Duct Bank Heat Rise Calculator | Neher-McGrath / IEC 60287

Calculate

Overview

The Duct Bank Heat Rise Calculator applies the Neher-McGrath / IEC 60287-2-1 equivalent-cylinder method to compute the steady-state temperature at the boundary between a buried concrete-encased duct bank and the surrounding soil. This interface temperature is the critical thermal reference point used in underground cable ampacity engineering: if it exceeds the soil's dryout threshold (typically 50–60 °C), moisture migrates away from the bank, effective soil resistivity rises, and ampacity degrades in service.

The calculator supports two complementary modes. Heat Rise mode starts from known cable losses and computes the resulting interface temperature — useful for checking an existing or proposed installation against a site thermal limit. Maximum Losses mode solves the inverse problem: given a temperature limit, what is the maximum allowable total loss per unit length? With the From Circuits input option, Maximum Losses mode also back-calculates the maximum permissible current per conductor, giving a quick ampacity screening figure.

This tool is intended for preliminary engineering screening and conceptual design, not as a substitute for a full Neher-McGrath ampacity study or the methods required by NEC Article 310.60. Bank geometry must have an aspect ratio ≤ 3:1, and cover depth must keep the equivalent cylinder below the ground surface (u > 1). Soft-check warnings flag conditions where the method's accuracy degrades or where site conditions warrant closer attention.

How to Use This Calculator

  1. Select Calculation Mode: Heat Rise to find interface temperature given losses; Maximum Losses to find the allowable losses given a temperature limit.

  2. Select Losses Input: Direct Total Losses if you know the total W/ft or W/m; From Circuits if you prefer to enter current and resistance.

  3. Select Geometry Units (in, ft, mm, m) and enter Bank Width, Bank Height, and Depth to Top of bank.

  4. Enter Soil Thermal Resistivity (°C·cm/W) and Ambient Soil Temperature (°C). Use 90 °C·cm/W if no site data is available.

  5. Enter losses (Heat Rise mode) or temperature limit (Maximum Losses mode) and click Calculate.

All temperatures are in °C. The calculator uses the Neher-McGrath / IEC 60287-2-1 equivalent-cylinder method for a 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 ((geom unit))
  • •Bank Height ((geom unit))
  • •Depth to Top of Bank ((geom unit))
  • •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 ((losses unit))
  • •Number of Circuits (Nc)
  • •Loaded Conductors per Circuit (k) — Options: 1 — single-phase or DC, 2 — single-phase + neutral, 3 — three-phase
  • •Current per Loaded Conductor (I) (A)
  • •AC Resistance Unit — Options: Ω/1000 ft, Ω/km
  • •Conductor AC Resistance (Rac) ((rac unit))
  • •Interface Temperature Limit (°C)

Outputs

    Formula

    Neher-McGrath / IEC 60287-2-1 Equivalent-Cylinder Method

    The buried duct bank is represented as a solid cylinder of equivalent cross-sectional area:

    $$\ln r_b = \frac{1}{2} \cdot \frac{x}{y} \cdot \left(\frac{4}{\pi} - \frac{x}{y}\right) \cdot \ln\left(1 + \frac{y^2}{x^2}\right) + \ln\frac{x}{2}$$

    where x = min(width, height), y = max(width, height), and rb is the equivalent radius in metres.

    Depth to centre of the equivalent cylinder:

    $$L = d_{top} + \frac{h}{2}$$

    where d_top is the cover depth and h is the bank height. The dimensionless depth ratio:

    $$u = \frac{L}{r_b} \quad (\text{must be} > 1)$$

    Neher-McGrath geometric factor:

    $$G = \ln\left(u + \sqrt{u^2 - 1}\right)$$

    Soil thermal resistance per unit length:

    $$R_{th} = \frac{\rho_e}{2\pi} \cdot G \quad [°C·m/W]$$

    where ρe is the soil thermal resistivity in °C·m/W (= °C·cm/W ÷ 100).

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

    $$\Delta T = W \cdot R_{th}$$ $$T_{interface} = T_{soil} + \Delta T$$

    Maximum Losses mode — given interface temperature limit T_limit:

    $$W_{max} = \frac{T_{limit} - T_{soil}}{R_{th}} \quad [W/m]$$

    When circuit parameters are provided, maximum current per conductor:

    $$I_{max} = \sqrt{\frac{W_{max}}{N_c \cdot k \cdot R_{ac}}} \quad [A]$$

    What is Duct Bank Heat Rise

    A duct bank is a bundle of electrical conduits — usually PVC or rigid steel — encased in concrete and buried below grade. It routes medium-voltage or high-voltage power cables from substations to buildings, between vaults, or along utility corridors. The concrete encasement provides mechanical protection and chemical stability, but it also impedes the natural escape of heat generated by current-carrying conductors inside the conduits.

