How to Calculate the Cable Cross-Section for a 100 V PA Line

Cable cross-section for a 100 V public address (PA) line is chosen primarily for permissible voltage drop (with heating checked as well): on long runs, a thin cable "eats" part of the voltage, and less power reaches the far loudspeakers. Below are the method, the same formula the VPA calculator uses, and how the online tool sizes the cable automatically.

Why Voltage Drop Decides Everything on a 100 V Line

A 100 V PA line is a high-voltage scheme with matching transformers: the amplifier steps the voltage up to 70–100 V, the line current stays low, and every loudspeaker carries a transformer that steps the voltage back down to the required level. This scheme was designed precisely to carry a signal tens and hundreds of meters over thin cable without major losses.

Losses still occur, though. Voltage drops across the conductor resistance, so less than 100 V reaches the far points — and loudspeaker power falls with the square of the voltage. Power loss is roughly twice the voltage drop: a 10% drop means about a 20% power loss and noticeably quieter sound at the end of the line. That is why the cross-section is chosen to stay within a permissible drop, usually 10–20% (the calculator default is 15%) depending on the speech-intelligibility requirements.

For more on the scheme itself and its limitations, see 70/100 V PA lines.

What Determines the Cross-Section: Length, Load, Voltage

The required cable cross-section grows with line length and total load power, and shrinks as the permissible drop increases. The key inputs for the calculation:

• Line length — measured along the actual cable route to the farthest loudspeaker, not as the crow flies;
• Total load power — the sum of the power of all loudspeakers on the line (per their transformer taps);
• Line voltage — 70 or 100 V;
• Permissible drop — set as a percentage (10–20%) based on the loudness and intelligibility requirements at the far point;
• Conductor material — copper (resistivity ≈ 0.0175 Ω·mm²/m) or aluminium (≈ 0.028 Ω·mm²/m, which needs a larger cross-section).

Load distribution is checked separately: if the loudspeakers sit closer to the amplifier, the drop is smaller; if most of the load is at the end of a long run, you will have to upsize the cable or split the line into several branches.

The Cross-Section Formula: the Same One the Calculator Uses

The minimum conductor cross-section for a given voltage drop is found from the formula built into the VPA online calculator:

S = 2 × k × ρ × L × P / U²,   where   k = (100 − D) / D.

Here D is the permissible voltage drop in percent, ρ is the conductor resistivity (copper ≈ 0.0175, aluminium ≈ 0.028 Ω·mm²/m), L is the line length to the farthest loudspeaker (m), P is the total load power on the line (W), and U is the line voltage (100 V). The factor of 2 accounts for both conductors (out and back).

The coefficient k = (100 − D)/D follows from a voltage-divider model: the line resistance and the referred load resistance (R = U²/P) are in series, and the line takes a share D/100 of the voltage. At D = 15% (the calculator default) k ≈ 5.67; at D = 10% k = 9 — the stricter the drop requirement, the larger k and the thicker the cable. Round the resulting S up to the nearest standard cross-section.

The formula helps you understand what drives the result; the full calculation — with a check against the real cable and against heating — is easier to run in the VPA online calculator.

Which Cable Is Used: Fire-Resistant КПСнг(А)-FRLS

Cable for a voice evacuation system must remain operational during a fire for the code-mandated time — the line has to "survive" until the evacuation is complete. That is why fire-resistant cables with the FRLS index (fire resistant, low smoke) are used — the typical solution is КПСнг(А)-FRLS (KPSng(A)-FRLS): a fire-safe, low-smoke design that meets the fire-safety requirements for cable products under GOST 31565 (Russian cable fire-safety standard).

Selection factors include: the number and cross-section of conductors for the design load, the fire-resistance class for the required line operating time, and routing separate from power circuits. The specific cable type, fire-resistance time, and installation method are defined in the project design: VPA supplies the equipment; design and installation are performed by a licensed contractor.

