Fire alarm voltage drop formula: the math behind NAC circuit calculations

The voltage drop formulas on this page and the amp-hour method from the battery guide, with a worked check for each, fit on one printable page (PDF), free, no email.

System Sensor's L-Series instructions connect wire resistance, connected load and appliance operating voltage. The worked examples below derive the arithmetic for fixed currents on a radial circuit. They use fictional equipment and cable values.

Establish resistance and source voltage

Let L be routed one-way length in feet and r be the resistance of one conductor in ohms per 1,000 ft:

Rloop = 2 × L × r ÷ 1,000

ΔV = I × Rloop

Vdevice = Vs − ΔV

Use NFPA 70 (2020), Chapter 9, Table 8 as the NEC resistance lookup reference for this study edition. Read its conductor construction, units, temperature basis and notes in your own copy. No resistance rows are reproduced here. The Alarm Ladder calculator uses a documented ideal-copper estimate at 75 °C, derived below. This is a useful engineering model for comparing lengths, loads and conductor sizes. Record whether the project calculation uses that estimate, NEC resistance data or the cable manufacturer's data, and keep the construction and temperature basis explicit.

If the supplied resistance already covers a conductor pair, do not double it. Likewise, do not enter a round-trip length as L and double it again.

Obtain Vs at the NAC output terminals for the supply condition being evaluated, including the specified battery condition and internal supply losses. Nominal battery voltage is not proof of available terminal voltage. The selected supply manual establishes that terminal-voltage basis; the battery guide's code navigation reference is NFPA 72 (2022), §10.6.7.

The calculator's copper resistance model

The calculator derives resistance from NBS Handbook 100, Copper Wire Tables, §2.2 and appendices 4–5, rather than copying an NEC resistance row. For AWG conductor diameter and cross-sectional area:

d(mm) = 0.127 × 92^((36 − AWG)/39)

A(mm²) = π × d² ÷ 4

With copper resistivity ρ20 = 1/58 Ω·mm²/m, one conductor's resistance per 1,000 ft is r20 = ρ20 × 304.8 ÷ A. Temperature correction is:

rT = r20 × [1 + 0.00393 × (T − 20)]

At the web tool's 75 °C assumption, the temperature multiplier is 1.21615. The stranded option multiplies the result by 1.02, the handbook's concentric-lay estimate. Cable construction and tolerances can differ from this model (the fire alarm cable types guide covers the common FPL, FPLR and FPLP constructions); the project calculation identifies its accepted resistance basis. Calculation temperature does not establish the cable's permitted operating temperature.

Use maximum appliance current at low voltage

Use each appliance's maximum listed current at the low end of its operating range, for the selected model, candela, audible setting and supply waveform. Strobe current rises as voltage falls in the SpectrAlert manufacturer example cited below. Using only its nominal 24 V current understates the low-voltage cable loss. System Sensor's SpectrAlert data sheet A05-0325 illustrates that voltage/current relationship, while the current instructions for the selected appliance supply its design inputs.

The fixed-current calculations below use those low-voltage maximum currents as upper bounds throughout the run. They do not assume that a strobe's actual current stays constant as voltage changes. Inrush, synchronization and supply loading remain separate equipment limits.

End-of-line load and lumped load

An end-of-line load places the actual load at the far end. The lumped-load method treats the sum of several appliance currents as if it were all at that far end. The equations are the same; the physical load arrangement differs. An end-of-line supervision resistor is not a substitute for the appliances' alarm current.

For a fixed total current on one radial run, the lumped model gives every segment the full current. This makes its cable loss at least as large as the corresponding distributed-load result. This comparison assumes the same fixed currents, cable and source; it does not cover arbitrary addressable notification or return-fed circuits.

Use these fictional inputs, with I representing the total maximum listed alarm current at the invented appliances' low-voltage limit: r = 4.2 Ω/1,000 ft per conductor, L = 300 ft, I = 0.600 A, Vs = 20.6 V and an invented appliance minimum of 16.4 V. The resistance is not an NEC value and is not assigned to an AWG size.

1. Out-and-back length: 2 × 300 = 600 ft.
2. Loop resistance: 600 × 4.2 ÷ 1,000 = 2.520 Ω.
3. Cable drop: 0.600 × 2.520 = 1.512 V.
4. Last-appliance voltage: 20.6 − 1.512 = 19.088 V.
5. Loss percentage: 100 × 1.512 ÷ 20.6 ≈ 7.340%.

