at about 486 Hz. Above the bottom of the audio band this is an inductor with a negligible resistance in it. At 10 MHz it presents about 3.5 Ω — twenty thousand times the resistance that was measured and recorded. Nothing about the bond has failed; it is doing exactly what an inductor does.

Why the rule is a ratio. Look at where length and width appear in the flat-conductor formula. Length is the factor outside the logarithm and is also inside it; width is only inside it. So inductance falls roughly in proportion to shortness and only logarithmically with width. Halving a 100 × 20 mm strap’s length takes it from 56.5 nH to 21.8 nH, a 61% reduction. Doubling its width instead reaches only 43.8 nH, a 23% reduction. That is why NASA-STD-4003A requirement EBR 68 asks for a length-to-width ratio below 5 to 1 and requirement EBR 66 asks for Class R straps to be as short as possible, in that order. A wide strap is not a substitute for a short one. Two straps in parallel halve the inductance only if they are far enough apart not to couple, and a braid is worse than a solid strap of the same width because the current has to follow the weave.

And then the bond stops working altogether. The strap’s inductance sits in parallel with the capacitance between the two bonded parts by every other route — the flange overlap, the gap, the bracket beside it. That is a parallel resonance, and at it the bond presents its maximum impedance rather than its minimum. Above it the capacitance carries the current and the strap is irrelevant. With 56 nH and 20 pF that resonance is around 150 MHz, inside the radiated emissions band. The peak impedance this page computes is the strap and the joint capacitance alone and is an upper bound: a real structure has many parallel paths, lossy joints and distributed capacitance, so the peak is lower and much broader. What survives the caveat is that the resonance exists and that a strap does not have a low impedance everywhere.

What this page is not about. It computes the impedance of the bond itself. It does not tell you how much current will flow in it, what isolation your grounding architecture requires, or whether a connection to structure belongs at that point at all — for the current a capacitor to chassis injects and the isolation resistance a platform demands, see the Y capacitor limit calculator. It also has nothing to do with earth electrodes in soil, which is a completely different problem with a completely different formula — see the earthing resistance calculator if that is what you are after. And the contact resistance at the two ends of the strap is usually larger than the strap, is not calculable from geometry, and degrades with time, corrosion and thermal cycling; it is what the DC measurement is really testing. Above roughly 10 to 30 MHz the answer stops being component values and becomes layout: the loop a part is mounted in, where the chassis is bonded, how the harness is routed. A component-value prediction carried to 100 MHz without that caveat is wrong.

Frequently asked questions

My bond measures 1 mΩ. Is it a good bond?

It is a good metal-to-metal contact, which is what the measurement demonstrates and what the requirement was written for. Whether it is a good bond at radio frequency depends on its inductance, which the DC measurement cannot see. Enter the geometry above and the page gives the frequency at which the same bond stops meeting the same number.

Why does a wide strap not fix the inductance?

Because width enters the formula only inside a logarithm while length enters outside it as well. Doubling the width of a typical strap buys about 20 to 25%; halving its length buys about 60%. That asymmetry is exactly why bonding standards write the rule as a length-to-width ratio — NASA-STD-4003A asks for below 5 to 1 — rather than as a minimum width.

Is a braided strap better than a solid one?

Usually worse for the same width, for two reasons. The current has to follow the weave, so the electrical length is longer than the mechanical one, and the many small contacts between strands are a nonlinear resistance that can generate intermodulation products of its own. Braid is chosen for flexibility and fatigue life, which are good reasons; it is not chosen for impedance.

What is the joint capacitance and how do I estimate it?

It is the capacitance between the two bonded parts by every path other than the strap: the overlap of two flanges, the gap the strap bridges, a bracket running alongside. Treat it as a parallel-plate estimate of the facing area and the gap, and treat the answer as an order of magnitude. It matters because it resonates with the strap, and the page’s resonance figure moves as the square root of it — so a factor of four in the estimate is a factor of two in the frequency.

Should I add a second strap?

