One meter of 1 mm² copper
School copper: ρ = 1.7×10⁻⁸ Ω·m, length 1 m, area 1 mm² (10⁻⁶ m²). The quotient is exactly 0.017 Ω.
R = 0.0170 Ω
Wire Resistance Calculator
Enter resistivity ρ in Ω·m, length l in meters, and cross-sectional area S in m². The calculator finds the resistance of a uniform wire from R = ρ·l/S. For ρ = 1.7×10⁻⁸ Ω·m, l = 1 m, and S = 10⁻⁶ m² (1 mm²) the result is 0.017 Ω. The model does not include a temperature correction, an AWG lookup, or voltage drop I·R.
Result
Enter ρ, length l, and area S. Resistance, the product ρ·l, and the chart appear here.
Resistance from a measured voltage and current: R = U/I. Series of known resistances: Rz = R1 + R2.
How it works
ρ1.7×10⁻⁸
l1 m
S10⁻⁶ m²
R0.017 Ω
The resistance of a uniform conductor is R = ρ·l/S. European textbooks sometimes call this Pouillet’s law: resistance rises with length and with resistivity, and it falls as the cross-section grows. With the symbols L and A the same formula is R = ρL/A. On this page L is the length l, and A is the area S. For ρ = 1.7×10⁻⁸ Ω·m, l = 1 m, and S = 10⁻⁶ m² the quotient is 0.017 Ω. The panel prints resistance with four decimal places, so you see 0.0170 Ω.
The calculator uses the three numbers you enter: resistivity ρ in Ω·m (field opor-drutu-a), length l (field opor-drutu-b), and area S (field opor-drutu-c). A comma and a period are the same decimal separator. Enter 1 mm² as 1e-6 or 0.000001. The entry 1.7e-8 means 1.7×10⁻⁸. The calculator converts length and area when the header switch changes (meters or feet). Resistivity stays in Ω·m.
What the result panel shows. Besides resistance R, the calculator shows the ρ, length, and area you entered, and the product ρ·l before it divides by S. At 1.7×10⁻⁸ Ω·m, 1 m, and 10⁻⁶ m² the product ρ·l is 1.7×10⁻⁸ Ω·m², and the resistance is 0.017 Ω. The chart draws R against length at the ρ and S from the fields, from one quarter of the entered length to twice that length.
Limits of the model. The calculator assumes a uniform cross-section, a steady temperature, and direct current. It does not compute diameter, an AWG number, a go-and-return loop, a temperature coefficient, or skin effect. An area S of zero or below is rejected. Zero resistivity or zero length gives R = 0. Resistance from voltage and current, and series sums, are on separate pages.
The “Fill this example” button enters the example numbers and refreshes the panel and the chart. Ten meters of the same 1 mm² copper gives 0.17 Ω, shown as 0.1700 Ω. A published copper value at 20 °C is about 1.68×10⁻⁸ Ω·m. The value 1.7×10⁻⁸ is a school rounding, not a measurement from this page.
Formula
R = ρ · l / S
The same relation in textbook symbols: R = ρL / A. On this page you enter length L as l, and cross-sectional area A as S.
Named model: the resistance of a uniform conductor, called Pouillet’s law in many European schoolbooks (Claude Pouillet). The calculator multiplies ρ by l and divides by S. It does not apply Ohm’s law U = I·R, it does not add series resistors, and it does not apply a temperature correction.
For ρ = 1.7×10⁻⁸ Ω·m, l = 1 m, and S = 10⁻⁶ m², the product ρ·l is 1.7×10⁻⁸ Ω·m², and R = 0.017 Ω. The unit: 1 Ω = 1 V/A.
Theory, derivation, and domain
Definition and the ohm
The resistance of a conductor is the ratio of voltage to current when the element is ohmic. For a wire of constant cross-section and one material, the same quantity can be computed from geometry before you measure U and I. The formula is R = ρ·l/S. Resistivity ρ is a material property. Length l is the path the current travels. Area S is the cross-section perpendicular to that path.
The ohm is a derived SI unit: 1 Ω = 1 V/A = 1 kg·m²·s⁻³·A⁻². The practical realization of the ohm in metrology uses the quantum Hall effect. This calculator does not perform that calibration. It divides the three numbers you enter and reports the quotient in ohms.