The result exceeds the fictional minimum by 19.088 − 16.4 = 2.688 V. A percentage alone does not establish compliance with an appliance listing.

Maximum one-way length and meter conversion

For a positive fixed design current, rearrange the lumped equation to solve for the one-way length that reaches the appliance minimum:

Lmax(ft) = 1,000 × (Vs − Vmin) ÷ (2 × I × r)

The fictional example gives Lmax = 1,000 × (20.6 − 16.4) ÷ (2 × 0.600 × 4.2) = 833.333… ft. This is the cable-loss limit of the stated model, not an equipment-approved circuit length.

When resistance is in ohms per 1,000 ft, convert a routed distance in meters using L(ft) = L(m) ÷ 0.3048. Thus 91.44 m ÷ 0.3048 = 300 ft. Convert the length result back with Lmax(m) = Lmax(ft) × 0.3048: 833.333… × 0.3048 = 254 m.

A source below the appliance minimum leaves no feasible length. At zero current the model produces no cable drop and no finite cable-loss length limit; an actual alarm load is still required for a useful design estimate.

Point-to-point (segment current) method vs lumped load

For point-to-point calculation, each cable segment carries the sum of the downstream appliance currents. Calculate each segment's out-and-back resistance, multiply by its downstream current, then accumulate losses from the source to each appliance.

Distribute the fictional 0.600 A as follows: maximum listed low-voltage currents of 0.100 A at 80 ft, 0.200 A at 200 ft, and 0.300 A at 300 ft. Each invented current bounds that appliance's draw over the operating window. Distances are measured along the same radial route from the source.

• Segment 1, 80 ft one way: R = 2 × 80 × 4.2 ÷ 1,000 = 0.672 Ω; current 0.100 + 0.200 + 0.300 = 0.600 A; drop 0.600 × 0.672 = 0.4032 V.
• Segment 2, 120 ft one way: R = 2 × 120 × 4.2 ÷ 1,000 = 1.008 Ω; current 0.200 + 0.300 = 0.500 A; drop 0.500 × 1.008 = 0.5040 V.
• Segment 3, 100 ft one way: R = 2 × 100 × 4.2 ÷ 1,000 = 0.840 Ω; current 0.300 A; drop 0.300 × 0.840 = 0.2520 V.

Voltages are 20.6 − 0.4032 = 20.1968 V at the first appliance, 20.1968 − 0.5040 = 19.6928 V at the second, and 19.6928 − 0.2520 = 19.4408 V at the third. The final loss is 0.4032 + 0.5040 + 0.2520 = 1.1592 V, compared with the lumped result of 1.512 V.

For N equal-current appliances at equal intervals, starting one interval from the source, summing those segment currents gives ΔVdistributed = ΔVlumped × (N + 1) ÷ (2N). With three equal loads at 100, 200 and 300 ft, each rated for a maximum 0.200 A at the low-voltage limit, the drop is 1.512 × 4 ÷ 6 = 1.008 V. This shortcut does not apply to the unequal example above.

Use the listed appliance window

The fictional 16.4 V minimum above teaches comparison only. A real minimum comes from the exact appliance, setting, waveform and compatible supply arrangement.

As a manufacturer example, System Sensor's L-Series wall-appliance instructions I56-5845-002 specify a 16–33 VDC operating window for the applicable 24 V nominal DC configuration. The same instructions specify 16.5–33 V with the MDL3 synchronization module. The actual combination establishes the window; 16 V is not a universal minimum. Both the maximum and minimum appliance voltages must remain within that window.

The circuit must also meet the equipment's output-loading, synchronization and operating/fault-condition limits. Do not use the healthy-state radial calculation alone to accept a Class A circuit.

Two worked NAC examples: one passes, one fails

These two examples use the same model as the voltage-drop calculator: ideal solid copper at 75 °C from the NBS Handbook 100 geometry and resistivity (§§1.1–2.2), with all the load lumped at the far end. Enter the same inputs in the tool and it returns the same numbers. All values are invented for practice. The 20.4 V source stands for the voltage available at the NAC terminals under the battery condition being checked, and the 16.0 V minimum stands for an appliance listing. Neither is a value from any product or from NFPA 72. Take the real figures from the panel and appliance manuals.

Both circuits feed the same load: eight strobes, each drawing a maximum of 0.150 A at the low end of its operating range, so I = 8 × 0.150 = 1.200 A.

Example 1 (passes). 14 AWG solid copper, 250 ft one way.

