Duct Bank Heat Rise Calculator — Bank/Earth Interface Temperature

Calculate

If you already know total bank losses per ft/m, use Direct Total. If you have current and resistance per conductor, use From Circuits.

Outside dimension of the concrete envelope.

Outside dimension of the concrete envelope.

Ground surface to the TOP of the concrete envelope (cover depth), not to the bank center — the tool adds half the height internally.

Moist soil typically 60–90; dry sand can exceed 150–300. RHO-90 is a common design reference, but enter project or site-measured data.

Undisturbed earth temperature at burial depth; 20 °C is the customary North American design value. Temperatures are in °C for thermal-method consistency.

Total heat per unit length of the entire bank — not per cable.

Site-specific bank/earth interface limit — not a conductor insulation rating (75/90/105 °C belong to a different calculation). Values around 50–60 °C are commonly used to manage soil dryout risk.

Overview

A duct bank is a group of conduits — commonly PVC, fiberglass, or rigid steel — encased in concrete and buried below grade to route power cables between substations, vaults, and buildings. The concrete encasement provides mechanical protection and chemical isolation, but it also creates a thermal shell that limits how quickly heat generated by current-carrying conductors can escape to the surrounding earth. The temperature at the outer surface of that concrete shell — the bank/earth interface temperature — is the primary thermal reference point in underground cable ampacity engineering.

The interface temperature rises above the ambient soil temperature in proportion to the total cable losses and the thermal resistance of the soil path. When it approaches the soil's critical temperature — typically 50–60 °C for mineral soils — moisture begins to migrate away from the heated surface. As the soil dries, its thermal resistivity rises sharply, the bank sheds heat less effectively, and the interface temperature climbs further. If unchecked, this positive-feedback process can reach thermal runaway. Keeping the interface temperature below the site-specific dryout limit is the central objective of duct bank thermal design.

This calculator implements the Neher-McGrath / IEC 60287-2-1 equivalent-cylinder method in two complementary modes. Heat Rise mode takes cable losses as input and computes the resulting interface temperature — useful for verifying that a proposed or existing installation stays within limits. Maximum Losses mode solves the inverse: given a temperature limit, what is the maximum total loss per unit length the bank can shed? With the From Circuits option, Maximum Losses mode also back-calculates the maximum current per conductor as a quick ampacity screening figure.

The method is applicable to rectangular concrete-encased duct banks with an aspect ratio (longer ÷ shorter dimension) up to 3:1 and a cover depth sufficient to keep the equivalent cylinder below the ground surface (dimensionless depth ratio u > 1). It assumes steady-state continuous loading, uniform soil of constant resistivity, and a single isolated bank. It does not compute conductor temperature or cable ampacity — use NEC Article 310.60 and a full Neher-McGrath study for final cable sizing.

What to Look at First

Interface temperature vs your site dryout limit. The first number to check is the computed interface temperature against the dryout threshold — typically 50–60 °C for mineral soils. A soft-check warning appears automatically when the interface temperature approaches this range. If it is exceeded, the constant-soil-resistivity assumption no longer holds and the result becomes non-conservative.

Thermal margin percentage. In Heat Rise mode with a limit entered, the result shows margin as a percentage of the thermal budget (T_limit − T_soil). A LARGE margin (> 50 %) indicates room for load growth or a more conservative soil assumption. A MINIMAL margin (< 15 %) means the bank is close to its thermal capacity at the entered conditions.

Depth to top, not to center. The most common input error is entering the depth to the center of the bank instead of the depth to the top of the concrete envelope. The calculator adds half the bank height internally — entering the center depth double-counts the half-height and produces an optimistic result.

Losses unit consistency. Check that the Losses Unit selector (W/ft or W/m) matches the source of your loss data. Mixing units by a factor of 3.28 causes proportional error in the interface temperature.

How to Use This Calculator

  1. Select Calculation Mode: Heat Rise to find the bank/earth interface temperature for a given cable loss; Maximum Losses to find the maximum allowable total loss for a given interface temperature limit.