Pouillet’s law and the form R = ρL/A
Claude Pouillet (1790–1868) is the name many European school traditions attach to the dependence of resistance on length and cross-section. English textbooks often write R = ρL/A and do not use that name. Both forms are the same model. The calculator uses the symbols on the fields: ρ, l, and S.
Resistivity is not an ohm from a voltmeter reading. An ohm from voltage and current is computed on the separate R = U/I page.
Derivation with the numbers on this page
Step 1. Enter ρ, l, and S in the units of the formula. For school copper: ρ = 1.7×10⁻⁸ Ω·m, l = 1 m, S = 10⁻⁶ m², which is 1 mm². Step 2. Multiply ρ by l: 1.7×10⁻⁸ × 1 = 1.7×10⁻⁸ Ω·m². Step 3. Divide by S: 1.7×10⁻⁸ / 10⁻⁶ = 0.017 Ω. The panel shows that quotient as 0.0170 Ω.
Step 4. Ten times the length at the same ρ and S gives ten times the resistance: 0.17 Ω, shown as 0.1700 Ω. Half the area at the same ρ and l doubles R. That proportion is the formula itself, not a separate mode.
Area, diameter, and square millimeters
The area of a circle is S = πd²/4. The calculator has no diameter field. You compute S first, then enter it. 1 mm² = 10⁻⁶ m² exactly, because 1 mm = 10⁻³ m and area scales with the square of that factor. Entering 1 in the area field means 1 m², not 1 mm².
Half the diameter gives one quarter of the area, so resistance becomes four times larger when ρ and l stay the same, and you enter the new S yourself. Half the area, already entered as S, doubles R. Those are two different comparisons.
Temperature, alternating current, and skin effect
Metals increase in resistance with temperature, approximately R = R₀ (1 + α·ΔT). For copper, α is on the order of 0.0039 per kelvin. This calculator does not ask for temperature and does not apply α. The result is the quotient of the ρ, l, and S you enter, not the resistance of a warm cable.
At high-frequency alternating current the current crowds toward the surface (skin effect) and the effective resistance rises. The calculator assumes direct current and a uniform current density over the cross-section. It does not compute reactance or impedance.
What this quotient does not replace
The relation R = U/I uses a measured voltage and current. This page has no voltage or current fields. Series connection adds known resistances, and a parallel connection adds reciprocals. Both are on separate pages. Joule heating P = I²R is separate as well: there R is already an input.
The length you enter is the length of one current path. If the current goes out and back, the loop length is about twice the distance between the ends. You enter that longer number yourself. The calculator does not double it. The result is not a breaker model, a wiring code, or a protection check.
The header unit switch
The header switch changes only length and area: meters or feet, square meters or square feet. The factors in the code are 3.2808399 ft per meter and 10.76391 ft² per m². Resistivity stays in Ω·m. After you change the header, the calculator converts l and S already entered so that R in ohms stays the same. The currency switch does not enter the formula.
Resistivity at 20 °C, by order of magnitude
These are typical published values, not a result of this calculator. You enter ρ yourself. The school figure 1.7×10⁻⁸ for copper is a rounding of the table value 1.68×10⁻⁸.
| Material | ρ at 20 °C | What that means on this page |
|---|---|---|
| Copper | about 1.68×10⁻⁸ Ω·m | School 1.7×10⁻⁸, 1 m, and 1 mm² give exactly 0.017 Ω. |
| Aluminum | about 2.65×10⁻⁸ Ω·m | The example at 2.8×10⁻⁸, 5 m, and 2 mm² gives 0.07 Ω. That is an order of magnitude, not a specific alloy. |
| Iron | about 9.7×10⁻⁸ Ω·m | Alloys differ from pure iron. The calculator uses the number in the ρ field. |
| Nichrome | about 1.1×10⁻⁶ Ω·m | The example at exactly 10⁻⁶ Ω·m, 3 m, and 1 mm² gives 3 Ω. |
How to use
- Enter resistivity ρ in Ω·m, for example 1.7e-8 for school copper. Table aluminum is closer to 2.65×10⁻⁸.
