Formula Used
- Measured method: R = V / I, where V is contact voltage drop and I is current.
- Power loss: P = V · I. Heating often scales with contact resistance.
- Holm constriction (circular spot): Same material: R ≈ ρ / (2a). Two materials: R ≈ (ρ₁ + ρ₂) / (4a).
- Multiple micro-contacts: For N equal spots in parallel: Req = Rsingle / N.
- Force model: R = K · F−n + Rfilm. Fit K and n from experimental data.
- Temperature correction (optional): ρ(T) = ρ₀[1 + α(T − T₀)], useful for metals over moderate ranges.
How to Use This Calculator
- Select a method that matches your measurement or design model.
- Enter values with the correct units, then press Calculate.
- Review resistance and power loss shown above the form.
- If needed, subtract fixture resistance using the series field.
- Use CSV or PDF buttons to save the latest report.
- Compare scenarios to improve connector reliability and safety.
Example Data Table
| Scenario | Method | Inputs | Computed contact resistance | Power loss |
|---|---|---|---|---|
| Relay contact, low drop | Measured | V=8 mV, I=5 A | 1.6 mΩ | 0.040 W |
| Gold to copper micro-contact | Holm | a=40 µm, ρ₁=2.44 µΩ·cm, ρ₂=1.68 µΩ·cm, N=2 | 0.64 mΩ | Depends on current |
| Connector under clamp force | Force model | K=2 mΩ, n=0.6, F=20 N, Rfilm=0.2 mΩ | ~0.63 mΩ | Depends on current |
| Four-wire bench test | Four-wire | I=1 A, V=1.2 mV | 1.2 mΩ | 0.0012 W |
This article explains how to interpret contact resistance results and plan better measurements. Use it alongside the calculator to compare methods, units, and operating conditions.
1) What contact resistance represents
Contact resistance is the extra electrical resistance at an interface where two conductors touch. It comes from microscopic asperities, thin films, and limited real contact area. In many connectors, values fall between tens of micro-ohms and a few milliohms, depending on material, finish, and force.
2) Why a four-wire approach improves accuracy
Lead and fixture resistance can be larger than the contact itself. A four-wire style measurement senses voltage directly across the interface while a separate pair drives current. This isolates the contact drop and reduces error when you are working with millivolt or microvolt signals.
3) Interpreting measured V/I results
The measured method computes R = V/I and also reports power P = V·I. For example, 1.6 mΩ at 10 A produces a 16 mV drop and about 0.16 W of heating at the interface. Small resistance changes become important at high currents.
4) Using series subtraction for fixtures
When you cannot fully remove lead effects, subtract a known series resistance. Measure your fixture on a shorted reference, then enter that value in the series field. If the subtraction makes resistance negative, the fixture estimate is too large or the test current is too low.
5) Constriction physics and spot radius
Constriction resistance reflects current crowding through a small effective radius a. The Holm approximation gives R ≈ ρ/(2a) for identical materials, and R ≈ (ρ1+ρ2)/(4a) for dissimilar materials. Doubling a roughly halves the constriction contribution.
6) Material resistivity and temperature effects
Resistivity varies by metal and temperature. Copper near 20°C is about 1.68 µΩ·cm, while gold is about 2.44 µΩ·cm. If you apply a temperature coefficient α, the calculator adjusts ρ(T) = ρ0[1+α(T−T0)], which can noticeably increase resistance at elevated temperatures.
7) Force, films, and aging behavior
Higher normal force usually increases real contact area, lowering resistance. The empirical force model Rc = K·F−n + Rfilm captures this trend and adds a film term for oxides or coatings. Aging, fretting, and contamination can raise Rfilm, even when force is unchanged.
8) Turning results into design decisions
Use resistance and power outputs to size conductors, choose plating, and set clamp forces. Compare scenarios such as “clean vs. oxidized” or “low vs. high force” by changing inputs and exporting reports. For critical joints, validate with repeat measurements and track drift over time.
FAQs
1) What is a good contact resistance value?
It depends on current and hardware. Many power connectors target tens to hundreds of micro-ohms, while small switches can tolerate milliohms. Use voltage drop and power to judge acceptability for your load.
2) Why does contact resistance change with force?
More force increases the real contact area by deforming asperities and breaking thin films. That reduces constriction resistance. The relationship is not linear, so the force model uses an exponent n fitted to your measurements.
3) When should I subtract series resistance?
Subtract series resistance when your leads, clamps, or shunts contribute a measurable voltage drop. Measure the fixture on a short or known reference first. Avoid subtracting an uncertain value larger than your measured resistance.
4) Is the Holm constriction result exact?
No. It is an approximation for a circular effective contact spot and uniform material properties. Surface roughness, multiple micro-contacts, films, and noncircular geometry can shift results. Treat it as a design estimate, not a guarantee.
5) Why are microvolt readings noisy?
Thermoelectric offsets, EMI, and instrument resolution can be comparable to the signal. Use stable connections, shielded leads, sufficient current, and averaging. A four-wire setup helps because it minimizes extra series drops and reduces sensitivity to lead changes.
6) How do I estimate heating at the contact?
Use the calculator’s power output. If you know contact resistance Rc and current I, compute P = I²Rc. Then check whether that heat can be dissipated without exceeding allowable temperature rise for your connector materials.
7) Can I compare two materials like copper and gold?
Yes. Enable the two-material option in the constriction method and enter resistivities for both. The model uses (ρ1+ρ2)/(4a) for a circular spot. Include a film term if coatings or oxides dominate your interface.