  2. Select Losses Input Method: Direct Total Losses if you know the total bank losses in W/ft or W/m; From Circuits if you prefer to enter current, AC resistance per conductor, number of circuits, and conductors per circuit.

  3. Select Geometry Units (inches, feet, millimetres, or metres) and enter Bank Width, Bank Height, and Depth to Top of Bank. Depth to Top is the distance from the ground surface to the TOP of the concrete envelope — not to its center.

  4. Enter Soil Thermal Resistivity in °C·cm/W. RHO-90 (enter 90) is the IEC and NEC reference value for ordinary moist mineral soil. For sandy, dry, or site-measured soils, enter the measured or design value.

  5. Enter Ambient Soil Temperature in °C. The standard North American design value is 20 °C; adjust for project latitude and burial depth.

  6. In Heat Rise mode, enter the loss data and, optionally, an Interface Temperature Limit to enable the WITHIN/OVER LIMIT margin screen. In Maximum Losses mode, enter the Interface Temperature Limit (required) and, if using From Circuits, the circuit parameters.

  7. Click Calculate. Read the interface temperature and margin (Heat Rise mode) or the maximum allowable loss and I_max screening figure (Maximum Losses mode). Review any soft-check warnings.

  8. The Interface Temperature Limit entered here is the bank/earth soil dryout criterion — not a conductor insulation rating. Conductor insulation ratings (75, 90, or 105 °C) belong to a separate ampacity calculation per NEC Article 310.60 and are substantially higher than the soil dryout limit.

All temperatures are in °C. Method: Neher-McGrath / IEC 60287-2-1 equivalent-cylinder, steady-state, continuous load (loss factor = 1.0).

Inputs & Outputs

Inputs

•Calculation Mode : Options: Heat Rise — given losses, find interface temperature, Maximum Losses — given temp limit, find allowable losses
•Losses Input Method : Options: Direct Total Losses (W/ft or W/m), From Circuits (I, Rac, circuit count)
•Geometry Units : Options: inches (in), feet (ft), millimetres (mm), metres (m)
•Bank Width (per Geometry Units)
•Bank Height (per Geometry Units)
•Depth to Top of Bank (per Geometry Units)
•Soil Thermal Resistivity (°C·cm/W)
•Ambient Soil Temperature (°C)
•Losses / Output Unit : Options: W/ft (watts per foot), W/m (watts per metre)
•Total Losses (per Losses Unit)
•Number of Circuits (Nc)
•Loaded Conductors per Circuit : Options: 3 — three-phase, three loaded conductors, 2 — single-phase, two loaded conductors, 1 — single loaded conductor
•Current per Loaded Conductor (I) (A)
•AC Resistance Unit : Options: Ω/1000 ft, Ω/km
•Conductor AC Resistance (Rac) (per AC Resistance Unit)
•Interface Temperature Limit (°C)

Outputs

•Interface Temperature (°C)
•Temperature Rise ΔT (°C)
•Soil Thermal Resistance Rth (°C·ft/W / °C·m/W)
•Thermal Margin (Heat Rise mode, with limit) (°C)
•Maximum Allowable Losses (Maximum Losses mode) (W/ft / W/m)
•Interface Temperature at Maximum Load (°C)
•Maximum Current per Conductor I_max (From Circuits) (A)

Formula

Duct Bank Heat Rise Formula

The buried duct bank is modelled as a thermally equivalent buried cylinder. All geometry is converted to metres before calculation.

Equivalent radius rb (IEC 60287-2-1):

ln(rb) = (1/2) · (x/y) · (4/π − x/y) · ln(1 + y²/x²) + ln(x/2)

where x = min(width, height), y = max(width, height), all in metres.

Anchor check: square bank (x = y) → rb = 0.5497 · x; aspect 1:3 → rb = 0.7172 · x.