- Enter length l. With meters in the header, 1 means one meter, and you enter 10 cm as 0.1.
- Enter area S in m². 1 mm² is 1e-6, and 2.5 mm² is 0.0000025. Do not enter an AWG number in this field.
- Click Calculate, or wait for the live result. For 1.7e-8, 1, and 1e-6 the calculator shows 0.0170 Ω and the product ρ·l.
- Check the chart of R against l. An area of zero is rejected. Looking for R = U/I? Open the resistance from Ohm’s law calculator.
Symbol list
R is resistance, ρ is resistivity, l is length, and S is cross-sectional area. For 1.7×10⁻⁸ Ω·m, 1 m, and 10⁻⁶ m² the result is 0.017 Ω.
- R
- Resistance of the segment, in ohms. R = ρ·l/S. At the reference inputs the panel shows 0.0170 Ω.
- ρ
- Resistivity in Ω·m, field opor-drutu-a. It stays in ohm-meters even when the header shows feet.
- l
- Length of the current path, field opor-drutu-b. Meters or feet follow the header. It is not a loop until you enter the doubled length yourself.
- S
- Cross-sectional area, field opor-drutu-c. 1 mm² = 10⁻⁶ m². S ≤ 0 is rejected, because division by zero is undefined.
- ρ·l
- Intermediate product in Ω·m². Only division by S yields ohms. At the reference inputs it is 1.7×10⁻⁸ Ω·m².
Worked examples
Each button enters the ρ, l, and S from the description and refreshes the panel. The result line is what the panel shows with four decimal places.
Ten meters of the same conductor
The same copper and the same 1 mm², over 10 m. Resistance rises in proportion to length, so the result is ten times larger.
R = 0.1700 Ω
Aluminum order of magnitude
ρ = 2.8×10⁻⁸ Ω·m, 5 m, and an area of 2 mm². Table aluminum at 20 °C is closer to 2.65×10⁻⁸. This example is an order of magnitude, not a specific alloy.
R = 0.0700 Ω
One hundred meters of thin wire
School copper, 100 m, area 1 mm². One current path, not a go-and-return loop.
R = 1.7000 Ω
A higher resistivity
ρ = 1×10⁻⁷ Ω·m sits between copper and resistance alloys. A 2 m run with an area of 0.5 mm² (5×10⁻⁷ m²).
R = 0.4000 Ω
A short, thinner segment
School copper, 0.5 m, area 0.25 mm² (2.5×10⁻⁷ m²). The smaller S raises resistance even though the run is short.
R = 0.0340 Ω
Resistance-alloy order
ρ = 1×10⁻⁶ Ω·m, 3 m, area 1 mm². Nichrome is often near 1.1×10⁻⁶. Here the number is round, so the result is exactly 3 Ω.
R = 3.0000 Ω
50 m of 2.5 mm²
School copper, 50 m of one conductor at 2.5 mm². A supply loop out and back would be twice as long. You enter that length yourself.
R = 0.3400 Ω
A thicker 10 mm² section
School copper, 1 m, area 10 mm² (10⁻⁵ m²). The larger S lowers the resistance to 0.0017 Ω.
R = 0.0017 Ω
A very thin wire
School copper, 2 m, area 0.1 mm² (10⁻⁷ m²). The small S gives the same order as 50 m of 2.5 mm², which is 0.34 Ω.
R = 0.3400 Ω
Ways to use this calculator
- You estimate 1 m of school copper at 1 mm². At ρ = 1.7×10⁻⁸ Ω·m the result is 0.017 Ω.
- You compare 1 m and 10 m at the same ρ and S. Resistance grows by the same factor as the length.
- You convert mm² to m² before you enter S. 2.5 mm² is 2.5×10⁻⁶ m².
- The resistance from this page can be entered on the Joule-heating page, where resistance is already an input rather than the quotient ρ·l/S.
Frequently asked questions
What does this calculator compute, and from which formula?