    The cables themselves produce losses proportional to I²Rac. These losses must flow outward through the concrete and conduit walls, across the bank-to-soil interface, and finally through the surrounding earth to the ambient environment. The soil temperature at the bank boundary — the interface temperature — rises above ambient by an amount proportional to the total losses and the soil thermal resistance. If the interface temperature exceeds about 50–60 °C, moisture migrates away from the hot surface, soil resistivity increases sharply, and the thermal resistance grows further in a positive-feedback spiral that can lead to thermal runaway. Controlling the interface temperature is therefore the central objective of duct bank thermal design.

    Neher-McGrath Equivalent-Cylinder Method

    The Neher-McGrath method, published in the AIEE in 1957 and standardised in IEC 60287-2-1:2023, models the buried duct bank as a solid cylinder of equivalent cross-sectional area. The equivalent radius rb is computed from a logarithmic formula involving the bank's aspect ratio, ensuring that the cylinder's cross-sectional area equals the original rectangular cross-section for any aspect ratio up to 3:1. A depth parameter u = L/rb (where L is the depth to the centre of the cylinder) must exceed 1 — a geometric requirement ensuring the equivalent cylinder does not break the ground surface.

    With rb and L established, the Neher-McGrath geometric factor G = ln(u + √(u² − 1)) and the soil thermal resistance per unit length Rth = ρe·G / (2π) follow directly. The soil thermal resistivity ρe (°C·cm/W) is the single most important soil parameter; typical values range from 50 °C·cm/W for moist clay to 250 °C·cm/W for dry sand. The IEC standard recommends 90 °C·cm/W as a conservative default when no site measurement is available.

    Heat Rise Mode vs Maximum Losses Mode

    The calculator provides two complementary views of the same thermal model.

    Heat Rise mode takes total losses as input and computes the interface temperature. This is the forward problem: you know the load and want to verify that the resulting interface temperature stays within limits. The total losses can be entered directly (W/ft or W/m) for simplicity, or derived from circuit parameters — current, conductor AC resistance, number of circuits, and conductors per circuit — for a more detailed load model. An optional temperature limit enables a WITHIN / OVER LIMIT screen that quantifies the thermal margin or exceedance.

    Maximum Losses mode solves the inverse problem: given a temperature limit, what is the maximum total loss per unit length the bank can handle? This gives the thermal capacity in W/ft or W/m, which can then be cross-checked against actual cable losses. When From Circuits is selected, the calculator also back-calculates the maximum current per conductor from the circuit parameters — a convenient screening tool for preliminary ampacity checks. Note that this current is a thermal-budget figure based on the entered resistance; it is not a NEC-compliant ampacity and does not account for derating factors such as ambient temperature correction or conduit fill.

    Soil Thermal Resistivity

    Soil thermal resistivity (often written ρe or ρT, sometimes called rho) is measured in °C·cm/W or the equivalent SI unit °C·m/W (1 °C·m/W = 100 °C·cm/W). It quantifies how strongly the soil resists heat flow: a higher value means more temperature rise per watt. The quantity depends on soil type, mineral composition, density, moisture content, and temperature.

    Soil Condition Typical ρe (°C·cm/W)
    Saturated clay 40–60
    Moist loam or clay 60–100
    IEC / NEC default 90
    Sandy or silty soil 100–150
    Dry sand, gravel 150–250
    Dry or rocky soil 200–400

    Site measurements per ASTM D5334 (thermal needle probe) or IEEE 442 are strongly recommended for installations at high load density or where long-term reliability is critical. The soft checks in this calculator flag values below 50 °C·cm/W (suspiciously low) and above 250 °C·cm/W (very high — engineered thermal backfill may be warranted).

    Validity Limits and Soft Checks

    The equivalent-cylinder approximation degrades when the aspect ratio (height ÷ width, or vice versa) exceeds 3:1. The calculator rejects inputs with aspect ratio > 3:1 and warns when the ratio approaches the limit (> 2.5:1). Similarly, the bank dimensions must keep u > 1 — if the cover depth is too shallow relative to the bank size, the equivalent cylinder breaks the ground surface and the method is not valid.

