Resistivity Calculator results come from a measured resistance with length and area, from conductivity or % IACS, or from sheet resistance. Each one is matched to common materials.
Measure the resistance end to end, then enter the length and the cross-section of the same piece.
Temperature
Metals gain resistivity as they warm. The table values are for 20 °C and are adjusted to your temperature.
Resistivity Table of Common Materials
| Material | Ω·m at 20 °C | Yours Against It |
|---|---|---|
| Silver | 1.590 × 10⁻⁸ | +8.5% |
| Copper | 1.680 × 10⁻⁸ | +2.7% |
| Annealed Copper | 1.724 × 10⁻⁸ | +0.1% |
| Aluminum | 2.650 × 10⁻⁸ | -34.9% |
| Tungsten | 5.600 × 10⁻⁸ | -69.2% |
| Iron | 9.710 × 10⁻⁸ | -82.2% |
| Platinum | 1.060 × 10⁻⁷ | -83.7% |
| Lead | 2.200 × 10⁻⁷ | -92.2% |
| Manganin | 4.820 × 10⁻⁷ | -96.4% |
| Constantan | 4.900 × 10⁻⁷ | -96.5% |
| Mercury | 9.800 × 10⁻⁷ | -98.2% |
| Nichrome | 1.000 × 10⁻⁶ | -98.3% |
| Graphite | 3.00 × 10⁻⁵ to 6.00 × 10⁻⁴ | Below |
| Germanium | 0.00100 to 0.500 | Below |
| Silicon | 0.100 to 60.0 | Below |
| Glass | 1.00 × 10⁹ to 1.00 × 10¹³ | Below |
| Hard Rubber | 1.00 × 10¹³ to 1.00 × 10¹⁵ | Below |
Resistivity Calculator Formula
Resistivity is how strongly a material resists current, apart from the size of the piece. Its symbol is ρ and its SI unit is the ohm-meter, Ω·m. Older texts call it specific resistance, and for insulators it is called volume resistivity. To calculate resistivity, multiply the resistance by the cross-section area and divide by the length.
A 100 m length of 2.5 mm² wire that measures 0.69 Ω is the default example. The Resistivity Calculator returns 1.72 × 10⁻⁸ Ω·m and reads it as annealed copper, 0.1% above the table value. This is the way to convert a resistance to a resistivity.
Resistance is not equal to resistivity. Resistance belongs to one object and changes with its length and thickness. Resistivity belongs to the material. A copper wire twice as long has twice the resistance, and its resistivity is unchanged. A larger cross-section lowers the resistance and leaves the resistivity where it was.
Measuring Resistance, Length and Area
The resistance usually comes from Ohm's law, which is voltage divided by current. Pass a known current through the sample, read the voltage across it and divide. A sample that drops 0.69 V at 1 A has 0.69 Ω. For low resistances, take the voltage with a second pair of leads so the contact resistance is left out.
The cross-section can be entered as an area, a diameter or an AWG number, with a separate unit for the aught sizes 1/0 to 4/0. A 4/0 entry gives 107.2 mm². To calculate the resistivity of a wire by gauge, pick AWG Gauge Number. A 100 ft run of 12 AWG that measures 0.159 Ω gives 1.73 × 10⁻⁸ Ω·m, and the line under the result shows the area used, 3.309 mm². The AWG to mm² Calculator lists the area for every gauge.
The same formula turned around converts resistivity to resistance. Multiply the resistivity by the length and divide by the area. That is the job of the Wire Resistance Calculator, which starts from the material and returns the ohms.
Resistivity Units in Wire Tables
Published figures use several units for the same quantity. The first card in the Resistivity Calculator restates the result in the three most common ones. Copper at 20 °C is the usual reference, and its values are below.
| Unit | Annealed Copper | Where It Is Used |
|---|---|---|
| Ω·m | 1.724 × 10⁻⁸ | SI unit, physics texts |
| µΩ·cm | 1.724 | Metal data sheets, lab reports |
| Ω·mm²/m | 0.01724 | Metric wire tables |
| Ω·cmil/ft | 10.37 | US wire tables |
The Ω·mm²/m form is handy because it is the resistance in ohms of one meter of 1 mm² wire. The US form does the same for one foot of wire with an area of one circular mil. A result of 1 Ω·m equals 100 Ω·cm, so a figure in ohm-centimeters is always 100 times larger.
Conductivity to Resistivity Calculator Mode
Conductivity is 1 divided by resistivity, and resistivity is 1 divided by conductivity. Choosing Conductivity or % IACS turns the tool into a conductivity to resistivity calculator. It accepts S/m, MS/m, S/cm, mS/cm, µS/cm and percent IACS.
