Dwight's Equation Anode Resistance Calculator
This calculator estimates the resistance to earth, in ohm, of one vertical cylindrical anode buried in uniform soil, using the Dwight's equation. Enter the soil resistivity, the anode length and the anode radius; the result updates as you type.
The formula is written with the radius r, not the diameter. Because the diameter is d = 2r, the term ln(4L/r) is exactly the same as ln(8L/d), so both common forms of the equation give the same answer as long as you enter the radius here.
Anode resistance to earth
R = ρ / (2π × L) × (ln(4 × L / r) − 1)
R = 100 / (2π × 3) × (ln(4 × 3 / 0.01) − 1) = 32.31 ohm
How to use the calculator
- Find the soil resistivity ρ in ohm-m. A site measurement is best; the table below gives representative values when you have none. If you have Wenner four-pin readings, convert them first with ρ = 2 × π × a × R.
- Enter the anode length L in meters (0.1 to 1000 m).
- Enter the anode radius r in meters (0.001 to 10 m). If you know the diameter, divide it by 2.
- Read the resistance to earth R in ohm, shown to 4 significant figures. It recomputes on every change.
- If a message appears under a field, correct that value. The length must be at least 4 times the radius on this page.
Representative soil resistivity (ohm-m)
| Soil type | Resistivity |
|---|---|
| Clay, saturated silt | 100 |
| Sandy or silty clay | 250 |
| Clayey sand or saturated sand | 500 |
| Sand | 1500 |
| Gravel | 5000 |
| Dry sand, rock | more than 5000 |
Source: FHWA Traffic Detector Handbook, Third Edition, Volume II (FHWA-HRT-06-139, October 2006), Appendix N, Table N-1.
The source says these values are left purposely vague because environmental effects, such as moisture and temperature, can change soil resistivity drastically. Measure the resistivity of your site when you can.
Worked case
Take a 20 mm diameter, 3 m long electrode in 100 ohm-m soil, the inputs of Example 1 in the same appendix. The radius is r = 0.01 m and the length is L = 3 m.
R = 100 / (2π × 3) × (ln(4 × 3 / 0.01) − 1) = 5.305 × 6.090 = 32.31 ohm
For the same electrode in wet soil with ρ = 50 ohm-m the result is 16.15 ohm, and in dry soil with ρ = 300 ohm-m it is 96.93 ohm. These results are computed with the formula above; because R is proportional to ρ, halving or tripling the resistivity halves or triples the resistance.
Frequently asked questions
What is the Dwight's equation used for?
It is an analytical approximation of the resistance to earth of a single vertical cylindrical anode in uniform soil. This calculator applies it to one anode from its length, its radius and the soil resistivity.
Why must the length be at least 4 times the radius?
This is a limit of this page, not of the published formula. The calculator accepts only anodes whose length L is at least 4 times the radius r and shows an error below that.
Should I enter the radius or the diameter?
Enter the radius. If you know the diameter d, use r = d/2. For example, a 20 mm diameter anode has r = 0.01 m.
Can I use Wenner four-pin results?
Yes, but convert them first: rho = 2 × π × a × R, where a is the pin spacing in meters, R is the measured resistance in ohm and rho is the soil resistivity in ohm-m. Then enter rho.
Disclaimer
This result is a preliminary estimate only and is not a substitute for a qualified engineer. It applies to one vertical cylinder in uniform soil. The soil table is representative and is not a measurement of your site.