    Six soft checks (S1–S6) are reported alongside every valid result:

    • S1 — Interface temperature in or above the soil dryout range (50–60 °C threshold)
    • S2 — Soil resistivity outside the plausible site-measurement range
    • S3 — Cover is shallow relative to bank size (u < 1.5; method accuracy degrades)
    • S4 — Aspect ratio is near the 3:1 limit
    • S5 — Thermal budget is very small (< 5 °C) in Maximum Losses mode
    • S6 — Computed maximum current exceeds 2000 A (requires a full ampacity study)

    Key Facts

    • The Neher-McGrath method was published in the AIEE Transactions in 1957 and remains the basis of NEC 310.60 ampacity tables for underground cables.
    • IEC 60287-2-1:2023 standardises the equivalent-cylinder approach for groups of cables in buried ducts.
    • Soil thermal resistivity is the single largest uncertainty in underground cable ampacity calculations — a 2× increase in ρe roughly halves the allowable load.
    • Concrete-encased duct banks have higher effective thermal resistance than direct-buried cables because concrete (ρ ≈ 60–100 °C·cm/W) and trapped air spaces impede heat flow.
    • IEEE Std 835 provides ampacity tables for cables in duct banks under standardised conditions; this calculator allows site-specific inputs.
    • Aspect ratio must be ≤ 3:1 for the equivalent-cylinder formula to maintain engineering accuracy.
    • The depth parameter u = L/rb must exceed 1.0 to keep the equivalent cylinder fully below the ground surface.
    • Engineered thermal backfill (ρe ≈ 50–70 °C·cm/W, compacted) is commonly used around high-load duct banks to reduce interface temperature rise.

    Applications

    • Verification of interface temperature for proposed duct bank installations before final cable sizing
    • Preliminary ampacity screening for medium-voltage (5–35 kV) or high-voltage distribution feeders in duct banks
    • Back-calculation of maximum allowable cable losses for a given soil and installation geometry
    • Sensitivity analysis: effect of soil resistivity, cover depth, or bank geometry on interface temperature
    • Input to comprehensive Neher-McGrath ampacity studies per NEC 310.60 and IEEE 835
    • Comparison of Direct Total Losses vs From Circuits input methods to validate loss estimates
    • Assessment of thermal margin for duct banks serving data centers, hospitals, or other critical facilities

    Example Calculation

    Example — Imperial (Heat Rise Mode, Direct Total Losses)

    Given:

    • Bank: 36 in wide × 24 in high, depth to top = 36 in
    • Soil resistivity ρe = 90 °C·cm/W, ambient soil temperature = 20 °C
    • Total losses = 15 W/ft, temperature limit = 50 °C

    Step 1 — Convert geometry to metres:

    • Width: 36 in × 0.0254 = 0.9144 m; Height: 24 in × 0.0254 = 0.6096 m
    • x = 0.6096 m, y = 0.9144 m; aspect = 0.9144/0.6096 = 1.50 (≤ 3:1 ✓)

    Step 2 — Equivalent radius:

    • ln(rb) = 0.5 × (0.6096/0.9144) × (4/π − 0.6096/0.9144) × ln(1 + (0.9144/0.6096)²) + ln(0.6096/2)
    • rb ≈ 0.336 m

    Step 3 — Depth to centre and u:

    • L = 0.9144 + 0.6096/2 = 1.219 m
    • u = 1.219/0.336 = 3.63 (> 1 ✓)

    Step 4 — Thermal resistance:

    • G = ln(3.63 + √(3.63² − 1)) = ln(3.63 + 3.49) = 1.963
    • ρe (SI) = 90/100 = 0.90 °C·m/W
    • Rth = 0.90 × 1.963 / (2π) = 0.281 °C·m/W (0.0857 °C·ft/W)

    Step 5 — Interface temperature:

    • 15 W/ft = 49.2 W/m
    • ΔT = 49.2 × 0.281 = 13.8 °C
    • T_interface = 20 + 13.8 = 33.8 °C

    Limit screen:

    • Budget = 50 − 20 = 30 °C; Margin = 50 − 33.8 = 16.2 °C (54% of budget)
    • WITHIN LIMIT — LARGE margin

    Standards & References

    • IEC 60287-2-1:2023 — Electric cables — Calculation of the current rating — Part 2-1: Thermal resistance calculations using the equivalent-cylinder method for groups of buried cables | https://www.iec.ch/
    • Neher & McGrath (AIEE 1957) — 'The Calculation of the Temperature Rise and Load Capability of Cable Systems', Transactions AIEE, Vol. 76, Part III, 1957
    • NEC Article 310.60 — Conductors rated 2001 V and over — ampacity tables and engineering supervision provisions for duct bank installations
    • IEEE Std 835-1994 — IEEE Standard Power Cable Ampacity Tables (includes duct bank configurations under standardised assumptions)
    • IEEE 442-2017 — IEEE Guide for Soil Thermal Resistivity Measurements (thermal needle probe method)
    • ASTM D5334 — Standard Test Method for Determination of Thermal Conductivity of Soil and Soft Rock by Thermal Needle Probe Procedure
    • El-Kady & Horrocks (IEEE PAS 1985) — Extended values of geometric factor of external thermal resistance of cables in duct banks

    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). Losses: W/ft (= 3.28084 W/m) or W/m. AC resistance: Ω/1000 ft (= 0.0032808 Ω/m) or Ω/km (= 0.001 Ω/m). Temperature: °C throughout.

