Sample results assume uniform material and constant cross-section.
| Material ρ (Ω·m) | L (m) | A (mm²) | Parallel n | R (Ω) |
|---|---|---|---|---|
| 1.68e-8 | 2 | 1 | 1 | 3.36e-2 |
| 2.82e-8 | 5 | 2.5 | 1 | 5.64e-2 |
| 1.10e-6 | 0.3 | 0.5 | 2 | 3.30e-1 |
The calculator uses the standard resistive relation:
R = ρL / A.
Here, ρ is resistivity in Ω·m, L is length in meters,
and A is cross-sectional area in m².
If you enter diameter, the area is computed as A = π(d/2)². When temperature correction is enabled, resistivity is adjusted using ρ(T) = ρ₀[1 + α(T − T₀)].
For n identical conductors in parallel, the equivalent resistance is R_eq = R_single / n.
- Enter resistivity and choose its unit.
- Provide the conductor length and its unit.
- Select area mode or diameter mode for geometry.
- Optionally enable temperature correction and fill T₀, T, and α.
- Set the number of identical parallel conductors, if needed.
- Press Calculate Resistance to view results above the form.
- Use Download CSV or Download PDF for reports.
1) Core relationship and assumptions
Electrical resistance for a uniform conductor is computed from R = ρL/A, where ρ is resistivity, L is the current path length, and A is the cross‑sectional area. The model assumes a constant material, steady temperature, and a consistent cross‑section along the length. It estimates bulk conductor resistance, not contact or connector losses.
2) Handling units without mistakes
Resistivity is commonly published in Ω·m, Ω·cm, or μΩ·cm. A frequent pitfall is mixing centimeters with meters or using area in mm² without converting. This calculator normalizes all inputs to SI before computing R, so you can enter practical shop units (cm, mm², in²) while still obtaining a correct Ω result.
3) Geometry inputs: area mode vs diameter mode
If you know the cross‑section directly, area mode is the most reliable. When diameter is easier to measure, diameter mode converts it using A = π(d/2)². For non‑circular conductors, use the true area from drawings, standards, or manufacturer tables. Small measurement errors in diameter produce larger area errors because of the square.
4) Typical resistivity reference values
At about 20 °C, copper is roughly 1.68×10−8 Ω·m and aluminum about 2.82×10−8 Ω·m, while nichrome can be around 1.10×10−6 Ω·m. These values vary with alloy, purity, and heat treatment. Use datasheet resistivity when accuracy matters, especially for resistive alloys and plated conductors.
5) Temperature correction for real operation
Many metals increase resistance as they warm. With temperature enabled, the tool adjusts resistivity using ρ(T) = ρ₀[1 + α(T − T₀)]. For copper, α is often near 0.0039 1/°C around room temperature, but the best value comes from the specific material spec. For wide temperature ranges, consult standards or a detailed curve.
6) Design sensitivity: length and area scaling
Resistance scales linearly with length and inversely with area. Doubling L doubles R; doubling A halves R. This makes conductor sizing a powerful lever in power distribution, heating, and sensor leads. When comparing options, keep the same temperature reference and watch the unit conversions—most “mystery” errors are conversion errors.
7) Multiple identical conductors in parallel
If you run n identical wires in parallel, the total resistance ideally becomes Rtotal = Rsingle/n because current divides between equal paths. This calculator includes a parallel conductor count to support bundled wires, litz‑style groups, or busbar laminations (when each path is comparable). Unequal lengths or joints reduce the ideal benefit.
8) Practical validation and common checks
After computing R, validate against a datasheet “ohms per meter/foot” value when available. If the result is off by 10× or 100×, recheck units, especially Ω·cm vs Ω·m and mm² vs m². Remember that real circuits add contact resistance, solder joints, and temperature rise under load, which can exceed the bulk‑material estimate.
FAQs
1) Which resistivity unit should I choose?
Use the unit from your material source. If a datasheet lists μΩ·cm, select that unit. The calculator converts internally, so mixing units is safe as long as each field’s unit is correct.
2) How is diameter converted into area?
For a round conductor, area is computed as A = π(d/2)². Enter the measured diameter and unit, and the calculator produces the equivalent cross‑sectional area automatically.
3) Why does resistance change with temperature?
In many metals, higher temperature increases electron scattering, raising resistivity. With temperature correction enabled, the tool adjusts ρ using a linear coefficient so R reflects operating conditions.
4) What value of α should I use?
Use the coefficient from your material specification. Copper is often near 0.0039 1/°C around room temperature, but alloys and temperature range can change α noticeably.
5) Can I use this for a hollow tube or strip?
Yes, if you enter the effective conductive cross‑sectional area. For a tube, use A = π(Ro² − Ri²). For strips, use width × thickness.
6) How do parallel conductors affect the result?
If conductors are identical and truly in parallel, total resistance is R/n. Use the “parallel conductors” option for bundles. Differences in length, joints, or temperature reduce the ideal improvement.
7) What if I only know “ohms per meter” for a wire?
You can still use this tool by back‑calculating resistivity from R, L, and A, but it’s usually simpler to multiply the published ohms‑per‑meter by your length and then adjust for temperature if needed.