1. Resistance of one conductor from the model: 3.0713 Ω per 1,000 ft.
2. Loop resistance: 2 × 250 × 3.0713 ÷ 1,000 = 1.5356 Ω.
3. Cable drop: 1.200 × 1.5356 = 1.843 V (9.03% of 20.4 V).
4. Last-appliance voltage: 20.4 − 1.843 = 18.557 V.
5. Check: 18.557 V is at least the 16.0 V minimum, so the circuit passes with 2.557 V to spare. The longest one-way run before it fails is 1,000 × (20.4 − 16.0) ÷ (2 × 1.200 × 3.0713) = 596.9 ft.

Open this example in the voltage-drop calculator (numbers filled in)

Example 2 (fails). The same load on 16 AWG solid copper, 450 ft one way.

1. Resistance of one conductor from the model: 4.8835 Ω per 1,000 ft.
2. Loop resistance: 2 × 450 × 4.8835 ÷ 1,000 = 4.3952 Ω.
3. Cable drop: 1.200 × 4.3952 = 5.274 V (25.85% of 20.4 V).
4. Last-appliance voltage: 20.4 − 5.274 = 15.126 V.
5. Check: 15.126 V is below the 16.0 V minimum, so the circuit fails by 0.874 V. On 16 AWG this load allows only 1,000 × 4.4 ÷ (2 × 1.200 × 4.8835) = 375.4 ft one way.

Open this example in the voltage-drop calculator (numbers filled in)

Two ways to fix it, each checked with the same equation: move up to 14 AWG for the same 450 ft run (20.4 − 1.200 × 2 × 450 × 3.0713 ÷ 1,000 = 17.083 V, which passes), or split the appliances across two circuits so each run carries less current. Either way, recheck the panel's output rating and the appliance listing as well, because the cable check is only one of those limits.

Download the Excel workbook

On the voltage-drop calculator, enter the circuit and select Download Excel workbook. The .xlsx file contains editable inputs and live formulas, plus the tool URL, generation date, resistance citation and calculation-aid notice. Change its blue input cells to recalculate in Excel. The web model uses 75 °C; the workbook exposes a temperature input from 10–100 °C.

Device groups, the battery-condition scenario and the evenly spaced model reflect the options selected at export. Export again to change that structure. Download as spreadsheet (CSV) provides a snapshot of the current calculation rather than a workbook with live formulas.

The voltage-drop calculator and wire-size calculator help check arithmetic; review their displayed resistance assumptions and calculation model. A grouped load list does not establish device positions. Use the battery guide for capacity and NAC vs SLC guide for pathway concepts. Return to Alarm Ladder or take the free 10-question check.

Related exam prep

• NEC voltage drop for the Texas journeyman exam on Bonding Jumper: the same calculation applied to branch circuits and feeders.

Sources

Show the list

• Copper Wire Tables, NBS Handbook 100, National Bureau of Standards, §2.2 and appendices 4–5. Retrieved 17 Oct 2026; AWG geometry, copper resistivity, temperature correction and stranded-conductor estimate. Rechecked 21 Oct 2026 (§§1.1–2.2, printed pp. 3–6) for the AWG diameter rule, the 58 m/(Ω·mm²) conductivity and the 0.00393 per °C coefficient used in the worked examples.
• SpectrAlert strobe and horn/strobe data sheet, A05-0325, System Sensor, p. 3. Retrieved 17 Oct 2026; historical manufacturer example of increasing strobe current at lower voltage, not a current product selection.
• Alarm Ladder voltage-drop calculator, Alarm Ladder. Implementation inspected 17 Oct 2026; documented model constants, meter conversion, maximum-length calculation and Excel/CSV export behavior.
• L-Series wall appliance instructions, I56-5845-002, System Sensor, pp. 1–2. Retrieved 17 Oct 2026 and rechecked 21 Oct 2026; wire loss, loading, the last-device voltage check, voltage windows and synchronization. Worked arithmetic and segment-current derivation are ours.
• NFPA 70 (2020), NFPA, Chapter 9, Table 8, referenced by number only. Access route retrieved 17 Oct 2026; final table content was not accessible in the public reader. No table values used in the examples.
• NFPA 72 (2022), NFPA, §10.6.7, referenced by number only. Access route retrieved 17 Oct 2026.
• MS-9200UDLS Series Manual, 52750 Rev M, Fire-Lite, §7. Retrieved 17 Oct 2026; separate current-loading and battery checks.