How the calculation works
Let L be one-way length in feet, r the resistance of one conductor in Ω per 1,000 ft at 75 °C, I the total alarm load in amperes, Vₛ the voltage available at the circuit source, and Vₘᵢₙ the device minimum from its listing. Convert meters to feet using L(ft) = L(m) ÷ 0.3048.
- Loop resistance: Rₗₒₒₚ = 2 × L × r ÷ 1,000.
- Cable voltage drop: ΔV = I × Rₗₒₒₚ.
- Drop percentage: 100 × ΔV ÷ Vₛ.
- Voltage at the last device: Vₗₐₛₜ = Vₛ − ΔV.
- Pass for the entered minimum: Vₗₐₛₜ ≥ Vₘᵢₙ.
- Maximum one-way length: Lₘₐₓ = 1,000 × (Vₛ − Vₘᵢₙ) ÷ (2 × I × r), for I > 0 and Vₛ ≥ Vₘᵢₙ.
These equations apply Ohm's law (Fluke, “What is Ohm's Law?”) to the outgoing and return conductors. If the source is already below the device minimum, no length passes. At zero current there is no finite voltage-drop length limit in this model.
Optional distributed-load estimate
For N equal-current devices equally spaced at L/N, 2L/N, …, L, each segment carries the current of the devices downstream. Summing those segment drops gives:
ΔVdistributed = (2 × r × L / 1,000) × (I / N²) × (1 + 2 + … + N) = ΔVlumped × (N + 1) / (2N)
The maximum length is Lₘₐₓ from the lumped formula divided by (N + 1)/(2N). One device gives the lumped result; ten give 55% of the lumped drop. The factor approaches one-half as N increases, but simply halving the drop is inaccurate for a small device count.
This is our algebraic derivation from the segment-current method described in Potter's Advanced Fire Training Manual, section 7. The optional estimate assumes equal currents and equal spacing; use an actual segment-by-segment design for different spacing, mixed currents, or branches.
Worked example
For 14 AWG solid uncoated copper, a 300 ft one-way run, and 1.5 A total load, the calculated resistance at 75 °C is approximately 3.071293 Ω/1,000 ft. The loop resistance is 2 × 300 × 3.071293 ÷ 1,000 = 1.842776 Ω. Drop is 1.5 × 1.842776 = 2.764164 V.
At a 24 V source, the last device receives approximately 21.236 V, an 11.517% drop, which passes an entered 16 V minimum. Maximum one-way length is approximately 868.255 ft. At a 20.4 V battery-condition source, the same load leaves 17.636 V at the last device and limits length to approximately 477.540 ft.
For ten equal-current devices evenly spaced over that same 300 ft, the optional estimate gives 2.764164 × 11/20 = 1.520290 V drop. These are fictional calculation inputs, not an equipment specification or exam question.
Copper reference data at 75 °C
Calculated from NBS Handbook 100, Copper Wire Tables: ρ₂₀ = 1/58 Ω·mm²/m and α₂₀ = 0.00393/°C (appendix 5, printed p. 40); AWG geometry (§2.2, p. 6); stranded allowance (appendix 4, p. 38).
d(mm) = 0.127 × 92^((36 − AWG)/39); A = πd²/4; r₂₀ = ρ₂₀ × 304.8/A; r₇₅ = r₂₀ × [1 + 0.00393 × (75 − 20)].
Multiply by 1.02 for the handbook's concentric-lay stranded estimate. These calculated values use ideal annealed, uncoated copper; they are not a cable manufacturer's maximum resistance specification. Actual stranding, tolerances and construction can change resistance. Confirm against your cable's published data. The 75 °C assumption does not establish cable suitability.
| AWG | Solid | Stranded estimate |
|---|---|---|
| 18 | 7.7651 | 7.9204 |
| 16 | 4.8835 | 4.9812 |
| 14 | 3.0713 | 3.1327 |
| 12 | 1.9316 | 1.9702 |
| 10 | 1.2148 | 1.2391 |
Table values are rounded for display; calculations retain full precision. No NEC Chapter 9 table data is used.
Design assumptions and limits
The editable 20.4 V battery check is a common design assumption illustrated in Potter's section 7. Confirm it for your equipment and end-of-discharge condition. This tool subtracts cable loss only; enter the available NAC terminal voltage after any internal panel losses. A 24 V nominal source is not a worst-case supply guarantee.
The lumped result is conservative for placement of the entered fixed current on the stated radial run. It does not account for voltage-dependent current, inrush, synchronization modules, connection losses, power-supply regulation, return-fed Class A operation, or additional branches. Use the device's listed maximum current for the applicable settings and waveform.
Check against your project's specifications and the AHJ / your procedure. A pass means only that this simplified voltage estimate meets your entered minimum. Confirm circuit current limits, maximum device voltage, conductor suitability, equipment compatibility, manufacturer instructions and the required design method separately.
Published sources
- National Bureau of Standards (hosted by NIST). Copper Wire Tables, Handbook 100 (1966), §2.2 and appendices 4–5.
- Fluke. What is Ohm's Law? Relationship between current, resistance and voltage.
- Potter Electric Signal Company. Advanced Fire Training Manual, 8700055, Rev H (May 2017), section 7. Segment-current method and example battery-condition assumption; confirm current equipment instructions.