Ground Rod Resistance & GEC Sizer
Calculate vertical ground rod resistance to earth using Dwight's formula, evaluate NEC 250.53(A)(2) 25-Ohm rule supplemental electrode mandates, and size Grounding Electrode Conductors.
NEC 250.53 & Dwight's Law: Ground electrode resistance to earth depends on soil resistivity ($\rho$), driven length ($L$), and diameter ($d$) per Dwight's formula $R = \frac{\rho}{2 \pi L} [\ln(4L/r) - 1]$. Under NEC 250.53(A)(2), if a single rod does not achieve 25 Ohms or less, a supplemental electrode must be installed at least 6 feet apart. Under NEC 250.66(A), the copper Grounding Electrode Conductor to a rod electrode is never required to exceed 6 AWG copper.
Soil & Electrode Parameters
Grounding Performance & Code Compliance
Click Calculate Ground Resistance to evaluate earth resistance and determine GEC conductor sizing.
Dwight's Equation & Parallel Mutual Resistance Formulas
NEC Table 250.66 Grounding Electrode Conductor Sizing for AC Systems
Governing copper and aluminum GEC sizes based on the largest ungrounded service-entrance conductor.
| Service Conductor Size (Copper) | Equivalent Service Size (Aluminum) | Minimum GEC (Copper) | Minimum GEC (Aluminum) | Max to Rod Electrode (NEC 250.66(A)) |
|---|---|---|---|---|
| 2 AWG or smaller | 1/0 AWG or smaller | 8 AWG | 6 AWG | 8 AWG Copper |
| 1 AWG or 1/0 AWG | 2/0 AWG or 3/0 AWG | 6 AWG | 4 AWG | 6 AWG Copper |
| 2/0 AWG or 3/0 AWG | 4/0 AWG or 250 kcmil | 4 AWG | 2 AWG | 6 AWG Copper (Capped) |
| Over 3/0 through 350 kcmil | Over 250 through 500 kcmil | 2 AWG | 1/0 AWG | 6 AWG Copper (Capped) |
| Over 350 through 600 kcmil | Over 500 through 900 kcmil | 1/0 AWG | 3/0 AWG | 6 AWG Copper (Capped) |
| Over 600 through 1100 kcmil | Over 900 through 1750 kcmil | 2/0 AWG | 4/0 AWG | 6 AWG Copper (Capped) |
Step-by-Step Worked Engineering Example
200-Ampere Residential Service in Sandy Loam Soil
Installation Context: A 200A single-phase 120/240V residential service is installed using 2/0 AWG copper service entrance conductors. The property sits on sandy loam subsoil with an average resistivity of ρ = 150 Ω·m. The electrician drives an 8.0-foot, 5/8-inch diameter copper-clad steel ground rod.
- Convert Dimensions to SI Units: Length $L = 8.0\text{ ft} \times 0.3048 = 2.4384\text{ m}$. Radius $r = (0.625\text{ in} / 2) \times 0.0254 = 0.007938\text{ m}$.
- Calculate Single Rod Resistance via Dwight's Formula: $$R_1 = \frac{150}{2 \pi \times 2.4384} \times \left[ \ln\left(\frac{4 \times 2.4384}{0.007938}\right) - 1 \right] = 9.789 \times [\ln(1228.7) - 1]$$ $$R_1 = 9.789 \times (7.1137 - 1) = 9.789 \times 6.1137 = 59.85\,\Omega$$
- Evaluate NEC 250.53(A)(2) 25-Ohm Rule: Since $59.85\,\Omega > 25.0\,\Omega$, a single ground rod fails the 25-Ohm threshold. The electrician is mandated to install a supplemental second electrode.
- Calculate Combined Resistance with 2nd Rod at 6-Foot Spacing: Using spacing $s = 6.0\text{ ft} = 1.8288\text{ m}$: $$R_2 = \frac{150}{4 \pi \times 2.4384} \times \left[ \ln(1228.7) - 1 + \left(\frac{2.4384}{1.8288}\right) \right] = 4.894 \times [6.1137 + 1.3333] = 36.45\,\Omega$$ Adding the supplemental rod reduces resistance by 39% to $36.5\,\Omega$. Per NEC 250.53(A)(2), the installation is now fully compliant without further testing.
- Size Grounding Electrode Conductor (GEC): For 2/0 AWG service entrance conductors, NEC Table 250.66 specifies a **4 AWG copper GEC** for general grounding (water pipe / building steel). However, per NEC 250.66(A), the portion connecting to the ground rods is **capped at 6 AWG copper**.
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