Depth to centre of the equivalent cylinder:

L = depth to top + bank height / 2

Dimensionless depth ratio (must be > 1):

u = L / rb

Neher-McGrath geometric factor:

G = ln(u + √(u² − 1))

Soil thermal resistance per unit length:

Rth = (ρe / 2π) · G     [°C·m/W],   ρe in °C·m/W (= °C·cm/W ÷ 100)
Rth_ft = Rth × 3.28084  [°C·ft/W]

Heat Rise mode — given total losses W (W/m):

ΔT = W_total · Rth
T_interface = T_soil + ΔT

From Circuits losses:

W_total = Nc · k · I² · Rac      (Nc circuits, k conductors per circuit, Rac in Ω/m)

Maximum Losses mode — given T_limit (°C):

W_max = (T_limit − T_soil) / Rth   [W/m, rounded down, 3 significant figures]
I_max = √( W_max_displayed / (Nc · k · Rac) )   [A, rounded down]

I_max is derived from W_max_displayed (the rounded-down value), not the exact W_max, ensuring the limit is not violated by display rounding.

What Is Duct Bank Heat Rise?

A duct bank is a system of conduits — commonly PVC, fiberglass, or rigid steel — encased in concrete and buried below grade to route power cables between substations, vaults, or building service entrances. The concrete encasement provides mechanical protection and chemical isolation for the cables, but it also creates a thermal insulating shell that limits how quickly heat can escape from the cables to the surrounding earth.

Cables inside the conduits generate heat through resistive losses proportional to I²Rac. This heat must conduct outward through the conduit walls, the concrete, and the surrounding soil before it dissipates into the undisturbed earth. The temperature at the outer surface of the concrete envelope — the bank/earth interface — rises above the ambient soil temperature by an amount determined by the total cable losses and the thermal resistance of the soil path.

The bank/earth interface temperature is the primary design reference in underground cable ampacity engineering. Soil behaves as a thermal insulator whose resistance depends strongly on moisture content: when the interface temperature exceeds approximately 50–60 °C, free moisture migrates away from the heated surface. As the soil dries, its thermal resistivity rises sharply — sometimes by a factor of three or more — reducing the bank's ability to shed heat. This sets up a positive-feedback loop that, in the worst case, leads to thermal runaway and cable failure.

Duct bank heat rise analysis using the Neher-McGrath / IEC 60287-2-1 equivalent-cylinder method provides a tractable closed-form solution for this problem. The method replaces the rectangular bank cross-section with a thermally equivalent buried cylinder, computes the soil thermal resistance from the cylinder geometry and the soil resistivity, and calculates the steady-state interface temperature for any given loss level — or, in reverse, the maximum loss level for a specified temperature limit.

Maximum Allowable Losses for a Temperature Limit

Maximum Losses mode solves the inverse of the standard heat-rise problem. Instead of asking "what is the interface temperature for these cable losses?", it asks "what is the maximum total loss the bank can shed without exceeding a specified interface temperature limit?"

The maximum allowable loss per unit length is computed directly from the thermal budget and the soil thermal resistance: W_max = (T_limit − T_soil) / Rth. The result is rounded down (floored) to three significant figures to ensure the limit is not violated by display rounding. The interface temperature at exactly W_max_displayed is then back-calculated and reported — it will be at or slightly below T_limit, confirming that the rounded-down value respects the limit.

When the From Circuits input method is selected, the calculator also back-calculates the maximum permissible current per conductor from W_max_displayed and the circuit parameters: I_max = √(W_max_displayed / (Nc · k · Rac)). This value is floored to one decimal place for conservatism. It is a loss-budget figure for the bank/earth interface only and is not a NEC-compliant ampacity — conductor insulation limits, conduit fill derating, and other adjustment factors required by NEC Article 310.60 are not included.

Soil Thermal Resistivity RHO

Soil thermal resistivity — written ρe, ρT, or simply "rho" in field practice — is measured in °C·cm/W (or equivalently °C·m/W, where 1 °C·m/W = 100 °C·cm/W). It quantifies how strongly the soil resists heat flow: a higher value means more interface temperature rise per watt of cable loss. Soil resistivity is the single largest source of uncertainty in underground cable thermal design.

Resistivity varies with soil type, mineral composition, compaction, and moisture content. Dry, coarse-grained soils (sands, gravels) can exceed 200–300 °C·cm/W; saturated clays can fall as low as 40–60 °C·cm/W. The most critical effect is the transition at the dryout threshold: a soil that is 90 °C·cm/W when moist may reach 250 °C·cm/W or more when dry. Because the equivalent-cylinder method assumes a constant, uniform resistivity, designs that allow the interface temperature to approach the dryout threshold must account for this degradation.