The calculator computes the resistance of a uniform wire from R = ρ·l/S, called Pouillet’s law in European textbooks. You enter resistivity, length, and cross-sectional area. At ρ = 1.7×10⁻⁸ Ω·m, l = 1 m, and S = 10⁻⁶ m² the result is 0.017 Ω, and the panel shows 0.0170 Ω. The same formula is sometimes written R = ρL/A. Here L is l, and A is S.
Which units should I enter for ρ, l, and S?
Resistivity in ohm-meters (Ω·m), length in meters or feet according to the header, and area in square meters or square feet. The result is in ohms. Enter 1 mm² as 1e-6 m², not as 1. A comma and a period are the same separator. The currency switch does not change the formula.
How do I enter a number in scientific notation?
The entry 1.7e-8 means 1.7×10⁻⁸. That is easier than a string of zeros. The field also accepts 0.000000017. All three fields need a number before a result appears. Placeholder text is not an entered value.
What happens when S is zero, and when ρ or l is zero?
An area S of zero or below is rejected, because division by zero is undefined. Zero resistivity or zero length gives R = 0: no material, or no path. Negative ρ or negative l is accepted as a number, and the quotient can be negative. A physical wire has positive ρ, l, and S.
Does the calculator find area from diameter, from mm², or from an AWG number?
No. You enter a finished area S. The circle formula S = πd²/4 is work you do first. 1 mm² is exactly 10⁻⁶ m². An AWG number is not recognized. The calculator does not convert a gauge into square meters.
Do temperature, alternating current, and skin effect enter the result?
No. The model is for direct current, a uniform cross-section, and the ρ you enter. The correction R = R₀(1 + α·ΔT) is not computed. For copper, α is on the order of 0.0039 per kelvin. Skin effect at high frequency is also outside this quotient.
How is this page different from the R = U/I calculator?
That page uses voltage and current, and resistance is their quotient. Here the inputs are material and geometry: ρ, l, and S. The result unit is the same ohm, but the fields are different. Ohm’s law with any one quantity missing is on yet another page.
Why does half the diameter not merely double the resistance?
The area of a circle depends on the square of the diameter. Half the diameter gives one quarter of the area, so R becomes four times larger when ρ and l stay the same. Half the area, already entered as S, doubles R. The calculator sees S, not a diameter.
Does the header unit switch change ρ?
No. ρ stays in Ω·m. The switch converts length (m or ft) and area (m² or ft²). After the header changes, l and S already entered are converted so that the resistance in ohms stays the same. When the entered length is zero, the chart uses a 1 m scale and the result R stays zero.
What does the chart show, and does it describe wiring or a loop?
The chart draws resistance at several lengths for the ρ and S in the fields, from one quarter of the entered length to twice that length. It illustrates that R is proportional to l. It is not an ohmmeter trace and not a breaker model. The calculator does not double a loop. If current goes out and back, you enter the longer path yourself.
How do I calculate wire resistance with R = ρ·l/S?
Multiply resistivity by length and divide by cross-sectional area. For 1.7×10⁻⁸ Ω·m, 1 m, and 10⁻⁶ m²: R = 0.017 Ω.
What is R for 1 m of copper with a 1 mm² cross section?
About 0.017 Ω at ρ = 1.7×10⁻⁸ Ω·m and S = 10⁻⁶ m². At 10 m the result would be ten times larger.
How do I convert 1 mm² into m² before the formula?
1 mm² = 10⁻⁶ m². Area S must be in square meters, or the result will be off by many orders of magnitude.
Does the calculator include conductor temperature?
No. You enter ρ as a constant. The correction R(T) = R₂₀·(1+α·ΔT) is not part of this page.
How is R = ρ·l/S different from R = U/I?
Here resistance comes from material and geometry. R = U/I is Ohm’s law from measured voltage and current. This form has no U or I fields.
Sources
The definition, the textbook name, and the orders of ρ come from physics and metrology sources. The calculator does not cite invented DOIs.
- Wikipedia — electrical resistivity and conductivity
- BIPM — The International System of Units (SI), 9th edition
- NIST SP 330 — The International System of Units
- Halliday, D.; Resnick, R.; Walker, J., Fundamentals of Physics — current and resistance.
- Young, H. D.; Freedman, R. A., University Physics — current, resistance, and resistivity.
Page updated November 3, 2026.