Example 1
ρ=1.7×10⁻⁸, l=1 m, S=10⁻⁶ m² → R≈0.017 Ω.
Wire Resistance Calculator
Type ρ [Ω·m], l [m] and S [m²]. The calculator computes R = ρ l / S: copper 1.7e-8, 1 m and 1 mm² (1e-6 m²) is about 0.017 Ω. Zero area does not divide.
R from U and I: R = U/I. Series: Rz = R1+R2.
Result
Resistivity ρ (Ω·m), Length l (m) and Area S (m²). The result shows up here.
How it works
Resistance of a wire segment is R = ρ l / S. Copper ρ = 1.7e-8 Ω·m, l = 1 m and S = 1e-6 m² (1 mm²) is about 0.017 Ω. The same ρ and S at l = 10 m is about 0.17 Ω: ten times longer, ten times the R. Aluminum ρ ≈ 2.8e-8 at the same l and S is about 0.028 Ω.
The form has three fields: resistivity ρ in Ω·m, length l in meters, cross-section S in m². The result is in ohms. Type 1 mm² as 1e-6 or 0.000001, not as 1. 1.7e-8 is the easy copper entry. A comma and a period both work for 0.000001.
S must be positive, because you do not divide by zero. Typed 0 in S is rejected. Zero in ρ or l gives R = 0: no material or no length. All three fields need a number before 0.017 Ω appears.
R = U/I is on the neighbouring page and takes measured voltage and current. Here material and geometry: a longer or thinner wire has larger R. Two ready-made R values in series live on resistors in series.
Halving the cross-section doubles R at the same l and ρ. Doubling l also doubles R. Aluminum ρ is larger than copper, so the same l and S give a larger R.
Type 1.7e-8, 1, and 0.000001, click Calculate, and check about 0.017 Ω. Then l = 10 at the same S: about 0.17 Ω. The calculator multiplies ρ by l and divides by S; it does not guess a copper grade.
How to use
- In the first field enter ρ in Ω·m, for example 1.7e-8 for copper. Aluminum is about 2.8e-8.
- In the second field enter l in meters, for example 1. In the third, S in m², for example 0.000001 (1 mm²).
- Click Calculate. The calculator computes ρ l / S. That triple gives about 0.017 Ω. At l = 10 m, about 0.17 Ω.
- S = 0 is rejected. Zero in ρ or l gives R = 0. All three fields need a number.
- Have measured U and I? Open R = U/I. Here it stays R from material and cross-section.
Formula
R = ρ · l / S
ρ in Ω·m, l in m, S in m².
Wire resistance letter list
R = ρ·l/S from material and geometry, not from U/I. Copper 1.7e-8, 1 m and 1 mm² is about 0.017 Ω.
- R
- Wire resistance [Ω]. 10 m of the same 1 mm² copper is about 0.17 Ω.
- ρ
- Resistivity [Ω·m]. Copper is about 1.7e-8. A material constant, not an ohm from a meter.
- l
- Length [m]. 1 m and 10 m at the same S. Not centimetres.
- S
- Cross-section [m²]. 1 mm² is 1e-6 m². Larger S, smaller R.
Real-life examples
Example 2
R ≈ 0.17 Ω.
Example 3
ρ≈2.8×10⁻⁸.
Example 4
Long wire run.
Example 5
ρ larger than copper.
Example 6
Thin wire.
Example 7
Large ρ.
Example 8
Installation cable.
Example 9
Thick wire, small R.
Example 10
Very thin wire.
Ways to use this calculator
- You estimate 1 m of 1 mm² copper: about 0.017 Ω.
- You compare 1 m and 10 m at the same S.
Frequently asked questions
How much R at ρ = 1.7e-8, l = 1 m, S = 1e-6 m²?
Resistance is about 0.017 Ω. That is a metre of copper with a 1 mm² cross-section. 1.7e-8 × 1 / 1e-6.
How much at l = 10 m and the same S?
You get about 0.17 Ω. Ten times the length at the same area gives ten times R.
Which units do I type?
Resistivity ρ [Ω·m], length l [m], area S [m²]. Result R [Ω]. Type 1 mm² as 1e-6, not as 1.
How do I type 1.7×10⁻⁸?
As 1.7e-8 or 1,7e-8. Scientific e-notation is easier. 0.000000017 also works, but it is easier to mistype.
How is this different from R = U/I?
Here R comes from the material and the geometry. There it comes from a measured voltage and current. Different fields, same unit R [Ω].
Does a comma in 0.000001 work?
Yes. 0.000001, 0,000001 and 1e-6 are the same S [m²]. 1e-6 is easier.
Why is aluminum different?
Because it is a different metal. Aluminum has a higher ρ than copper, so the same l and S give a larger R.
Where are two R in series?
On the series-resistors page. There you already add two ohm results. Here you compute one R from ρ, l and S.
What about S = 0?
The calculator refuses zero square metres. R = ρ l / S at zero area does not exist.
Does a thinner wire double R?
Not by diameter. Thinner means smaller S. Half the area doubles R. Half the diameter cuts S by four, so R grows four times.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.