RHO-90 (90 °C·cm/W) is the conservative reference value used in IEC 60287-2-1 and reflected in NEC Table B.310.15(B)(2)(c). It represents a typical moist mineral soil and is the appropriate starting point when no site measurement is available. For installations at high load density or in soils known to be dry or sandy, site-specific measurement is strongly recommended. Engineered thermal backfill — specially graded, moisture-stable material — compacted around the duct bank can reduce the effective resistivity to 50–70 °C·cm/W and significantly increase thermal capacity.

Bank/Earth Interface Temperature vs Conductor Temperature

A common source of confusion in duct bank thermal design is the distinction between the bank/earth interface temperature and the conductor operating temperature. These two temperatures are separated by several layers of thermal resistance — conduit air gaps, conduit wall, concrete fill, and any other thermal barriers inside the bank — and can differ by tens of degrees under load.

The interface temperature computed by this calculator is the temperature at the outer surface of the concrete envelope where it contacts the surrounding soil. It is the relevant parameter for assessing soil dryout risk and for validating the constant-ρe assumption. A typical design limit for this temperature is 50–60 °C, chosen to keep soil moisture stable rather than from any cable rating consideration.

The conductor operating temperature, by contrast, is governed by the cable insulation rating — 75, 90, or 105 °C for common NEC conductor categories. Determining the conductor temperature requires adding the thermal resistance of all layers between the bank/earth interface and the conductor surface (conduit fill, conduit wall, concrete encasement) to the soil thermal resistance computed here. This additional analysis is required by NEC Article 310.60 and is outside the scope of this calculator. Entering a conductor insulation rating (75 °C, 90 °C) as the interface temperature limit in Maximum Losses mode will produce a result that is significantly non-conservative.

Soil Dryout and Duct Bank Thermal Stability

The most significant long-term failure mode in underground cable installations is not a sudden dielectric breakdown but a slow, cumulative dryout of the soil immediately surrounding the duct bank. As cable load increases, the interface temperature rises. When it crosses the soil's critical temperature — typically 50–60 °C for mineral soils — the vapor pressure of soil moisture exceeds atmospheric pressure and moisture begins to migrate outward, away from the heat source.

As moisture leaves, the soil resistivity around the bank increases. With higher resistivity, the same cable loss produces a higher interface temperature, which drives further moisture loss. If the load is not reduced, this positive-feedback process can continue until the soil around the bank is nearly completely dry, at which point the interface temperature may jump dramatically — a condition known as thermal runaway.

Thermal stability is maintained by keeping the interface temperature below the soil's dryout threshold for the assumed resistivity. This calculator flags results where the interface temperature approaches or exceeds 50 °C with a soft-check warning. When the design operating temperature is close to the dryout limit, engineered thermal backfill, a more conservative resistivity assumption, or a reduced load factor should be considered. A full thermal stability analysis (sometimes called a moisture migration analysis) may be required for critical or high-load installations.

Key Facts

  • The Neher-McGrath method, published in the AIEE Transactions in 1957, remains the mathematical foundation of NEC Article 310.60 ampacity calculations for cables in underground ducts.
  • IEC 60287-2-1:2023 standardizes the equivalent-cylinder approach for groups of cables in buried conduits, providing the rb formula implemented in this calculator.
  • Soil thermal resistivity is the single largest uncertainty in underground cable thermal design — a factor-of-two increase in ρe roughly halves the allowable cable current.
  • The bank/earth interface temperature limit of 50–60 °C is a soil dryout criterion, not a cable insulation temperature rating; conductor ratings of 75–105 °C apply to a separate layer of the thermal circuit.
  • Concrete encasement typically has a thermal resistivity of 50–100 °C·cm/W — similar to moist soil — but trapped air voids in conduit fill add significant thermal resistance inside the bank.
  • The equivalent-cylinder formula is accurate to within a few percent for aspect ratios up to 3:1; above this limit, finite-element thermal methods must be used.
  • Engineered thermal backfill — a carefully graded sand-cement mixture — can reduce the effective soil resistivity around a duct bank to 50–70 °C·cm/W, substantially increasing thermal capacity.
  • The I_max output in Maximum Losses mode is a loss-budget screening figure for the bank/earth interface — it is not a NEC 310.60 ampacity and does not include insulation thermal resistance, conduit fill derating, or other adjustment factors.