A Worked Example

Take a 100 V line, a cable route of 500 m to the farthest point, total loudspeaker power of 200 W, and a permissible drop of 15% (the default; so k = (100 − 15)/15 ≈ 5.67). Plugging into the formula:

S = 2 × 5.67 × 0.0175 × 500 × 200 / 100² ≈ 1.98 mm².

The nearest larger standard cross-section is 2.5 mm²: against the real cable resistance the actual drop is about 12.9% (within 15%), while the line current I = P/U = 2 A is well below the rating. At a stricter 10% drop the same line would need 4 mm² (see the table below). If the required cross-section is large for the route, there are alternatives: split the line into two branches (reducing each one's length and load), move some loudspeakers closer to the amplifier, or raise the permissible drop to 20% if intelligibility allows. Each option changes both the equipment count and its power — so the cable is sized not in isolation, but together with the loudspeaker layout and the amplifier.

Table: ready cross-section for your length and power (copper, 15%)

A quick answer with no manual math: find the row for your cable route length and the column for the total loudspeaker power — the cell gives the standard copper conductor cross-section, mm². Values are computed by the VPA calculator at a permissible drop of 15% (the default) and a 100 V line.

Values are the copper conductor cross-section, mm² (standard range 0.5–120 mm²). For a stricter 10% or a looser 20%, recompute in the calculator. For aluminium, go one or two steps larger. If the line is split into branches, divide the power by the number of branches and read the table by the power of a single branch.

How the VPA Calculator Sizes the Cable Automatically

The online tool at voice-pa.com performs the complete electroacoustic calculation: sound pressure level point by point and speech intelligibility (STI per IEC 60268-16), automatic selection of loudspeaker count and layout, amplifier power with a 25% margin, and then the cable cross-section for the specified voltage drop, plus UPS and battery capacity. It offers floor-plan upload with a heat map and export to Word, Excel, PDF, and DXF (AutoCAD).

The calculator does not just round the formula: it scans the standard range of cross-sections (0.5 to 120 mm²) with two checks for each:

• voltage drop — against the actual resistance of the specific cable (a divider model), not the ideal formula; it takes the smallest cross-section whose drop stays within the limit (15% by default);
• heating — the continuous line current I = P/U must not exceed the current rating of the chosen cross-section; on short, high-power lines it is heating, not drop, that sets the cross-section.

For an aluminium conductor the calculator automatically scales the resistance (about 1.6× that of copper) and lowers the current rating (about 0.78× the copper value), so aluminium needs a larger cross-section. The cable is fire-resistant per GOST 31565 (see below). If no standard cross-section passes, the tool suggests splitting the line into branches.

Compliance is checked against SP 3.13130.2026 (Russian fire-safety code, for indoor spaces) and GOST R 42.3.01-2021 (Russian standard for outdoor civil alert zones). The tool is free and requires no sign-up — you can calculate the cable cross-section online and instantly see how it changes with a different line length or load. The resulting calculation is a basis for engineering design: VPA supplies the equipment; design and installation are performed by a licensed contractor, and compliance with the codes is documented in the project design.

VPA Equipment and Supply

For the calculated line, VPA supplies 70/100 V amplifiers, mixers, and loudspeakers — the mixer amplifiers section helps you select an amplifier of the right power. VPA brand equipment (VOICEPA LLC) is certified to EAEU (Eurasian Economic Union) requirements, with a 24-month warranty and a service life of at least 10 years.

Warehouse in Moscow with delivery across all of Russia; corporate (B2B) orders are placed via "Request a Quote".

Frequently Asked Questions

Build your line in a couple of minutes: enter the route length, load, and permissible drop — and the VPA calculator will size the cable along with the loudspeaker count, amplifier power, UPS, and export to Word, Excel, PDF, and DXF. Once the bill of materials is ready, place your order via "Request a Quote": warehouse in Moscow with delivery across all of Russia, and VPA equipment certified to EAEU requirements with a 24-month warranty.