Formula used
Resistivity links resistance, geometry, and length:
- ρ = R·A / L (resistivity from measured resistance)
- R = ρ·L / A (resistance from material and geometry)
- L = R·A / ρ (length when resistivity is known)
- A = ρ·L / R (area when resistivity is known)
For round conductors: A = πr². For rectangular conductors: A = w·t.
How to use this calculator
- Select the quantity you want to calculate.
- Enter the known values and choose their units.
- Choose an area method: direct, round wire, or rectangle.
- Click Calculate to view results above the form.
- Use CSV or PDF export for lab notes and documentation.
Example data table
Approximate resistivity near 20 °C. Values vary by alloy and temperature.
| Material | Resistivity ρ (Ω·m) | Conductivity σ (S/m) | Typical use |
|---|---|---|---|
| Copper | 1.68 × 10^-8 | 5.95 × 10^7 | Power wiring and windings |
| Aluminum | 2.82 × 10^-8 | 3.55 × 10^7 | Transmission lines |
| Silver | 1.59 × 10^-8 | 6.29 × 10^7 | High-performance contacts |
| Nichrome | 1.10 × 10^-6 | 9.09 × 10^5 | Heating elements |
Resistivity guide
1) What resistivity represents
Resistivity (ρ) is a material property that describes how strongly a substance opposes electric current. Lower ρ means easier electron flow. For metals, ρ is typically very small, often near 10^-8 Ω·m, while alloys and heater materials are much higher.
2) Linking material and geometry
The core relationship is R = ρ·L/A. Resistance grows linearly with length and falls as cross‑sectional area increases. Doubling the length doubles R. Doubling the area halves R. This calculator lets you solve any one variable from the others.
3) Why area input method matters
Area is often the largest source of uncertainty. A round wire uses A = πr², so small diameter errors amplify into area errors. For example, a 1.00 mm diameter wire has A ≈ 0.785 mm². If diameter is 0.95 mm, area drops to ≈ 0.709 mm², a change near 10%.
4) Unit consistency and conversions
Using mixed units is common in labs. Length may be in meters, diameter in millimeters, and area in mm². Internally, the calculator converts everything to SI (m, m², Ω·m) to keep the formulas consistent, then displays helpful secondary units like Ω·cm and mm².
5) Conductivity as a companion metric
Conductivity is the inverse of resistivity: σ = 1/ρ. It is reported in siemens per meter (S/m). High‑conductivity materials (large σ) are preferred for power delivery, while high‑resistivity materials are useful for heaters and precision resistors.
6) Typical data ranges
Pure copper is near 1.68×10^-8 Ω·m at about 20 °C, while aluminum is near 2.82×10^-8 Ω·m. Nichrome is around 10^-6 Ω·m, roughly two orders of magnitude higher than common conductors, which helps it generate heat at practical lengths.
7) Practical measurement tips
Measure resistance with firm, clean contacts. For small resistances, lead resistance can dominate, so use a four‑wire method when possible. Measure length along the current path, and measure diameter at multiple points to estimate an average and reduce error.
8) Where this calculator is used
Engineers use resistivity calculations to estimate voltage drop in wiring, design sensing elements, validate material batches, and compare coatings. In education, it connects microscopic material behavior to macroscopic circuit resistance, reinforcing the role of geometry in real conductors.
FAQs
1) What is the difference between resistivity and resistance?
Resistivity is a material property. Resistance depends on both the material and the conductor geometry. Two wires of the same material can have very different resistance if their lengths or areas differ.
2) Why does temperature change resistivity?
In many metals, higher temperature increases lattice vibrations, which increases electron scattering and raises resistivity. Some semiconductors show the opposite trend. Always compare values at a stated reference temperature.
3) Which area method should I choose?
Use direct area if you already have cross‑section data. Use round wire for cables and leads when you measure diameter or radius. Use rectangular bar for strips, busbars, and flat conductors.
4) Can I compute conductivity from my result?
Yes. The calculator provides conductivity as σ = 1/ρ in S/m. This is useful when comparing datasheets that list conductivity rather than resistivity.
5) What units are most common for resistivity?
In physics and engineering, Ω·m is standard. Ω·cm is common in materials work, especially for semiconductors. This tool converts between them to help you match your reference data.
6) My resistance is very small. What should I do?
Use a low‑resistance meter or a four‑wire (Kelvin) measurement to reduce lead and contact errors. Also keep connections tight and surfaces clean to avoid unstable readings.
7) Why are my results different from a reference table?
Differences can come from temperature, impurities, alloy composition, work hardening, or measurement error in diameter and length. Tables often give approximate values for a specific temperature and purity grade.