Applications

  • Preliminary thermal screening for proposed duct bank installations: confirming that the bank geometry and soil conditions can support the planned load before detailed cable sizing begins.
  • Back-calculation of maximum allowable cable losses for a given burial geometry and site soil conditions — the thermal capacity of the bank expressed in W/ft or W/m.
  • Sensitivity analysis: quantifying the effect of changes in soil resistivity, cover depth, bank dimensions, or ambient soil temperature on interface temperature and thermal margin.
  • Verification of engineered thermal backfill specifications — confirming that a specified ρe and geometry meet the interface temperature limit at the design load.
  • Design of electrical utility duct banks for medium-voltage (5–35 kV) feeder circuits, large service entrances, and campus distribution systems.
  • Input data preparation for comprehensive Neher-McGrath ampacity studies per NEC 310.60, establishing the bank/earth interface temperature as the boundary condition for the full thermal circuit.

Example Calculation

Example 1 — Interface Temperature of a Loaded Bank

Given: Bank 24 × 36 in (610 × 914 mm), depth to top of bank 30 in (762 mm), soil RHO-90 (ρe = 90 °C·cm/W), ambient soil temperature 20 °C, total losses 12.19 W/ft (40 W/m), interface temperature limit 45 °C.

Step 1 — Identify x and y:

  • Width = 36 in = 0.9144 m; Height = 24 in = 0.6096 m
  • x = min(0.6096, 0.9144) = 0.6096 m; y = max = 0.9144 m; aspect = 1.50 ≤ 3:1 ✓

Step 2 — Equivalent radius:

  • ln(rb) = ½ × (0.6096/0.9144) × (4/π − 0.6096/0.9144) × ln(1 + (0.9144/0.6096)²) + ln(0.6096/2)
  • ln(rb) = 0.5 × 0.667 × (1.273 − 0.667) × ln(3.25) + ln(0.3048) = −0.950
  • rb = exp(−0.950) = 0.387 m (15.2 in)

Step 3 — Depth to centre and u:

  • L = 0.762 + 0.9144/2 = 0.762 + 0.457 = 1.219 m
  • u = 1.219/0.387 = 3.15 > 1 ✓

Step 4 — Geometric factor and thermal resistance:

  • G = ln(3.15 + √(3.15² − 1)) = ln(3.15 + 2.988) = 1.815
  • ρe (SI) = 90/100 = 0.90 °C·m/W
  • Rth = (0.90/2π) × 1.815 = 0.260 °C·m/W (0.853 °C·ft/W)

Step 5 — Interface temperature:

  • W = 40 W/m (= 12.19 W/ft)
  • ΔT = 40 × 0.260 = 10.4 °C
  • T_interface = 20 + 10.4 = 30.4 °C

Limit screen:

  • Budget = 45 − 20 = 25 °C; Margin = 45 − 30.4 = 14.6 °C; 14.6/25 = 58.4% of budget
  • Result: WITHIN LIMIT — LARGE margin

Example 2 — Loss Budget for a 50 °C Limit

Given: Same bank geometry (24 × 36 in, 30 in cover, RHO-90, 20 °C ambient), interface temperature limit 50 °C. From Circuits: 6 circuits × 3 conductors per circuit, Rac = 0.10 Ω/km (0.0305 Ω/1000 ft) per conductor.