    Limitations

    • Valid for steady-state, continuous load only (loss factor = 1.0). Cyclic or intermittent loading requires load-factor correction outside this calculator.
    • Aspect ratio must not exceed 3:1 (width-to-height or height-to-width); above this limit the equivalent-cylinder formula loses accuracy.
    • Cover must be sufficient to keep u > 1 (equivalent cylinder fully below ground surface). Very shallow banks may be infeasible.
    • Does not account for mutual heating from adjacent duct banks or buried cables — only a single isolated bank is modelled.
    • Does not compute conductor temperature, conduit temperature, or ampacity. For ampacity, use NEC 310.60 or a full Neher-McGrath study.
    • Does not model transient thermal behaviour, soil freeze-thaw cycles, or water table effects.
    • The interface temperature is the bank/earth boundary temperature. Temperatures inside the bank (in conduits and on conductors) are higher by additional thermal resistances not computed here.
    • Soil resistivity is assumed uniform and constant. Seasonal variation, moisture migration above the dryout threshold, and soil heterogeneity are not modelled.

    Common Mistakes to Avoid

    • Entering conductor diameter instead of bank (duct bank) width and height — the inputs describe the whole bank envelope, not individual conduits.
    • Using soil resistivity in °C·m/W instead of °C·cm/W — enter 90 (not 0.90) for a typical site. The calculator expects the °C·cm/W unit.
    • Using a resistivity from a different project or assuming a value without measurement — ρe is highly site-specific and dominates the result.
    • Treating the Maximum Losses output as an ampacity — it is a total-loss budget, not a NEC-compliant ampacity. Use NEC 310.60 for final sizing.
    • Ignoring soft checks, especially S1 (interface temperature in the dryout range) — this condition may invalidate the constant-ρe assumption.
    • Using Maximum Losses mode without entering the From Circuits parameters and expecting an I_max — I_max requires Nc, k, and Rac.

    Frequently Asked Questions

    What is the bank/earth interface temperature and why does it matter?
    The interface temperature is the soil temperature immediately at the outer surface of the duct bank. It is the reference point for cable ampacity engineering because soil thermal resistivity increases sharply if the temperature rises above the soil's moisture-loss threshold (typically 50–60 °C). Once moisture migrates away, the bank operates in drier, more resistive soil, the interface temperature rises further, and ampacity degrades. Keeping the interface temperature below the site-specific dryout threshold is the primary thermal design objective.
    How do I choose a soil thermal resistivity value?
    Site-specific measurement per ASTM D5334 or IEEE 442 is best practice for critical or high-load installations. When no measurement is available, IEC 60287-2-1 and NEC Table B.310.15(B)(2)(c) use 90 °C·cm/W as a conservative default for ordinary soil. Sandy or dry conditions may require 150–250 °C·cm/W. The soft check S2 in this calculator flags suspiciously low or high values.
    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 very flat or very tall banks. The method is valid up to a width-to-height (or height-to-width) ratio of 3:1. Beyond this limit the cylinder's thermal field no longer approximates the rectangular bank well, so the calculator rejects the input. If your bank exceeds 3:1, split it into sub-banks or use a finite-element thermal solver.
    Can I use this calculator for direct-buried cables?
    No — the Neher-McGrath equivalent-cylinder method as implemented here is specific to rectangular duct banks. For direct-buried single cables or cable groups, IEC 60287-2-1 provides separate methods (the external thermal resistance formulas for single cables and groups) that account for mutual heating. Direct-buried ampacity tables in NEC 310.16 or IEEE 835 are the typical starting point for those configurations.
    Why is the Maximum Losses current (I_max) not a NEC ampacity?
    The I_max output is derived purely from the thermal budget of the bank/earth interface. It does not include conductor insulation temperature limits, conduit fill derating, ambient temperature correction, or any other NEC adjustment factors. NEC Article 310.60 ampacity (or a full Neher-McGrath study) accounts for all these layers of thermal resistance from conductor to ambient. Use I_max only as a rough screening figure; size conductors per NEC 310.60.

    Frequently Used Together

    Engineers often use these calculators in combination for complete project workflows:

    Wire Size Ampacity Nec Calculator

    Conduit Fill Calculator Nec

    Fault Current Calculator

    Related Calculators

    Explore similar calculators that might be useful for your project:

    Electrical Load Calculator

    Feeder Tap Rule

    Breaker Size Calculator

    Fuse Size Calculator

    Emergency Lighting Duration Calculator

    Voltage Drop Calculator

    Pcb Trace Width Calculator

    Ev Charger Load Calculator

    Every Electrical Formula. One Free Sheet.

    NEC calcs, motor sizing & code coordination — one printable page.

    • Instantly check voltage drop, ampacity & motor current
    • Catch the 7 wiring errors that fail code inspections
    • 12 design checks to run before submitting drawings

    No spam. Unsubscribe any time.