NEC 250.53 • Dwight's Formula • NEC Table 250.66

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

Average soil resistivity (ρ in Ohm-meters).
Full depth of electrode embedded below grade.
Electrode outside diameter (minimal effect on resistance).
Quantity and geometric spacing of driven electrodes.
Governs Grounding Electrode Conductor (GEC) per NEC Table 250.66.

Grounding Performance & Code Compliance

Single Rod Resistance
-- Ω
Dwight's formula result
System Earth Resistance
-- Ω
Combined parallel network
NEC 250.53 25-Ω Rule
--
Supplemental rod trigger
Required GEC Size
-- AWG
Copper (NEC 250.66 & 250.66(A))

Click Calculate Ground Resistance to evaluate earth resistance and determine GEC conductor sizing.

Dwight's Equation & Parallel Mutual Resistance Formulas

Dwight's Single Rod Formula: R = [ ρ / (2 π L) ] × [ ln(4L / r) - 1 ]
Two Parallel Rods at Spacing (s): R2 = [ ρ / (4 π L) ] × [ ln(4L / r) - 1 + (L / s) ]
NEC 250.53(A)(2) Rule: If R1 > 25 Ω ⇒ Supplemental 2nd Electrode Mandated at s ≥ 6.0 ft
NEC 250.66(A) Rod GEC Limit: GEC to rod electrode maximum required size is 6 AWG Copper

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.

  1. Convert Dimensions to SI Units: Length $L = 8.0\text{ ft} \times 0.3048 = 2.4384\text{ m}$. Radius $r = (0.625\text{ in} / 2) \times 0.0254 = 0.007938\text{ m}$.
  2. Calculate Single Rod Resistance via Dwight's Formula: $$R_1 = \frac{150}{2 \pi \times 2.4384} \times \left[ \ln\left(\frac{4 \times 2.4384}{0.007938}\right) - 1 \right] = 9.789 \times [\ln(1228.7) - 1]$$ $$R_1 = 9.789 \times (7.1137 - 1) = 9.789 \times 6.1137 = 59.85\,\Omega$$
  3. 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.
  4. 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.
  5. 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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