Thermal budget and W_max:

  • Budget = 50 − 20 = 30 °C; Rth = 0.260 °C·m/W (from Example 1)
  • W_max (exact) = 30/0.260 = 115.4 W/m
  • W_max (floored, 3 significant figures) = 115 W/m (35.1 W/ft)
  • T_interface at 115 W/m = 20 + 115 × 0.260 = 20 + 29.9 = 49.9 °C ≤ 50 °C ✓

Maximum current per conductor:

  • Rac = 0.10 Ω/km = 0.0001 Ω/m per conductor
  • I_max (exact) = √(115 / (6 × 3 × 0.0001)) = √(115/0.0018) = √63,889 = 252.76 A
  • I_max (floored to 1 decimal) = 252.7 A

Note: 252.7 A is a loss-budget figure based on the bank/earth interface thermal constraint — it is not an ampacity. NEC 310.60 requires accounting for additional thermal resistances inside the bank and applicable derating factors.

Units

  • Geometry units: inches (in), feet (ft), millimetres (mm), metres (m) — all converted internally to metres before calculation
  • Soil resistivity: °C·cm/W (= 100 × °C·m/W). Enter 90 for RHO-90, not 0.90.
  • Losses: W/ft (= 3.28084 W/m) or W/m — selectable; affects input, output display, and I_max derivation
  • AC resistance: Ω/1000 ft (= 0.0032808 Ω/m) or Ω/km (= 0.001 Ω/m) — per conductor, not per circuit loop
  • Temperature: °C throughout, including ambient soil, interface, and limit
  • Thermal resistance: °C·m/W (metric display) or °C·ft/W (imperial display, = °C·m/W × 3.28084)

Limitations

  • The model is a bank-level, steady-state screen. It carries a continuous load at loss factor 1.0 (conservative for cyclic loading) through uniform soil with constant properties; it does not model time-dependent soil dryout or thermal runaway, seasonal soil temperature variation, groundwater, thermal backfill boundaries, pavement or other surface cover, or adjacent heat sources such as steam lines and neighboring banks. There are no per-duct positions, no internal concrete gradient to the hottest conduit, no duct air films, and no conductor/insulation thermal circuit — hence no conductor temperature and no ampacity. The circuit-based loss entry covers conductor I²R only: dielectric losses, sheath and shield losses, and temperature-dependent resistance changes are not modeled. The equivalent-radius method assumes the bank region is thermally favorable relative to the surrounding soil and is published as valid for aspect ratios up to 3:1 with the bank fully below grade; the screen enforces both gates rather than extrapolating. Results are planning estimates that feed a full Neher-McGrath or IEC 60287 study — they do not replace one, and they do not replace measured soil thermal resistivity on critical installations.

Common Mistakes to Avoid

  • Entering depth to the center of the bank instead of depth to the top of the concrete envelope. The calculator adds half the bank height internally to compute the depth to the equivalent cylinder center.
  • Entering conductor diameter or conduit diameter instead of the bank envelope dimensions. Bank Width and Bank Height are the outside dimensions of the entire concrete encasement.
  • Using soil resistivity in °C·m/W rather than °C·cm/W. Enter 90 for a typical design soil (not 0.90). The calculator expects °C·cm/W throughout.
  • Assuming the IEC/NEC default of 90 °C·cm/W without checking site soil type. Sandy, gravelly, or dry soils may require 150–250 °C·cm/W.
  • Treating the Maximum Losses output W_max as a cable ampacity. It is a total heat budget for the bank as a whole, not a per-cable or per-conductor ampacity per NEC 310.60.
  • Using a conductor insulation temperature rating (75 °C, 90 °C, 105 °C) as the interface temperature limit. The interface limit is a soil dryout criterion — typically 50–60 °C — not a cable rating.
  • Failing to account for mutual heating when multiple duct banks run in parallel in the same trench. This calculator models only a single isolated bank.
  • Entering AC resistance at 20 °C (data-sheet DC resistance corrected for frequency) rather than at operating temperature. Rac increases with conductor temperature; use the cable manufacturer value at the expected operating point.
  • Ignoring soft-check warnings when the interface temperature approaches or exceeds 50 °C. The constant-resistivity assumption breaks down above the soil dryout threshold, and the result becomes non-conservative.
  • Expecting I_max from Maximum Losses mode to include NEC derating factors. I_max is derived from the soil thermal budget alone and does not include conduit fill, ambient temperature correction, or any other NEC adjustment.