IACS is the International Annealed Copper Standard. The NIST copper wire tables give it as 58 m/Ω·mm² at 20 °C, which is 58 MS/m or 1.7241 × 10⁻⁸ Ω·m. That value is 100% IACS. As an IACS to resistivity calculator, the tool turns 61% IACS into 2.83 × 10⁻⁸ Ω·m and reads it as aluminum.
The second card works the other way for any result. The default example shows 57.97 MS/m and 99.95% IACS. A figure above 100% is possible, since silver and very pure copper conduct better than the 1913 standard.
Sheet Resistance to Resistivity
Thin films are measured as sheet resistance, in ohms per square. The PVEducation text defines sheet resistivity as the resistivity divided by the layer thickness. Multiplying back by the thickness gives the resistivity, which is the Sheet Resistance and Thickness mode.
A film that measures 0.5 mΩ/sq at 35 µm thick works out to 1.75 × 10⁻⁸ Ω·m, and the Resistivity Calculator matches it to annealed copper at +1.5%. A 100 nm film at 10 Ω/sq is 1.00 × 10⁻⁶ Ω·m. Sheet resistance is normally read with a four-point probe, which keeps contact resistance out of the result.
Resistivity Table and Temperature
The fourth card compares the result with a table of materials at 20 °C. The values come from the HyperPhysics resistivity table at Georgia State University, with annealed copper set to the IACS figure. A large gap from every material usually means a unit slip in the area or length.
| Material | Ω·m at 20 °C | Coefficient per °C |
|---|---|---|
| Silver | 1.59 × 10⁻⁸ | 0.0038 |
| Annealed copper | 1.724 × 10⁻⁸ | 0.00393 |
| Aluminum | 2.65 × 10⁻⁸ | 0.00429 |
| Tungsten | 5.6 × 10⁻⁸ | 0.0045 |
| Iron | 9.71 × 10⁻⁸ | 0.00651 |
| Nichrome | 1.00 × 10⁻⁶ | 0.0004 |
Metals gain resistivity as they warm. Over moderate ranges the change follows a straight line set by the temperature coefficient α. The Temperature section takes the temperature at the time of measurement and the one to convert to.
The default copper result of 1.72 × 10⁻⁸ Ω·m becomes 2.098 × 10⁻⁸ Ω·m at 75 °C, a rise of 21.6%. It also works in reverse. Copper measured at 40 °C reads 1.86 × 10⁻⁸ Ω·m, and converting to 20 °C brings it back to 1.724 × 10⁻⁸ Ω·m. The warm figure is the one that matters for a loaded conductor in the Voltage Drop Calculator.
Water, Soil and Volume Resistivity
How is water resistivity calculated?
Water meters read conductivity, usually in µS/cm. Enter that reading in the conductivity mode and the result is the resistivity. Pure water at 25 °C has a conductivity of 0.055 µS/cm, which Veolia gives as the theoretical limit of 18.2 MΩ·cm.
As a water resistivity calculator, the tool returns 1.82 × 10⁵ Ω·m for that reading, and the first card shows 18.18 MΩ·cm. Tap water near 500 µS/cm comes out at 20.0 Ω·m, or 2.000 kΩ·cm.
For these units the fourth card reads Liquid Reading, Not in Table, since the resistivity of water depends on what is dissolved in it. It compares the reading with the pure water limit of 18.18 MΩ·cm, and this tap water shows 9,091× Lower. The second card restates the reading as 0.5000 mS/cm, 0.05000 S/m and 50.00 mS/m. The temperature conversion is for metals and is not applied to water.
How is soil resistivity measured?
In the field it is measured with four pins in a line, the Wenner method. The resistivity is 2π times the pin spacing times the meter reading. A report held by the US Defense Technical Information Center gives the same rule as 191.5 times the spacing in feet times the ohms, for an answer in Ω·cm.
The tool is not a field soil resistivity calculator, because the Wenner formula is not built in. A soil box sample is different. It is a block of soil with a known cross-section and pin spacing, so the Resistance, Length and Area mode gives its resistivity directly.
How do you calculate the volume resistivity of a material?
Volume resistivity is the same quantity, named to separate it from surface resistivity on insulators. Measure the resistance through the thickness of a flat sample between two electrodes. Multiply by the electrode area and divide by the thickness.
In the Resistivity Calculator, enter the thickness as the length and the electrode area as the cross-section. A 2 mm sheet that measures 1 GΩ across a 10 cm² electrode comes out at 5.00 × 10⁸ Ω·m, which is past every metal in the table.