It halves the inductance if the two straps are far enough apart that their fields do not couple, and buys much less if they run side by side. It also moves the resonance with the joint capacitance up by the square root of two rather than removing it. The bigger win is almost always a shorter single strap, and the biggest is not needing a strap at all: a continuous conductive joint with the two surfaces in contact has no strap inductance because it has no strap.

Does this apply to a ground wire in a cabinet?

Yes, and the numbers are worse, because a round wire of the same cross-section has more inductance than a flat strap and a metre-long green wire has around a microhenry. That is why an EMC earth is a strap or a plane and a safety earth is a wire: they are answering different questions, and a wire that satisfies the safety one can be several ohms at 10 MHz.

Related calculators

References

NASA-STD-4003A w/CHANGE 1, Electrical Bonding for NASA Launch Vehicles, Spacecraft, Payloads, and Flight Equipment. Baseline approved 5 February 2013, revalidated 19 January 2016. A US Government work. Bonding classes and their maximum DC resistances — Class C power return (requirements EBR 7 to 13), Class H shock hazard at 0.1 Ω (EBR 14 to 19), Class R radio frequency and EMI at 2.5 mΩ (EBR 20 to 28), Class L lightning at 2.5 mΩ (EBR 29 to 40), Class S electrostatic discharge at 1.0 Ω (EBR 41 to 61). Requirement EBR 66 asks for Class R straps to be as short as possible and requirement EBR 68, clause 5.1.2.b(2), asks for a length-to-width ratio of less than 5 to 1 to minimise the inductance. The standard states that there is no RF design basis for the historical 2.5 milliohm requirement except to ensure a good metal-to-metal contact.
Evans RW. Electrical Bonding: A Survey of Requirements, Methods, and Specifications, NASA report, March 1998 (NTRS 19980201283). A US Government work. Section 4.3 records that some procedures limit bond strap length-to-width ratios to 3 to 1 or 5 to 1, and that a strap’s impedance exceeds 2.5 mΩ at roughly 20 kHz, reaching at least 100 mΩ at 1 MHz and 1 Ω at 10 MHz; section 4.4 gives strap and jumper inductance formulas, attributed to Terman’s Radio Engineers’ Handbook (McGraw-Hill, 1943), and describes the resonance above which the capacitive reactance falls below the inductive reactance and the total impedance comes back down. One caution: as transcribed, that section’s round-jumper formula prints a plus 0.75 where the classical Rosa result has a minus 0.75. The exact partial-inductance computation used to verify this page’s arithmetic confirms the minus sign, and this site’s ground-loop page uses it.
Terman FE. Radio Engineers’ Handbook. McGraw-Hill, 1943. The source of the flat-conductor inductance formula used here, L = (µ₀/2π)·l·[ln(2l/(w+t)) + 0.5 + 0.2235(w+t)/l]. It is the geometric-mean-distance approximation: 0.2235(w+t) is the self-GMD of a rectangle of sides w and t. Checked here against the exact partial self-inductance of a rectangular bar, computed as the four-dimensional average of the exact two-filament mutual inductance over both cross sections: better than 1% for length-to-width ratios of 5 and above, and 4 to 6% low for a strap as wide as it is long.
ECSS-E-ST-20-07C Rev.2, 3 January 2022, Space engineering — Electromagnetic compatibility. Clause 4.2.10 grounding and clause 4.2.11 electrical bonding hold the European spacecraft requirements, including bond resistances in the milliohm range. Freely downloadable from ECSS and copyrighted; cited by clause, not reproduced.
MIL-B-5087B, Bonding, Electrical, and Lightning Protection, for Aerospace Systems. The US military standard whose bonding classes NASA-STD-4003A follows, and the origin of the 2.5 mΩ Class R figure. Superseded for new NASA work by NASA-STD-4003A; still the document most often named.
Ramo S, Whinnery JR, Van Duzer T. Fields and Waves in Communication Electronics, 3rd ed., Wiley. The one-dimensional skin-effect solution for a conducting slab, from which this page’s AC resistance expression comes, and the definition δ = √(ρ ÷ πfµ) used for the skin depth.