Frequently Asked Questions

What is the bank/earth interface temperature and why does it matter?
The bank/earth interface temperature is the soil temperature immediately at the outer surface of the concrete duct bank envelope. It is the central thermal reference in underground cable design because soil thermal resistivity increases sharply when this temperature exceeds the soil's dryout threshold — typically 50–60 °C for mineral soils. Above this threshold, moisture migrates away from the heated zone, resistivity rises, and ampacity degrades in a positive-feedback loop. Keeping the interface temperature below the site-specific dryout limit is the primary objective of duct bank thermal design.
How do I choose an interface temperature limit?
The interface temperature limit is a site-specific soil dryout criterion, not a cable insulation rating. Common values are 50 °C (conservative, widely used in North America) and 60 °C (used when drier conditions are acceptable or when a thermal stability analysis has been performed). For critical installations or where native soil is sandy or silty, 50 °C with site-measured ρe data is best practice. Confirm the limit with the project's geotechnical or cable engineer.
How do I choose a soil thermal resistivity value?
Site-specific measurement per ASTM D5334 (thermal needle probe) or IEEE 442 is best practice for critical or high-load installations. When no measurement is available, RHO-90 (90 °C·cm/W) is the IEC 60287-2-1 reference value for ordinary moist mineral soil, also used in NEC Table B.310.15(B)(2)(c). Sandy, gravelly, or dry soils may require 150–250 °C·cm/W. Engineered thermal backfill can achieve 50–70 °C·cm/W when properly specified and compacted.
What is the aspect ratio limit and why does it exist?
The equivalent-cylinder formula is derived from a conformal-mapping approximation that becomes inaccurate for highly elongated cross-sections. IEC 60287-2-1 validates the method for aspect ratios (longer dimension ÷ shorter dimension) up to 3:1. Beyond this limit the cylinder's thermal field diverges from the rectangular bank geometry, and the calculator rejects the input. Banks with aspect ratios greater than 3:1 should be modelled with finite-element thermal software or split into sub-banks with independent calculations.
Why is the maximum current I_max not a NEC ampacity?
I_max is computed from the total loss budget of the bank/earth interface: it is the current at which cable losses exactly equal W_max_displayed, using only the entered conductor AC resistance. A NEC 310.60 ampacity adds multiple further thermal resistances — conduit air gap, conduit wall, concrete encasement — and applies correction factors for ambient temperature, conduit fill, and other derating conditions. I_max will therefore overestimate the NEC-compliant ampacity and must not be used for final conductor sizing.
Can I use this calculator for direct-buried cables (not in a duct bank)?
No. The equivalent-cylinder formula applies specifically to a rectangular concrete-encased duct bank acting as a unified thermal body. For single direct-buried cables or small cable groups, IEC 60287-2-1 provides separate external thermal resistance formulas. Direct-buried ampacity tables in NEC 310.16 and IEEE Std 835 are the standard starting point for those configurations. Mutual heating between closely spaced cables in a direct-buried group requires additional analysis.
What happens if the soil resistivity exceeds 250 °C·cm/W?
The calculator accepts values up to 400 °C·cm/W and will display a soft-check warning for values above 250 °C·cm/W, flagging that the soil is very resistive and that engineered thermal backfill may be warranted. At very high resistivity the interface temperature for moderate cable losses can be surprisingly high — check the result carefully against your site's dryout limit. Replacing the native soil around the bank with thermal backfill at 50–90 °C·cm/W can reduce the effective resistance significantly where the installation geometry allows.
What does the soft-check warning about interface temperature mean?
The soft-check warning is triggered when the computed interface temperature (or the entered limit in Maximum Losses mode) approaches or exceeds 50 °C. It indicates that the constant-resistivity assumption underlying the calculation may not hold: soil moisture migration above the dryout threshold progressively increases the effective resistivity and can lead to a cycle of rising temperature and rising resistance. The warning does not invalidate the calculation but signals that a full thermal stability analysis, engineered backfill, or a lower operating temperature target should be considered.

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Electrical Quick Reference — Keep It Open During Design

8 NEC formulas for voltage drop, ampacity, motor current, and CT burden. One sheet, every project.

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