Connector Contact Resistance
Rc = ρ / (π × a)
Quick answer
This calculator solves Rc = ρ / (π × a) for Contact Resistance. With Resistivity (Ω·m) 0.5 Ω·m, Contact Spot Radius 100 µm, the result is 1.592 kΩ.
Calculator
Formula
Description
When two conductors are pressed together, they make contact only at small asperity points rather than across the entire apparent contact area. The constriction resistance at each contact spot depends on the material resistivity and the effective contact radius. Higher contact force increases the contact area by plastic deformation of asperities, reducing resistance. This model explains why connector contact resistance depends strongly on contact force, surface finish, and contamination. Gold plating is used on connectors not because gold is a better conductor but because it resists oxidation, maintaining clean metal-to-metal contact.
Variables
- Rc — Constriction resistance at one contact spot (Ω)
- ρ — Resistivity of the contact material (Ω·m)
- a — Effective radius of the contact spot (m)
Practical Notes
Typical connector contact resistance: gold-plated 1-10 mΩ, tin-plated 2-50 mΩ, bare copper 5-100 mΩ (varies with age and environment). Contact resistance increases over time due to oxidation and fretting corrosion. Specify gold plating (0.75 µm minimum) for signal contacts with low insertion cycles, and harder gold (gold-cobalt alloy) for contacts that are frequently mated.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Rc | Contact Resistance | mΩ | mΩ, Ω, kΩ, MΩ |
| rho | Resistivity (Ω·m) | — | Ω·m |
| a | Contact Spot Radius | µm | µm |
Step by step
- 1. What you know: Resistivity (Ω·m) 0.5 Ω·m, Contact Spot Radius 100 µm
- 2. The relation: Rc = ρ / (π × a)
- 3. Substitute: rho = 0.5 Ω·m, a = 100 µm
- 4. Result: Contact Resistance = 1.592 kΩ
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 1.5 kΩ | 5.8% |
| E24 | 1.6 kΩ | 0.53% |
Worked examples
Minimum range
Given: Resistivity (Ω·m) 0.025 Ω·m, Contact Spot Radius 1 µm
Result: Contact Resistance = 7.958 kΩ
Low range
Given: Resistivity (Ω·m) 0.25 Ω·m, Contact Spot Radius 10 µm
Result: Contact Resistance = 7.958 kΩ
Typical
Given: Resistivity (Ω·m) 0.5 Ω·m, Contact Spot Radius 100 µm
Result: Contact Resistance = 1.592 kΩ
High range
Given: Resistivity (Ω·m) 0.8 Ω·m, Contact Spot Radius 1000 µm
Result: Contact Resistance = 0.2546 kΩ
Maximum range
Given: Resistivity (Ω·m) 8 Ω·m, Contact Spot Radius 10000 µm
Result: Contact Resistance = 0.2546 kΩ
How Contact Resistance changes with Resistivity (Ω·m)
| Resistivity (Ω·m) (input) | Contact Resistance (result) |
|---|---|
| 0.05 Ω·m | 0.1592 kΩ |
| 0.125 Ω·m | 0.3979 kΩ |
| 0.25 Ω·m | 0.7958 kΩ |
| 0.375 Ω·m | 1.194 kΩ |
| 0.5 Ω·m | 1.592 kΩ |
| 0.75 Ω·m | 2.387 kΩ |
| 1 Ω·m | 3.183 kΩ |
| 2 Ω·m | 6.366 kΩ |
| 3.5 Ω·m | 11.14 kΩ |
| 5 Ω·m | 15.92 kΩ |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 1592000 |
| Ω | 1592 |
| kΩ | 1.592 |
| MΩ | 0.001592 |
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<p><a href="https://vbatpower.com/formulas/connector-contact-resistance/">Connector Contact Resistance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Connector Contact Resistance?
Use Rc = ρ / (π × a). With Resistivity (Ω·m) 0.5 Ω·m, Contact Spot Radius 100 µm, Contact Resistance works out to 1.592 kΩ.
What is the formula for Connector Contact Resistance?
The formula is Rc = ρ / (π × a). When two conductors are pressed together, they make contact only at small asperity points rather than across the entire apparent contact area.
What units does Connector Contact Resistance use?
Contact Resistance is shown in mΩ, Ω, kΩ, MΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Wire & Cable formulas →Need more features?
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