To estimate voltage drop, multiply the wire’s resistance per conductor by the one-way route length and by two, then use that loop resistance with the speaker’s nominal impedance in a voltage-divider calculation. The result is an estimate: a real loudspeaker’s impedance changes with frequency.
What you need to calculate
- One-way route length (L): Measure the cable path from amplifier to speaker, not the combined length of both conductors.
- Wire resistance (r): Use the cable maker’s resistance for the actual wire and note whether it is specified per conductor or for the two-conductor pair.
- Nominal speaker impedance (Z): Use the speaker’s stated impedance as a practical estimate of its load.
- Amplifier output voltage (Vamp): Needed only if you want the voltage drop in volts. For a percentage, the ratio can be calculated without knowing it.
Calculate the loop resistance
With a two-conductor cable, current travels to the speaker on one conductor and back to the amplifier on the other. If the wire specification gives resistance per conductor per unit length, calculate the total loop resistance as:
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Rloop = 2 × r × L
For example, a 50-foot one-way route has about 100 feet of conductor in the electrical loop. If a cable chart already gives resistance for the hot-and-common pair over the total route, that is the loop resistance: do not multiply it by two again. Shure’s installer chart is for the pair; it gives 4 ohms for a 500-foot run of 16 AWG copper, and notes that dividing the pair value by two gives the single-conductor resistance (Shure Sound Installers Guide).
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Treating the speaker as a resistance equal to its nominal impedance, the cable and speaker form a voltage divider:
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Vspeaker = Vamp × Z / (Z + Rloop)
The voltage drop is:
Vdrop = Vamp − Vspeaker = Vamp × Rloop / (Z + Rloop)
As a fraction of amplifier voltage, the drop is:
Vdrop / Vamp = Rloop / (Z + Rloop)
To express that fraction as a percentage, multiply it by 100. For example, if the calculated fraction is 0.05, the estimated voltage drop is 5% of the amplifier voltage. This is a calculation example, not a recommended maximum: there is no single acceptable-loss threshold for every installation.
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Choose a wire gauge for a planned loss target
If you have chosen a maximum fractional drop p, rearrange the divider equation to find the largest loop resistance that meets it:
Rloop ≤ pZ / (1 − p)
Here, enter p as a decimal: 5% is 0.05. Compare that limit with the cable’s published resistance for the pair at your one-way route length. If only per-conductor resistance is published, first calculate the round-trip value with 2 × r × L.
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Use the resulting resistance to compare candidate gauges. Thicker copper wire has lower resistance, and the same loop resistance causes a greater fractional voltage drop with a lower-impedance speaker. Klipsch’s guidance chart reflects this by showing different maximum lengths for 4-, 6-, and 8-ohm loads and different gauges; Shure also provides copper speaker-line loop resistance by AWG and total length (Klipsch speaker-wire gauge guidance; Shure Sound Installers Guide). Use a chart for an initial choice, but use the cable’s own published resistance when a closer estimate is important.
Understand what the estimate leaves out
The calculation models the speaker as a fixed resistance equal to its nominal impedance. Actual loudspeaker impedance varies by frequency, so this is not a prediction of frequency response or exact operating voltage across the full audio band. Connector resistance, amplifier output impedance, cable temperature, and cable construction can also change the result. Cable resistance can vary among cable types and manufacturers, as Biamp’s discussion of cable loss notes (Biamp cable voltage-drop guidance).
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When a 70-volt system is relevant
For a very long installed-audio run, a compatible 70-volt distributed system may be a system-level alternative to conventional low-impedance speaker wiring. It requires equipment and speaker transformers designed for that system; its guidance is not interchangeable with the low-impedance voltage-divider calculation above. HARMAN gives a manufacturer example of 1.1 dB loss with 12 AWG all-copper wire at 1,000 feet in a 70-volt system, and says such systems can carry signals beyond 1,000 feet (HARMAN 70-volt distributed-audio primer). For conventional speaker wiring, Peavey advises keeping cable runs short and using heavy-gauge wire for long runs (Peavey support FAQs).
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